[{"data":1,"prerenderedAt":1187},["ShallowReactive",2],{"layer:light:understand":3},{"layer":4,"contentHash":1168,"dependencyHashes":1169,"approval":1181,"releaseId":1186},{"schemaVersion":5,"conceptId":6,"locale":7,"depth":8,"revision":5,"title":9,"subtitle":10,"summary":11,"objectives":12,"estimatedMinutes":18,"plate":19,"blocks":40,"sourceIds":1163,"reviewStatus":1164,"authoring":1165},1,"light","en","understand","How light behaves: rays, angles and rules you can use","Shadow arithmetic, the law of reflection, what refraction really is, and the two kinds of colour mixing","Turn the facts of Discover into rules that predict. Work out shadow sizes with similar triangles, meet umbra and penumbra, apply the law of reflection to mirrors and periscopes, see why light bends when its speed changes, and separate the two opposite kinds of colour mixing.",[13,14,15,16,17],"Draw a correct ray diagram, measuring every angle from the normal.","Predict the size of a shadow from the lamp, object and screen positions, and explain why edges blur.","Apply the law of reflection to plane mirrors, periscopes and pairs of mirrors at an angle.","Explain refraction as a consequence of light changing speed, and calculate apparent depth.","Distinguish additive mixing of light from subtractive mixing of pigments, and say why an object looks coloured.",40,{"title":20,"rows":21},"Lesson plate",[22,25,28,31,34,37],{"label":23,"value":24},"Depth","Understand",{"label":26,"value":27},"Reading time","≈ 40 minutes",{"label":29,"value":30},"Prior knowledge","Discover: straight lines, shadows, mirrors",{"label":32,"value":33},"Chapters","12",{"label":35,"value":36},"Labs","Shadow benches, ray boxes, mixing, matching game",{"label":38,"value":39},"Maths used","Ratios, similar triangles, degrees",[41,45,51,57,60,65,94,99,104,107,123,136,148,186,191,196,199,203,236,241,271,289,295,300,303,318,331,335,346,362,367,370,399,412,417,421,458,463,466,498,503,507,520,525,528,564,576,580,592,597,600,624,628,666,679,683,687,695,700,703,707,710,745,749,763,776,781,784,817,821,825,847,852,856,860,864,868,872,877,961,965,1126,1144,1148,1153],{"id":42,"type":43,"markdown":44},"intro-understand","prose","In Discover you met the facts: light goes straight, mirrors bounce it, water bends it, a prism splits it.\n\nThis layer asks *how* and *why*, and turns the facts into things you can **predict with numbers**. By the end you should be able to say how big a shadow will be before you make it, which way a ray will go when it hits a mirror or a water surface, how many reflections two mirrors will give, and why a tomato looks red.\n\nThe tool that does nearly all the work is one simple idea: draw light as **rays** — straight arrows — and follow them.",{"id":46,"type":47,"variant":48,"title":49,"markdown":50},"how-to-read-u","callout","observation","How to use this lesson","Each chapter turns one observation into a rule you can use. Wherever there is a calculation, do it yourself before reading the answer; wherever there is a lab, move the slider before reading what happens.\n\nYou will need a ruler, and it helps to have a torch, a small mirror and a glass of water within reach.",{"id":52,"type":53,"title":54,"eyebrow":55,"navLabel":56},"u-ch1","chapter","The ray model: drawing light as arrows","Chapter 01","1 The ray model",{"id":58,"type":43,"markdown":59},"ray-model","Physicists explain light with several different pictures, and each is right for a different job. The simplest is the **ray model**:\n\n- Light travels out from every point of a source in **all** directions.\n- Each path is a **ray**: a straight line, drawn with an arrowhead to show which way the light is going.\n- Rays carry on straight for ever until something absorbs them, reflects them, or refracts them at a boundary between two materials.\n- Rays do not interfere with each other. Two beams can cross without either being disturbed.\n\nThat is the whole model, and it is enough to explain shadows, mirrors, lenses, cameras, telescopes and your own eye. You will meet its limits in the Deepen and Extend layers — light is really a wave, and sometimes it *does* creep a little way round corners — but for everything at the size of a room, rays work beautifully.",{"id":61,"type":47,"variant":62,"title":63,"markdown":64},"def-ray-beam","definition","Ray, beam, pencil","A **ray** is one straight path that light takes. It is a drawing tool: you cannot isolate a single ray in the real world.\n\nA **beam** is a bundle of rays travelling together. Beams come in three useful shapes: **parallel** (a laser, or sunlight, which has come so far that the rays are effectively parallel), **diverging** (spreading out from a torch or a lamp), and **converging** (squeezed together towards a point by a lens or a curved mirror).\n\nA narrow diverging beam from a single point is sometimes called a **pencil** of rays.",{"id":66,"type":67,"title":68,"items":69},"steps-ray-rules","steps","How to draw a ray diagram that actually works",[70,74,78,82,86,90],{"title":71,"tag":72,"text":73},"Draw the source as a point","step 1","Even a big source can be treated as a few points to start with. Mark it.",{"title":75,"tag":76,"text":77},"Draw rays leaving in all directions","step 2","Then keep only the two or three that matter for your question — usually the ones that graze the edges of an object.",{"title":79,"tag":80,"text":81},"Use a ruler. Always.","step 3","Rays are straight. A wobbly line will give you the wrong answer and you will not be able to see why.",{"title":83,"tag":84,"text":85},"Mark every boundary","step 4","Wherever light meets a mirror, glass or water, draw the dotted **normal** — the line at right angles to the surface at that point.",{"title":87,"tag":88,"text":89},"Continue every ray to its end","step 5","Either it hits the screen, or it enters the eye, or it leaves the diagram. Half-drawn rays hide mistakes.",{"title":91,"tag":92,"text":93},"Dot the imaginary bits","step 6","Where you trace rays backwards to find where they seem to come from, use a dotted line. That is a virtual path; no light is really there.",{"id":95,"type":47,"variant":96,"title":97,"markdown":98},"nuance-eye-rays","nuance","Which way do the arrows point?","The ancient Greeks, including Euclid, thought that the eye sent something *out* to feel objects, like a blind person's stick. It is a natural idea — we say we \"cast a glance\" and \"shoot a look\" — and small children often say the same thing when asked.\n\nIt cannot be right. If sight came out of your eyes, a dark room would be no obstacle. The Arab scholar **Ibn al-Haytham** (Alhazen, about 965–1040) settled it with experiments and argument around 1020, and every ray in every diagram since has pointed *into* the eye, never out of it.\n\nThis matters for drawing: the arrows on your rays go **from the object to the eye**.",{"id":100,"type":53,"title":101,"eyebrow":102,"navLabel":103},"u-ch2","Shadow size: the arithmetic of a cone of light","Chapter 02","2 Shadow size",{"id":105,"type":43,"markdown":106},"shadow-geometry","Put a small lamp at a point and an object in the way. The two rays that just graze the top and bottom of the object keep going straight, and where they hit the screen, they mark the edges of the shadow.\n\nThose rays make two triangles that share the same angle at the lamp — **similar triangles**. That gives an exact rule:\n\nThe shadow is bigger than the object by exactly the ratio of the two distances from the **lamp**.\n\nThat is worth saying slowly, because the distance that matters is measured from the lamp, not from the wall. Put the object halfway and the shadow is ×2. At a third of the way, ×3. Pressed against the screen, ×1 — exactly life size, which is why shadow puppets are pressed to the cloth when the puppeteer wants a small, sharp character, and pulled back towards the lamp when a demon should tower over the audience.",{"id":108,"type":109,"items":110},"f-shadow","formulas",[111,114,117,120],{"expression":112,"caption":113},"shadow ÷ object = D ÷ d","D is lamp-to-screen, d is lamp-to-object. Both measured from the lamp.",{"expression":115,"caption":116},"shadow = object × D ÷ d","The same rule, arranged to give the answer directly.",{"expression":118,"caption":119},"d = D ÷ 2 → shadow = ×2","Object halfway between lamp and screen: the shadow is twice life size.",{"expression":121,"caption":122},"d = D → shadow = ×1","Object touching the screen: the shadow is exactly the size of the object.",{"id":124,"type":125,"title":126,"problem":127,"steps":128,"help":134},"we-shadow-1","worked_example","How big is the shadow?","A 10 cm ball is held 50 cm from a small torch bulb. A wall stands 200 cm from the same bulb. How wide is the ball's shadow on the wall?",[129,130,131,132,133],"Identify the two distances **from the lamp**: lamp to object d = 50 cm, lamp to screen D = 200 cm.","Find the ratio: D ÷ d = 200 ÷ 50 = **4**.","Multiply the object by the ratio: 10 cm × 4 = **40 cm**.","Check it makes sense: the ball is close to the lamp, so a big shadow is expected. ✓","Sanity check by sliding the ball to the wall: d = 200, ratio = 1, shadow = 10 cm. It can never be smaller than the ball.",{"simplerExplanation":135},"How many times further is the wall than the ball? Four times. So the shadow is four times as wide.",{"id":137,"type":125,"title":138,"problem":139,"steps":140,"help":146},"we-shadow-2","Working backwards: where should the puppet stand?","A shadow puppeteer has a lamp and a cloth screen 300 cm apart. A 30 cm puppet must throw a shadow exactly 150 cm tall. How far from the lamp should the puppet be held?",[141,142,143,144,145],"The magnification needed is 150 ÷ 30 = **5**.","But magnification = D ÷ d, and D = 300 cm.","So 5 = 300 ÷ d, which gives d = 300 ÷ 5 = **60 cm from the lamp**.","That puts the puppet 300 − 60 = 240 cm from the screen — most of the way back towards the lamp.","Check: 30 × 300 ÷ 60 = 30 × 5 = 150 cm. ✓",{"anotherExample":147},"For a shadow only twice life size (60 cm), the magnification is 2, so d = 300 ÷ 2 = 150 cm — exactly halfway.",{"id":149,"type":150,"component":151,"componentVersion":5,"config":152,"objective":180,"textAlternative":181,"help":182},"u-lab-shadow","interactive","shadow-lab",{"objects":153,"source":169,"maxDistanceCm":170,"challenges":171},[154,158,162,166],{"id":155,"label":156,"heightCm":157},"ball","Ball, 10 cm",10,{"id":159,"label":160,"heightCm":161},"puppet","Shadow puppet, 30 cm",30,{"id":163,"label":164,"heightCm":165},"cup","Cup, 8 cm",8,{"id":167,"label":168,"heightCm":161},"ruler","Ruler standing up, 30 cm","point",300,[172,175,178],{"prompt":173,"targetRatio":174},"Put the puppet where its shadow is exactly 5 times life size.",5,{"prompt":176,"targetRatio":177},"Now make the same puppet cast a shadow only 1.5 times life size.",1.5,{"prompt":179,"targetRatio":5},"Find the one position where the shadow matches the object exactly.","Test the rule shadow = object × D ÷ d by sliding an object along a 3 metre bench and comparing the prediction with the measurement.","A point lamp at 0 cm, a screen fixed at 300 cm, and an object you drag along the bench. A readout shows the lamp-to-object distance, the shadow width, and the magnification.\n\nA 30 cm puppet at **60 cm** from the lamp gives 300 ÷ 60 = 5, so the shadow is **150 cm** tall. Drag it out to **150 cm** and the ratio falls to 2, giving a **60 cm** shadow. Push it all the way to **300 cm**, against the screen, and the ratio is 1: the shadow is exactly **30 cm**.\n\nNotice what the graph of shadow size against distance looks like: it is not a straight line. Near the lamp the shadow grows explosively — at 30 cm it is already ×10 — while out near the screen, moving the object 20 cm barely changes anything.\n\nThree challenges ask for magnifications of ×5, ×1.5 and ×1. Predict the distance with D ÷ d before you drag.",{"hints":183},[184,185],"Magnification is always lamp-to-screen divided by lamp-to-object.","To get ×5 on a 300 cm bench, you need d = 300 ÷ 5.",{"id":187,"type":47,"variant":188,"title":189,"markdown":190},"careful-shadow-source","careful","This rule assumes a *point* lamp","Everything above treats the lamp as a single point. Real lamps have size — a tube light is 120 cm long, and even a torch bulb is a few millimetres across.\n\nWhen the source has size, the neat rule still gives roughly the right *middle* of the shadow, but the edges stop being sharp and start to blur. That blur is the subject of the next chapter, and it is not a nuisance to be ignored: it is why your shadow at noon has crisp feet and fuzzy shoulders.",{"id":192,"type":53,"title":193,"eyebrow":194,"navLabel":195},"u-ch3","Umbra and penumbra: why shadow edges blur","Chapter 03","3 Fuzzy edges",{"id":197,"type":43,"markdown":198},"umbra-prose","Stand in sunlight and look carefully at your own shadow. Down at your feet the outline is razor-sharp; you can count your toes. Up at your head — especially if you raise an arm — the edge is soft and grey and the fingers merge into a blob.\n\nThe reason is that the Sun is not a point. It is a disc about **0.53°** across in our sky. Every part of that disc is throwing light past you, from a slightly different direction.\n\nSo behind you there are really two regions:\n\n- The **umbra**: the part of the screen that *no* part of the source can see. Fully dark.\n- The **penumbra**: the ring around it that *some* of the source can see and some cannot. Partly lit, so grey, and it fades smoothly from dark to bright.\n\nNear your feet the two distances are tiny and the penumbra is a hair's width. At head height the light has 1.7 metres of travel in which to blur, and the penumbra is over a centimetre wide.",{"id":200,"type":47,"variant":62,"title":201,"markdown":202},"def-umbra","Umbra and penumbra","**Umbra** (Latin for *shade*): the full shadow, where the object blocks the whole source. If you stood there and looked back, you would see no part of the lamp at all.\n\n**Penumbra** (*almost-shade*): the partial shadow around it. Standing there, you would see part of the lamp peeping past the edge of the object — so some light reaches you, and the shadow is grey rather than black.\n\nThe bigger the source, or the further the screen is behind the object, the wider the penumbra and the smaller the umbra. Push it far enough and the umbra vanishes completely.",{"id":204,"type":205,"caption":206,"columns":207,"rows":211},"table-fuzz","table","How far the edge of a sunlight shadow spreads, from the Sun's angular width of 0.53° (blur = 2 × distance × tan 0.265°)",[208,209,210],"Object is this far above the ground","Width of the fuzzy edge","What you see",[212,216,220,224,228,232],[213,214,215],"1 cm (a leaf on the path)","about 0.1 mm","Utterly sharp",[217,218,219],"10 cm (your shoe)","about 1 mm","Sharp",[221,222,223],"1 m (your hand held out)","about 0.9 cm","Beginning to soften",[225,226,227],"1.7 m (your head)","about 1.6 cm","Clearly soft; fingers merge",[229,230,231],"10 m (a rooftop edge)","about 9.3 cm","A wide grey band",[233,234,235],"50 m (a bird in flight)","about 46 cm","No visible shadow at all — the blur is wider than the bird",{"id":237,"type":47,"variant":238,"title":239,"markdown":240},"aha-bird","aha","Why a flying bird casts no shadow","A crow flapping past 50 metres up does not put a bird-shaped dark patch on the road. Nothing does, up there.\n\nAt 50 m the Sun's width smears the edge of any shadow over about **46 cm**. A crow is maybe 20 cm across. Its umbra — the region where the bird blocks the *whole* Sun — has already shrunk to nothing long before the light reaches the ground, leaving only a penumbra so wide and so faint that the road looks evenly bright.\n\nWatch the same crow swoop down to land and a shadow suddenly appears and races towards it, sharpening as the bird gets close. Nothing changed about the bird.",{"id":242,"type":150,"component":151,"componentVersion":5,"config":243,"objective":264,"textAlternative":265,"help":266},"u-lab-penumbra",{"objects":244,"source":256,"maxDistanceCm":257,"challenges":258},[245,248,252],{"id":246,"label":247,"heightCm":157},"disc","Cardboard disc, 10 cm",{"id":249,"label":250,"heightCm":251},"hand","A hand, 18 cm",18,{"id":253,"label":254,"heightCm":255},"pole","Pole, 100 cm",100,"both",400,[259,261],{"prompt":260,"targetRatio":5},"With the wide source, find the position where the umbra disappears completely.",{"prompt":262,"targetRatio":263},"Make the umbra exactly half the width of the object.",0.5,"Switch between a point lamp and a wide lamp and watch a sharp shadow turn into an umbra surrounded by a grey penumbra.","The same shadow bench, but now with a switch between a **point** source and a **wide** source 20 cm across. The screen is at 400 cm.\n\nWith the **point** source, the 10 cm disc at 100 cm gives one clean shadow 40 cm wide with a knife-sharp edge.\n\nSwitch to the **wide** source and the single shadow splits into two regions: a fully dark **umbra** in the middle and a grey **penumbra** around it, fading outwards. With the disc at 100 cm and the screen at 150 cm the umbra is about 5 cm and the penumbra about 25 cm.\n\nNow drag the disc back towards the lamp, or the screen further away, and watch the umbra shrink while the penumbra grows. At one particular position the umbra **vanishes entirely**: no point on the screen is hidden from the whole lamp, and the shadow becomes a soft grey smudge with no black in it at all.\n\nThat is exactly what happens to a bird's shadow high above the ground, and it is why a solar eclipse is total only along a narrow track.",{"simplerExplanation":267,"hints":268},"A big lamp is many little lamps side by side. Each one casts its own slightly-shifted shadow, and where they overlap you get black, where only some overlap you get grey.",[269,270],"Pull the screen further away and the penumbra always widens.","Umbra vanishes when the source is wider than the object, far enough back.",{"id":272,"type":273,"prompt":274,"options":275,"explanation":288},"pred-two-lamps","prediction","A single small lamp throws one sharp shadow of a ball on a wall. You switch on a **second** small lamp, a little to the left of the first. What appears on the wall?",[276,279,282,285],{"id":277,"label":278},"a","One shadow, twice as dark",{"id":280,"label":281},"b","One shadow, half as dark",{"id":283,"label":284},"c","Two separate shadows, each lighter than before, overlapping in a darker middle",{"id":286,"label":287},"d","No shadow at all, because the second lamp fills it in","**c.** Each lamp makes its own complete shadow, in a slightly different place. Where only lamp 1 is blocked, light from lamp 2 still arrives, so that region is grey rather than black. Same for the other side. Where *both* are blocked, nothing arrives and you get a small, fully dark region — an umbra — with two grey penumbras on either side.\n\nThis is the whole secret of the previous chapter. A wide lamp is simply an infinite row of little lamps, and the umbra is the small region shaded from all of them at once. It is also why a football stadium with many floodlights gives players several faint shadows instead of one sharp one, and why a photographer's big soft-box gives kinder shadows than a bare flash.",{"id":290,"type":291,"conceptId":292,"relation":293,"explanation":294},"u-conn-eclipse","connection","eclipses","helps_understand","A total solar eclipse is the Moon's umbra landing on the Earth; a partial eclipse is its penumbra. The Moon is 0.52° wide and the Sun 0.53°, which is why totality is so brief and so rare.",{"id":296,"type":53,"title":297,"eyebrow":298,"navLabel":299},"u-ch4","The law of reflection","Chapter 04","4 Law of reflection",{"id":301,"type":43,"markdown":302},"reflection-law","Send a narrow beam at a flat mirror and it bounces off. There is a rule, and it is exact.\n\nFirst you need the **normal**: an imaginary line drawn at right angles (90°) to the mirror surface, at the exact point where the ray lands. All angles in optics are measured from the normal, never from the mirror surface — a habit worth forming now, because it is the source of half of all mistakes later.\n\nThen:\n\n1. The **angle of incidence** (between the incoming ray and the normal) equals the **angle of reflection** (between the normal and the outgoing ray).\n2. The incoming ray, the reflected ray and the normal all lie in the same flat plane.\n\nThat is it. Two lines. Everything a mirror does — every image, every periscope, every kaleidoscope, every reflecting telescope — comes out of those two lines applied over and over.",{"id":304,"type":109,"items":305},"f-reflection",[306,309,312,315],{"expression":307,"caption":308},"angle i = angle r","Angle of incidence equals angle of reflection. Both measured from the normal.",{"expression":310,"caption":311},"i = 0° → r = 0°","A ray fired straight at the mirror comes straight back along its own path.",{"expression":313,"caption":314},"i = 45° → r = 45°","The periscope case: the ray turns through a right angle.",{"expression":316,"caption":317},"turn = 180° − 2i","How much the ray direction changes. At i = 45° the turn is 90°.",{"id":319,"type":150,"component":320,"componentVersion":5,"config":321,"objective":324,"textAlternative":325,"help":326},"u-lab-ray","light-ray",{"initialAngle":161,"showNormal":322,"showAngles":322,"challengeAngle":323},true,55,"Aim a ray at a mirror at any angle, read both angles from the normal, and hit a target angle exactly.","A ray box on the left, a flat mirror across the middle, and a dotted **normal** standing up from the point where the ray lands. Both angles are displayed live.\n\nIt opens with the ray coming in at **30°** to the normal, and the reflected ray leaving at **30°** on the other side. Drag the incoming ray around and the two readings stay locked together: 10° and 10°, 45° and 45°, 70° and 70°.\n\nThere is a **challenge**: make the reflected ray leave at exactly **55°**. The only way is to bring the incoming ray in at 55° too.\n\nTwo special cases are worth finding. At **0°**, straight down the normal, the ray reflects straight back on itself. And near **80°**, a very glancing hit, the ray barely changes height — which is why a puddle reflects the whole street when you look along it at a shallow angle, but only shows you the mud when you look straight down.\n\nWatch what the reflected ray does when you tilt the *mirror* by 10° instead of the ray: the reflected ray swings by **20°**, twice as much.",{"simplerExplanation":327,"hints":328},"Measure both angles from the dotted line standing up out of the mirror, not from the mirror itself. Those two angles are always equal.",[329,330],"Angles are measured from the normal. A ray at 70° to the normal is only 20° from the glass.","Tilt the mirror by one degree and the reflected ray moves by two.",{"id":332,"type":47,"variant":188,"title":333,"markdown":334},"careful-angle-from","Measure from the normal, not from the mirror","If a question says \"a ray strikes a mirror at 30° to the **surface**\", the angle of incidence is **60°**, not 30°, because the normal is 90° from the surface.\n\nGet into the habit of drawing the dotted normal first, before you measure anything. Then read both angles off it. Most wrong answers in reflection questions are this one mistake, not a misunderstanding of the physics.",{"id":336,"type":125,"title":337,"problem":338,"steps":339},"we-mirror-tilt","Tilt the mirror by 10°, and the reflection swings by 20°","A ray hits a mirror at an angle of incidence of 40°. Somebody tilts the mirror by 10°. By how much does the reflected ray change direction?",[340,341,342,343,344,345],"Before: the normal is where it is, the incidence angle is 40°, and the reflected ray leaves at 40° on the other side. The total turn of the ray is 180° − 2 × 40° = **100°**.","Tilting the mirror by 10° tilts the **normal** by 10° as well — the normal is glued to the mirror.","The incoming ray has not moved, so the angle between it and the new normal is now 40° − 10° = **30°** (or 50°, depending on which way you tilt).","The new turn of the ray is 180° − 2 × 30° = **120°**.","The change is 120° − 100° = **20°**.","General rule: **tilt a mirror by θ and the reflected beam swings by 2θ.** This is why a mirror galvanometer, a laser show and a barcode scanner all use tiny mirror movements to sweep a beam a long way.",{"id":347,"type":348,"itemId":349,"prompt":350,"check":351,"hints":356,"feedback":359},"u-prac-reflection","practice","light.understand-reflection-angle","A ray of light strikes a plane mirror so that it makes an angle of 25° **with the mirror surface**. What is the angle of reflection, measured from the normal, in degrees?",{"kind":352,"answer":353,"tolerance":354,"unit":355},"number",65,0,"°",[357,358],"The normal is at 90° to the surface. If the ray is 25° from the surface, how far is it from the normal?","Angle of incidence = 90° − 25° = 65°, and reflection equals incidence.",{"correct":360,"incorrect":361},"Correct: 90° − 25° = 65° is the angle of incidence, and the angle of reflection equals it, so **65°**.","Careful — the question gave the angle from the *surface*. Subtract it from 90° to get the angle from the normal: 90 − 25 = 65°. Reflection then equals incidence: 65°.",{"id":363,"type":53,"title":364,"eyebrow":365,"navLabel":366},"u-ch5","What a plane mirror does to an image","Chapter 05","5 The mirror image",{"id":368,"type":43,"markdown":369},"plane-image","Every ray leaving your nose spreads out, hits the mirror, and obeys the law of reflection. Trace the reflected rays *backwards* with a dotted line and they all meet at one point — as far behind the glass as your nose is in front.\n\nNo light is actually at that point. Put a screen there (behind the mirror) and nothing lands on it. That is what we mean by a **virtual** image: the light only *appears* to come from there.\n\nFour properties, all testable in a minute with a small mirror:\n\n- **Same size** as the object, however far away you stand.\n- **Upright**, not upside down.\n- **As far behind** the mirror as the object is in front.\n- **Laterally inverted**: left and right swapped.",{"id":371,"type":372,"tone":373,"items":374},"spec-plane-mirror","spec","blue",[375,379,383,387,391,395],{"label":376,"big":377,"value":378},"Size","Same","Never magnified. The image of your face is exactly life size, which is why you can put on a bindi accurately.",{"label":380,"big":381,"value":382},"Orientation","Upright","Not turned over. Compare with a spoon or a camera, which do flip the picture.",{"label":384,"big":385,"value":386},"Position","As far behind","Stand 1.5 m away and your twin is 1.5 m behind the glass — 3 m from you.",{"label":388,"big":389,"value":390},"Sideways","Swapped","Lateral inversion. Your right hand becomes the image's left.",{"label":392,"big":393,"value":394},"Type","Virtual","Cannot be caught on a screen. Nothing is really behind the glass.",{"label":396,"big":397,"value":398},"Mirror needed","Half","To see all of yourself you need a mirror only half your height, at the right position.",{"id":400,"type":125,"title":401,"problem":402,"steps":403,"help":410},"we-half-mirror","The smallest mirror you can see all of yourself in","You are 160 cm tall, with your eyes 150 cm off the ground. What is the shortest vertical mirror on the wall in which you can see yourself from head to toe — and does it matter how far back you stand?",[404,405,406,407,408,409],"Take the ray from the **top of your head** (160 cm) to your eye (150 cm). It must bounce off the mirror. By the law of reflection, it hits the mirror exactly **halfway** in height between the two: (160 + 150) ÷ 2 = **155 cm**.","Take the ray from your **toes** (0 cm) to your eye (150 cm). Same argument: it hits the mirror at (0 + 150) ÷ 2 = **75 cm**.","So all the rays you need land between 75 cm and 155 cm on the wall.","Mirror length needed = 155 − 75 = **80 cm**, which is exactly half of 160 cm.","Now the surprise: **your distance from the mirror never entered the calculation.** Walk backwards and the image gets further away, but the rays still strike the same two points on the wall. Half your height is enough from any distance.","So a mirror advertised as \"full length\" only needs to be 80–90 cm tall for most people. The extra is for seeing other people, and for comfort.",{"simplerExplanation":411},"Light from your head reaches your eye by bouncing off the mirror halfway between them. Same for your feet. So the mirror only ever needs to cover half of you — and moving back does not change that.",{"id":413,"type":47,"variant":414,"title":415,"markdown":416},"misc-mirror-backup","misconception","\"Stand back and you will see more of yourself\"","You will not. Many people instinctively step back from a small mirror to fit more of themselves in, the way you would step back from a doorway.\n\nIt does not work, and the worked example above shows why: the piece of mirror your head needs is always at the halfway height between your head and your eye, however far away you stand. Stepping back makes your image smaller *and* further away by exactly the same factor, so it fills the same amount of mirror.\n\nWhat *does* help is moving the mirror, or tilting it.",{"id":418,"type":47,"variant":238,"title":419,"markdown":420},"aha-lateral","A mirror does not really swap left and right","Here is a puzzle. A mirror reverses left and right — so why does it not reverse up and down? Your reflection's head is still up.\n\nThe truth is that a mirror swaps neither. It swaps **front and back**: the tip of your nose, which pokes towards the mirror, becomes the nearest part of the image, and the back of your head becomes the furthest. Everything is turned inside out along the one direction facing the glass.\n\nWhat happens next is that *you* interpret it. You imagine yourself turning around to face the way your image faces — and when you turn around, you swap your own left and right. The mirror did the front-to-back swap; your imagination supplied the rest.\n\nTest it: lie on your side in front of a mirror. Now the reversal obediently looks like an up-down one.",{"id":422,"type":150,"component":423,"componentVersion":5,"config":424,"objective":452,"textAlternative":453,"help":454},"u-lab-mirror-facts","match-pairs",{"prompt":425,"mode":426,"pairs":427},"Match each property of a plane-mirror image to the everyday consequence it has.","connect",[428,431,434,437,440,443,446,449],{"a":429,"b":430},"Image is the same size","Your face in a mirror is life size, at any distance",{"a":432,"b":433},"Image is as far behind as you are in front","Stand 1.5 m away and your twin is 3 m from you",{"a":435,"b":436},"Image is laterally inverted","AMBULANCE is painted backwards on the bonnet",{"a":438,"b":439},"Image is virtual","Put a screen behind the mirror and nothing lands on it",{"a":441,"b":442},"Image is upright","Unlike a camera or a spoon, nothing is turned upside down",{"a":444,"b":445},"A half-height mirror is enough","An 80 cm mirror shows all of a 160 cm person",{"a":447,"b":448},"Tilt the mirror by 10°","The reflected beam swings by 20°",{"a":450,"b":451},"Angle of incidence = angle of reflection","A ray fired straight at a mirror comes straight back","Connect each property of the plane-mirror image to the everyday effect it produces.","A connect-the-pairs game with eight properties on the left and eight consequences on the right; drag a line between each matching pair.\n\nSame size connects to *your face is life size at any distance*. As far behind as in front connects to *stand 1.5 m away and your twin is 3 m from you*. Laterally inverted connects to *AMBULANCE painted backwards*. Virtual connects to *a screen behind the mirror catches nothing*. Upright connects to *nothing is turned over, unlike a camera*. A half-height mirror is enough connects to *an 80 cm mirror shows all of a 160 cm person*. Tilt the mirror by 10° connects to *the beam swings by 20°*. And angle of incidence equals angle of reflection connects to *a ray fired straight at a mirror comes straight back*.\n\nWrong connections spring apart; the game counts your moves, so the aim is to think first rather than try everything.",{"hints":455},[456,457],"Two of the pairs are about angles rather than the image itself.","\"Virtual\" always means: no light is actually there.",{"id":459,"type":53,"title":460,"eyebrow":461,"navLabel":462},"u-ch6","Why paper is not a mirror","Chapter 06","6 Rough and smooth",{"id":464,"type":43,"markdown":465},"diffuse-prose","White paper reflects about 80% of the light that lands on it. A household mirror reflects about 90%. Almost the same — so why can you see your face in one and not the other?\n\nBecause of what happens to the *arrangement* of the rays.\n\nA mirror is smooth on a scale far finer than a wavelength of light. A bundle of parallel rays arrives; every one of them meets a surface facing the same way, so every one of them turns through the same angle and leaves still parallel. The pattern survives. This is **regular** (or specular) reflection.\n\nPaper, under a microscope, is a tangle of fibres pointing everywhere. Every ray obeys the law of reflection perfectly — but each one meets a tiny surface tilted differently, so each leaves at its own angle. The bundle is shattered into every direction at once. This is **diffuse** (or scattered) reflection.\n\nThe law of reflection is not broken by rough surfaces. It is obeyed individually by every microscopic patch, and the scrambling is the sum of all those honest, separate bounces.",{"id":467,"type":205,"caption":468,"columns":469,"rows":473},"table-regular-diffuse","Regular and diffuse reflection compared — the same law of reflection, two different surfaces",[470,471,472],"Property","Regular (mirror-like)","Diffuse (scattered)",[474,478,482,486,490,494],[475,476,477],"Surface","Smooth on a very fine scale","Rough on a very fine scale",[479,480,481],"Parallel rays in","Leave parallel, still in formation","Leave in every direction",[483,484,485],"Do you get a picture?","Yes — a clear image","No — an even glow",[487,488,489],"Where you can see it from","Only from one direction at a time","From everywhere at once",[491,492,493],"Examples","Mirror, still water, polished steel, a wet road at night","Paper, wall paint, cloth, a cinema screen, the Moon",[495,496,497],"Law of reflection obeyed?","Yes","Yes — by each tiny patch separately",{"id":499,"type":47,"variant":500,"title":501,"markdown":502},"example-screen","example","Why a cinema screen is deliberately rough","It would seem sensible to make a cinema screen out of mirror. It would waste almost no light.\n\nIt would also be useless. A mirror screen would send the entire film, as a neat parallel beam, to exactly one seat. Everybody else would see a dark rectangle with one blinding spot in it.\n\nA rough white screen scatters the projector's light into every direction at once, so every seat in the hall gets a share. The picture is dimmer than a mirror would give any single viewer, and that is exactly the price of letting four hundred people watch the same film.\n\nThe same choice is made by whiteboards (matt so the whole class can read them), and by the matt paint on a classroom wall, which is why you do not see the tube light reflected as a blinding spot in it.",{"id":504,"type":47,"variant":48,"title":505,"markdown":506},"obs-wet-road","A puddle switches modes in front of you","A dry road at night is a diffuse reflector: headlights scatter off it, the whole road glows dimly and evenly, and lane markings are easy to see.\n\nWet it, and a film of water fills the roughness and gives a smooth surface. Now the reflection becomes regular: the road turns into a patchy mirror, reflecting oncoming headlights straight into drivers' eyes as dazzling streaks, while the markings disappear. This is a real, measurable cause of night-time accidents in the monsoon.\n\nYou can see the change in miniature: look along a polished stone floor almost edge-on and it becomes a mirror; look straight down at the same floor and it is matt.",{"id":508,"type":273,"prompt":509,"options":510,"explanation":519},"pred-moon-mirror","The Moon reflects only about 12% of the sunlight that falls on it — less than a sheet of grey card, far less than a mirror. If the Moon were made of polished mirror instead, what would we see at full moon?",[511,513,515,517],{"id":277,"label":512},"A much brighter full moon, lighting up the whole night",{"id":280,"label":514},"A mostly black disc with one tiny, dazzling spot of reflected Sun on it",{"id":283,"label":516},"Exactly the same, because it reflects the same sunlight",{"id":286,"label":518},"Nothing at all — a mirror in space is invisible","**b.** A mirror-Moon would obey the law of reflection tidily, so almost all the sunlight would bounce off in one direction, away from us. Only the one small patch positioned to fire the Sun's image directly at the Earth would be lit — you would see a fierce star-like glint on a black disc, and the countryside would be dark.\n\nThe Moon looks like a soft glowing lamp precisely *because* its surface is rough dust and rubble, scattering sunlight in all directions, some of it towards us wherever you look on the disc. Diffuse reflection is what makes an object look like an object, rather than a mirror showing you something else.",{"id":521,"type":53,"title":522,"eyebrow":523,"navLabel":524},"u-ch7","Two mirrors: reflections of reflections","Chapter 07","7 Two mirrors",{"id":526,"type":43,"markdown":527},"two-mirrors","Stand two mirrors face to face with a coin between them and you see a corridor of coins vanishing into the distance. Each image is being reflected again, and again, and each round trip loses a little light to absorption, so the corridor fades and finally goes dark.\n\nBring the mirrors to an **angle** instead of parallel, and something tidier happens: you get a definite, countable number of images, arranged in a ring. The number depends only on the angle:\n\n**number of images = 360 ÷ angle − 1**\n\nAt 90° that gives 360 ÷ 90 − 1 = 3 images. At 60°, 5 images. At 45°, 7. As you close the mirrors the count climbs; open them flat to 180° and 360 ÷ 180 − 1 = 1, which is just an ordinary single mirror, as it should be.",{"id":529,"type":205,"caption":530,"columns":531,"rows":535},"table-mirror-angle","Number of images of one object placed between two plane mirrors, from 360 ÷ angle − 1",[532,533,534],"Angle between the mirrors","360 ÷ angle","Images you can count",[536,540,543,546,549,552,556,560],[537,538,539],"180° (flat, one mirror)","2","1",[541,542,538],"120°","3",[544,545,542],"90° (a right angle)","4",[547,548,545],"72°","5",[550,551,548],"60° (a kaleidoscope)","6",[553,554,555],"45°","8","7",[557,558,559],"36°","10","9",[561,562,563],"Parallel (0°)","Infinite","A fading corridor of images",{"id":565,"type":125,"title":566,"problem":567,"steps":568,"help":574},"we-kaleidoscope","How many images in a three-mirror kaleidoscope?","A kaleidoscope is made from three long mirror strips of equal width, taped into a triangular tube with their shiny faces inwards. What angle do neighbouring mirrors make, and how many images of one bangle-chip would a pair of them give?",[569,570,571,572,573],"Three equal strips make an **equilateral triangle**, so each pair of mirrors meets at **60°**.","For one pair: images = 360 ÷ 60 − 1 = 6 − 1 = **5 images**, plus the chip itself makes 6 objects arranged in a ring.","That is why every kaleidoscope pattern has **six-fold** symmetry — turn the picture by 60° and it looks the same.","With all three mirrors working at once, reflections of reflections tile the whole field of view, and the six-fold pattern repeats outwards as far as you can see.","Swap to four mirrors in a square and every angle becomes 90°, giving 3 images per pair and a four-fold pattern instead.",{"anotherExample":575},"Two mirrors at 45° in a shop-window display give 7 copies of a single item, arranged in a neat octagonal ring.",{"id":577,"type":47,"variant":500,"title":578,"markdown":579},"example-periscope-geom","A periscope, drawn properly","Two plane mirrors, one at the top of a tube and one at the bottom, each tilted at **45°** to the tube and parallel to each other.\n\nLight arrives horizontally at the top mirror. Its normal is at 45° to the incoming ray, so the ray reflects at 45° on the other side — a total turn of 180° − 2 × 45° = **90°**. The light now travels straight down the tube.\n\nAt the bottom mirror the same thing happens again, turning it through another 90°, so it leaves horizontally into your eye.\n\nTwo useful consequences: the image is **upright** (two lateral inversions cancel out, which is why it is the second mirror that makes a periscope usable), and the view is shifted, not magnified — a periscope lets you see *over* something, not *closer*. A bent tube with one mirror would not work at all.",{"id":581,"type":348,"itemId":582,"prompt":583,"check":584,"hints":586,"feedback":589},"u-prac-mirrors","light.understand-mirror-count","Two plane mirrors are set at 72° to each other with a marble between them. How many images of the marble will you see?",{"kind":352,"answer":585,"tolerance":354},4,[587,588],"Use images = 360 ÷ angle − 1.","360 ÷ 72 = 5.",{"correct":590,"incorrect":591},"Right: 360 ÷ 72 = 5, and 5 − 1 = **4 images**.","Apply the formula: 360 ÷ 72 = 5, then subtract one for the object itself, giving 4 images.",{"id":593,"type":53,"title":594,"eyebrow":595,"navLabel":596},"u-ch8","Refraction: what bending really is","Chapter 08","8 Refraction",{"id":598,"type":43,"markdown":599},"refraction-why","Light does not have the same speed everywhere. In empty space it is the full 3 × 10⁸ m\u002Fs. In water it is about **2.25 × 10⁸** m\u002Fs, and in ordinary glass about **2.0 × 10⁸** m\u002Fs.\n\nWhen a beam crosses a boundary **at a slant**, one edge of the beam arrives at the slower material before the other edge does. That edge slows first while the other is still going fast, and the whole beam pivots — exactly like a marching band wheeling into a corner, or a car that puts two wheels onto soft sand at the side of the road and slews round.\n\nThat pivot is **refraction**. And notice the condition: *at a slant*. Send the beam in straight along the normal, perfectly square to the surface, and both edges slow at the same instant. No pivot. The light slows down but travels straight on.",{"id":601,"type":67,"title":602,"items":603},"steps-refraction-rules","The two rules, and how to remember them",[604,608,612,616,620],{"title":605,"tag":606,"text":607},"Into a slower material","bends towards","Air into water, or air into glass: the ray bends **towards** the normal. The angle inside is smaller than the angle outside.",{"title":609,"tag":610,"text":611},"Into a faster material","bends away","Water into air, or glass into air: the ray bends **away** from the normal. The angle outside is bigger.",{"title":613,"tag":614,"text":615},"Straight along the normal","no bend","At 0°, the light slows or speeds up but does not change direction at all. Only the slant makes it turn.",{"title":617,"tag":618,"text":619},"It is reversible","both ways","Send light backwards along the same path and it retraces it exactly. A ray diagram works in either direction.",{"title":621,"tag":622,"text":623},"A parallel slab shifts, not turns","glass block","Going into a flat glass block bends one way and coming out bends back. The ray leaves parallel to how it arrived, just displaced sideways.",{"id":625,"type":47,"variant":62,"title":626,"markdown":627},"def-refractive-index","Refractive index","The **refractive index** of a material, written *n*, is how many times slower light goes in it than in a vacuum:\n\n*n* = speed in vacuum ÷ speed in the material\n\n- Air: 1.0003, so near enough 1. Light barely notices air.\n- Water: **1.33** — light goes 3 × 10⁸ ÷ 1.33 = 2.25 × 10⁸ m\u002Fs.\n- Ordinary glass: **1.5** — 2.0 × 10⁸ m\u002Fs.\n- Diamond: **2.42** — only 1.24 × 10⁸ m\u002Fs, less than half speed.\n\nThe bigger *n* is, the more strongly the material bends light. Diamond's enormous index is exactly why a cut diamond throws light about so dramatically, and why a diamond looks utterly different from a piece of glass cut to the same shape.",{"id":629,"type":630,"title":631,"note":632,"scale":633,"rungs":634},"ladder-index","ladder","How much different materials slow light down","Refractive index, a linear scale. Higher means slower light and stronger bending.","linear",[635,638,642,646,650,654,658,662],{"label":636,"value":5,"display":637},"Vacuum","n = 1 exactly",{"label":639,"value":640,"display":641},"Air",1.0003,"n = 1.0003",{"label":643,"value":644,"display":645},"Ice",1.31,"n = 1.31",{"label":647,"value":648,"display":649},"Water",1.33,"n = 1.33",{"label":651,"value":652,"display":653},"Cooking oil",1.47,"n ≈ 1.47",{"label":655,"value":656,"display":657},"Window glass",1.52,"n ≈ 1.5",{"label":659,"value":660,"display":661},"Sapphire",1.77,"n = 1.77",{"label":663,"value":664,"display":665},"Diamond",2.42,"n = 2.42",{"id":667,"type":125,"title":668,"problem":669,"steps":670,"help":677},"we-apparent-depth","Why a pool looks shallower than it is","A swimming pool is filled to a true depth of 1.2 m. Looking straight down, how deep does the bottom appear to be? (Refractive index of water = 1.33.)",[671,672,673,674,675,676],"Light from the bottom travels up through the water and speeds up as it leaves into the air, bending **away** from the normal.","Your brain traces those rays back in straight lines, and they meet higher up than the real bottom.","For a view from nearly straight above, the rule is: **apparent depth = real depth ÷ n**.","apparent depth = 1.2 ÷ 1.33 = **0.90 m**.","So the bottom looks about 90 cm down when it is really 120 cm down — three-quarters of the true depth.","For a 2 m pool: 2.0 ÷ 1.33 = **1.5 m**. For a 3 m deep pool: 3.0 ÷ 1.33 = **2.26 m**. The deeper the water, the bigger the error in absolute terms.",{"simplerExplanation":678},"Water always makes things look about three-quarters of their real depth — so a pool that looks safe may be a third deeper than it appears.",{"id":680,"type":47,"variant":188,"title":681,"markdown":682},"careful-depth","This one is a genuine danger","Because water looks about three-quarters of its real depth, a pond, quarry, canal, stepwell or river pool that appears waist-deep can easily be over your head.\n\nNever judge depth by eye. Never jump or dive into water whose bottom you have not checked by wading in slowly, and never swim alone in open water. Rescuers in India deal with this every summer.\n\nThe same refraction is why a stick poked at a fish underwater misses: the fish is *deeper* and further out than it looks. Fishing communities know to aim low, and the kingfisher's brain does the correction automatically.",{"id":684,"type":47,"variant":414,"title":685,"markdown":686},"misc-refraction-slow","\"Light slows down because it keeps bumping into atoms\"","This is the usual explanation, and it is not right. If light were being absorbed and re-emitted at random by atoms, it would come out of the glass scattered in all directions — glass would be white, like snow, not clear.\n\nWhat actually happens is that the light wave makes the electrons in the material wobble, those wobbling electrons radiate their own wave, and the original wave and the new wave add together to give a combined wave that travels more slowly and *in the same direction*.\n\nThe individual photons never travel slower than *c*. The wave does. That distinction takes a few more years of physics to make fully, and it is worth knowing early that the simple bumping story is a placeholder, not the truth.",{"id":688,"type":150,"component":320,"componentVersion":5,"config":689,"objective":691,"textAlternative":692,"help":693},"u-lab-refract-ray",{"initialAngle":690,"showNormal":322,"showAngles":322},50,"Send a ray into a water surface at different angles and see how far it bends, and what happens when you go steeper or shallower.","The ray box now shines onto a flat water surface instead of a mirror, with the dotted **normal** drawn at the point of entry and both angles displayed.\n\nAt **50°** to the normal in air, the ray bends towards the normal on entering the water and continues at about **35°**. A part of the light also reflects off the surface, which is why you see both the sky and the bottom in a pond.\n\nPull the incoming ray back to **20°** and the ray inside bends to about 15° — a smaller angle in, a smaller bend. Push it to **0°**, straight down the normal, and there is **no bend at all**: the ray goes straight in.\n\nGo the other way, to a glancing **80°**, and the ray inside reaches only about 48°, while the reflected part of the beam becomes strong and bright. That is why a lake seen from across the water is a mirror, and the same lake seen from a boat directly above is clear.\n\nThe pattern to take away: the angle inside the water is always **smaller** than the angle in air, the two grow together, and at zero there is no bending at all.",{"simplerExplanation":694},"Going into water, the ray always tips closer to the upright dotted line. Straight in means straight on.",{"id":696,"type":53,"title":697,"eyebrow":698,"navLabel":699},"u-ch9","Why things have colours","Chapter 09","9 Colour",{"id":701,"type":43,"markdown":702},"colour-objects","White light contains every colour. When it lands on an object, the object **absorbs** some of those colours and **reflects** the rest. What bounces back to your eye is what you call its colour.\n\n- A tomato absorbs blue and green light and reflects red. You call it red.\n- A leaf absorbs red and blue and reflects green.\n- Something that reflects nearly everything looks **white**.\n- Something that absorbs nearly everything looks **black** — and gets hot, because the absorbed light becomes heat. That is why a black kurta is punishing in a Chennai summer.\n\nSo colour is not a property an object has on its own. It is a conversation between the object and the light falling on it, and if you change the light, you change the colour.",{"id":704,"type":47,"variant":48,"title":705,"markdown":706},"obs-sodium","Change the light and the colours change","Old orange street lamps (low-pressure sodium) gave out light of essentially **one** colour. Under them, a red car and a black car both look dark grey-brown, and a blue shirt looks black — because there simply is no blue light present for it to reflect. Some Indian highways and tunnels still use them.\n\nThe same thing happens in a photographer's darkroom under a red safelight, and under the deep blue of the last half hour before night. In a green-lit room, a red rangoli goes black.\n\nNext time you are in a shop with unusual lighting, take a cloth outside before you buy it. Shopkeepers know exactly what their lights do to fabric colour.",{"id":708,"type":43,"markdown":709},"mixing-prose","Now for the part that confuses almost everybody, because there are **two completely different kinds of mixing**, and school art lessons teach one while screens use the other.\n\n**Adding light.** Start with darkness and shine coloured lamps onto the same white patch. Every lamp adds more light, so the patch gets brighter. Red + green = **yellow**. Green + blue = **cyan**. Red + blue = **magenta**. All three = **white**. The three that do this best are **red, green and blue** — the primary colours of light. Your phone screen, a TV, a stage lighting rig and the pixels of a photograph all work this way.\n\n**Subtracting with pigments.** Start with white light and put paint or ink in its way. Every pigment *removes* colours, so the mixture always gets darker. The printing primaries are **cyan, magenta and yellow**, and all three together give a muddy near-black. Paints, dyes, inks, rangoli powders and filters all work this way.\n\nSame word, opposite arithmetic. One adds light to darkness; the other takes light away from white.",{"id":711,"type":205,"caption":712,"columns":713,"rows":716},"table-mixing","Adding coloured light versus mixing coloured paint — the two kinds of mixing, side by side",[470,714,715],"Mixing light (additive)","Mixing pigment (subtractive)",[717,721,725,729,733,737,741],[718,719,720],"You start with","Darkness","White light",[722,723,724],"Each thing you add","Adds light","Removes light",[726,727,728],"So mixtures get","Brighter","Darker",[730,731,732],"Primaries","Red, green, blue","Cyan, magenta, yellow",[734,735,736],"Red + green gives","Yellow","A dark muddy brown",[738,739,740],"All three primaries give","White","Near black",[742,743,744],"Where you meet it","Screens, stage lights, pixels","Paints, inks, printers, rangoli, dyes",{"id":746,"type":47,"variant":414,"title":747,"markdown":748},"misc-primary","\"The primary colours are red, blue and yellow\"","That is what most of us were taught with poster paints, and it is a rough-and-ready version of the **pigment** primaries. The accurate pigment set, used by every colour printer in the world, is **cyan, magenta and yellow** — which is why your printer cartridge says CMY (plus K for black).\n\nThe **light** primaries are different again: **red, green and blue**. Hold a magnifying glass up to a bright white patch on a phone screen and you will see the three lamps lit side by side; look at a yellow patch and you will find no yellow lamp at all — only red and green, with the blue switched off. Your eye does the rest.\n\nSo \"the primary colours\" is not one list. Ask first: am I adding light, or taking it away?",{"id":750,"type":150,"component":751,"componentVersion":5,"config":752,"objective":756,"textAlternative":757,"help":758},"u-lab-mixing","prism-lab",{"modes":753,"rounds":165},[754,755],"mixing","filters","Overlap red, green and blue lamps to make every other colour, then put filters in white light and watch colours disappear.","Two modes.\n\n**Mixing.** Three lamps — red, green and blue — shine overlapping circles on a white screen, each with its own brightness slider. Turn up red and green together and the overlap is **yellow**; green and blue give **cyan**; red and blue give **magenta**; all three at full give **white**. Turn any one down a little and the white drifts towards a tint. There is no yellow lamp anywhere: yellow is what your eye reports when red and green arrive together.\n\n**Filters.** A beam of white light passes through coloured filters you drop into its path. A red filter absorbs everything except red, so a red patch comes out — and the beam is much dimmer, because most of the light was thrown away as heat. Add a **green** filter behind the red one and the screen goes **black**: the red filter already removed all the green, and the green filter removes the red that is left, so nothing survives. A magenta filter (which passes red *and* blue) followed by a yellow one (red and green) leaves only **red**.\n\nEight questions ask you to predict the result before you drop the filter in.",{"simplerExplanation":759,"hints":760},"Lamps add colours together and get brighter. Filters take colours away and get darker. Stack two filters with no colour in common and you get black.",[761,762],"Yellow light and a yellow lamp are not the same thing — yellow on a screen is red plus green.","A filter passes its own colour and absorbs the rest.",{"id":764,"type":273,"prompt":765,"options":766,"explanation":775},"pred-red-in-green","A red rangoli powder pattern is lit only by pure **green** light in an otherwise dark room. What does it look like?",[767,769,771,773],{"id":277,"label":768},"Red, as usual",{"id":280,"label":770},"Green",{"id":283,"label":772},"Black",{"id":286,"label":774},"Yellow, because red and green make yellow","**c — black.** Red powder is red because it absorbs green and blue and reflects red. Under pure green light there is no red arriving for it to reflect, and the green that does arrive is absorbed. Almost nothing comes back to your eye, so the pattern looks black.\n\nOption d is the trap: red + green = yellow is true for *adding two lamps*, but here there is only one lamp and a pigment that removes light. Nothing is being added.\n\nThis is a lovely thing to do at home with a coloured torch or a phone screen showing a solid colour in a dark room. Lay out several colours of paper and see which ones go black.",{"id":777,"type":53,"title":778,"eyebrow":779,"navLabel":780},"u-ch10","Splitting white light","Chapter 10","10 Dispersion",{"id":782,"type":43,"markdown":783},"dispersion-how","A prism splits white light because the refractive index of glass is **not quite the same for every colour**. Violet light is slowed a little more than red light, so violet is bent a little more at each face of the prism, and after two refractions the colours have fanned apart.\n\nThe spread is small — for ordinary glass the index is about 1.51 for red and about 1.53 for violet — but bending twice and then travelling a metre to a screen turns that tiny difference into a visible band.\n\nIsaac Newton settled the argument in 1666. Before him, people believed the prism was somehow *adding* colour to pure white light, dyeing it as it passed through. Newton's crucial experiment was to take just one colour out of the spectrum with a slit, and send **that** through a second prism. It bent further — but it did not split again. It stayed the same colour. Then he recombined the whole spectrum with a second, inverted prism and got white light back.\n\nConclusion: white light is a **mixture**. The prism separates; it does not create.",{"id":785,"type":786,"title":787,"items":788},"timeline-colour","timeline","Working out what colour is",[789,793,797,801,805,809,813],{"time":790,"title":791,"text":792},"c. 1020","Ibn al-Haytham","In Cairo, the *Book of Optics* argues from experiment that light travels from objects into the eye, and studies reflection, refraction and the rainbow.",{"time":794,"title":795,"text":796},"1304","Theodoric of Freiberg","Uses a spherical flask of water as a giant raindrop and reproduces the rainbow, working out that the primary bow involves one internal reflection.",{"time":798,"title":799,"text":800},"1637","Descartes","Calculates the 42° angle of the primary bow and the 51° angle of the secondary, though he cannot yet explain the colours.",{"time":802,"title":803,"text":804},"1666","Newton's prism","Shows that white light is a mixture: a single colour cut from the spectrum will not split further, and a second prism recombines the fan into white.",{"time":806,"title":807,"text":808},"1801","Young's two slits","Light passed through two narrow slits makes stripes, which only makes sense if light is a **wave** with a wavelength.",{"time":810,"title":811,"text":812},"1814","Fraunhofer lines","Dark lines found in the solar spectrum turn out to name the elements in the Sun. Colour becomes a way of doing chemistry at a distance.",{"time":814,"title":815,"text":816},"1861","Maxwell","The first colour photograph, made by photographing a tartan ribbon three times through red, green and blue filters — additive mixing, proved.",{"id":818,"type":47,"variant":500,"title":819,"markdown":820},"example-newton-disc","Newton's disc: putting the colours back","Paint the seven spectrum colours as sectors on a cardboard disc, push a pencil through the middle and spin it fast. The colours blur into a dirty off-white.\n\nIt is not a perfect white, because poster paint colours are dull compared with pure spectral light, but the point survives: your eye adds together anything arriving faster than about 1\u002F25 of a second, so spinning the disc **adds** the colours back into one.\n\nThis is additive mixing done with time instead of overlapping lamps — and it is the same trick a film projector uses to turn 24 still pictures a second into movement.",{"id":822,"type":47,"variant":96,"title":823,"markdown":824},"nuance-seven","Why exactly seven colours?","There are not seven. The spectrum is continuous: every colour blends smoothly into the next, and you could name a hundred bands or a thousand.\n\nNewton chose **seven** — adding orange and indigo to an earlier list of five — partly because he wanted the number of colours to match the seven notes of a musical scale and the seven known planets. It was an aesthetic decision, not a measurement.\n\nMost people find indigo genuinely hard to pick out as separate from blue and violet. It stayed in the list because textbooks copied Newton, and **VIBGYOR** is a useful thing to remember — but do not go looking for seven sharp stripes in a rainbow. There are none.",{"id":826,"type":348,"itemId":827,"prompt":828,"check":829,"hints":841,"feedback":844},"u-prac-colour","light.understand-filter-stack","White light passes through a **red** filter and then a **blue** filter placed one behind the other. What reaches the screen?",{"kind":830,"options":831,"correct":840},"choice",[832,834,836,838],{"id":277,"label":833},"Purple light",{"id":280,"label":835},"Red light",{"id":283,"label":837},"Blue light",{"id":286,"label":839},"No light at all — it is black",[286],[842,843],"A filter lets its own colour through and absorbs everything else.","What is left after the red filter? Now what does the blue filter do to that?",{"correct":845,"incorrect":846},"Right — **black**. The red filter removes everything but red; the blue filter then absorbs that red, and nothing survives.","Work through it in order. The red filter passes only red, absorbing blue and green. The blue filter absorbs anything that is not blue — and all that is left is red. So nothing gets through: the screen is black. Filters **subtract**; they never add up to purple.",{"id":848,"type":53,"title":849,"eyebrow":850,"navLabel":851},"u-ch11","Mix-ups worth clearing up","Chapter 11","11 Common mix-ups",{"id":853,"type":47,"variant":414,"title":854,"markdown":855},"mix-shadow-reflection","\"A shadow is a reflection\"","They are opposites. A **reflection** is light that bounced off something and reached you. A **shadow** is light that never arrived at all.\n\nA reflection carries information — colour, brightness, detail. A shadow carries only an outline, and always the same flat grey, whatever colour the object was.",{"id":857,"type":47,"variant":414,"title":858,"markdown":859},"mix-mirror-flip","\"A mirror turns the image upside down\"","A plane mirror keeps the image the right way up. What it does is reverse front and back, which we read as a left-right swap.\n\nThe things that genuinely turn a picture upside down are a **pinhole**, a **convex lens** with the object beyond its focus, a **concave mirror** beyond its focus, a camera and your own eye. In all of those, rays cross over on the way, so top becomes bottom.",{"id":861,"type":47,"variant":414,"title":862,"markdown":863},"mix-seeing-eye","\"You see because your eyes send out a look\"","It certainly feels that way, and it survived in physics for over a thousand years. But a perfectly dark room would not stop it, and it does not. Light must travel **from** the object **into** the eye — always that direction.\n\nAsk anyone who says otherwise to find a black cat in a sealed dark room.",{"id":865,"type":47,"variant":414,"title":866,"markdown":867},"mix-hot-light","\"Anything that gives light must be hot\"","For most of history this was true: fire, filament bulbs, the Sun. Not any more, and not in nature either.\n\nA firefly's light is cool enough to sit on your hand. An LED runs warm only because it is a little wasteful, and its light itself carries no fire. Deep-sea fish, some fungi and glowing plankton all make **cold light** by chemistry. The general word is *luminescence*, as opposed to *incandescence* — glowing because you are hot.",{"id":869,"type":47,"variant":414,"title":870,"markdown":871},"mix-invisible-beam","\"You can see a beam of light going past you\"","You cannot see light unless it is going **into** your eye. A laser beam crossing a clean room, seen from the side, is invisible.\n\nWhen you do see a beam — headlights in fog, a projector cone in a dusty hall, sunbeams through a gap — you are seeing dust, smoke or water droplets *in* the beam, each of them scattering a little of it sideways towards you. Clear the air and the beam disappears while losing none of its power.",{"id":873,"type":53,"title":874,"eyebrow":875,"navLabel":876},"u-ch12","Pulling it together","Chapter 12","12 Pulling it together",{"id":878,"type":879,"title":880,"terms":881},"gloss-understand","glossary","Words to be precise about",[882,886,890,894,898,902,906,910,914,918,922,926,930,933,937,941,945,949,953,957],{"term":883,"meaning":884,"example":885},"Normal","A line drawn at right angles to a surface at the point where a ray meets it. All optical angles are measured from it.","A ray \"at 30° to the mirror\" is at 60° to the normal.",{"term":887,"meaning":888,"example":889},"Angle of incidence","The angle between the incoming ray and the normal.","Written i.",{"term":891,"meaning":892,"example":893},"Angle of reflection","The angle between the normal and the reflected ray. Always equal to the angle of incidence.","Written r.",{"term":895,"meaning":896,"example":897},"Law of reflection","Angle of incidence = angle of reflection, and both rays and the normal lie in one plane.","The whole behaviour of every mirror.",{"term":899,"meaning":900,"example":901},"Regular reflection","Reflection from a smooth surface: parallel rays stay parallel, so you get an image.","Mirror, still water, polished steel.",{"term":903,"meaning":904,"example":905},"Diffuse reflection","Reflection from a rough surface: rays scatter in all directions, so you get a glow, not a picture.","Paper, wall paint, a cinema screen.",{"term":907,"meaning":908,"example":909},"Virtual image","An image the light only appears to come from; it cannot be caught on a screen.","Your reflection behind a mirror.",{"term":911,"meaning":912,"example":913},"Real image","An image made where light rays actually meet, which can be caught on a screen.","The picture inside a pinhole camera.",{"term":915,"meaning":916,"example":917},"Lateral inversion","The left-right swap that a plane mirror gives an image.","AMBULANCE written backwards.",{"term":919,"meaning":920,"example":921},"Umbra","The fully dark part of a shadow, where no part of the source can be seen.","The sharp core of your shadow at your feet.",{"term":923,"meaning":924,"example":925},"Penumbra","The partly lit grey border of a shadow, where part of the source is still visible.","The soft edge around your head-shadow.",{"term":927,"meaning":928,"example":929},"Refraction","The change of direction of light crossing at a slant into a material where its speed is different.","The bent straw in a glass.",{"term":626,"meaning":931,"example":932},"The speed of light in vacuum divided by its speed in the material. Bigger means slower and more bending.","Water 1.33, glass 1.5, diamond 2.42.",{"term":934,"meaning":935,"example":936},"Apparent depth","The shallower depth water seems to have because of refraction: real depth ÷ n.","A 1.2 m pool looks 0.90 m deep.",{"term":938,"meaning":939,"example":940},"Dispersion","The splitting of white light into colours, because the refractive index differs slightly for each colour.","A prism; a rainbow.",{"term":942,"meaning":943,"example":944},"Spectrum","The continuous band of colours white light contains.","Red through to violet, no sharp lines.",{"term":946,"meaning":947,"example":948},"Additive mixing","Adding coloured light. Primaries red, green, blue; mixtures get brighter; all three give white.","Every screen you own.",{"term":950,"meaning":951,"example":952},"Subtractive mixing","Removing colours with pigments or filters. Primaries cyan, magenta, yellow; mixtures get darker.","Paints, inks, printer cartridges.",{"term":954,"meaning":955,"example":956},"Incandescence","Giving out light because you are hot.","A flame, a filament bulb, the Sun.",{"term":958,"meaning":959,"example":960},"Luminescence","Giving out light without being hot.","A firefly, an LED, glowing plankton.",{"id":962,"type":963,"prompt":964},"u-reflect-design","reflection","A photographer wants soft shadows on a face; a shadow-puppet artist wants shadows as sharp as possible; a dentist wants no shadow in the patient's mouth at all. Using what you now know about umbra and penumbra, describe the kind of light source each one should choose, and where they should put it.",{"id":966,"type":967,"title":968,"questions":969},"quiz-understand","quiz","Check that the rules are solid",[970,983,996,1009,1022,1035,1048,1061,1074,1087,1100,1113],{"itemId":971,"prompt":972,"options":973,"correct":283,"why":982},"light.understand-q-normal","A ray strikes a plane mirror at 20° to the mirror **surface**. The angle of reflection, measured from the normal, is:",[974,976,978,980],{"id":277,"label":975},"20°",{"id":280,"label":977},"40°",{"id":283,"label":979},"70°",{"id":286,"label":981},"90°","The normal is 90° from the surface, so the angle of incidence is 90 − 20 = 70°. Reflection equals incidence: 70°.",{"itemId":984,"prompt":985,"options":986,"correct":283,"why":995},"light.understand-q-mag","A 6 cm object is 40 cm from a point lamp; the screen is 200 cm from the lamp. The shadow is:",[987,989,991,993],{"id":277,"label":988},"1.2 cm",{"id":280,"label":990},"12 cm",{"id":283,"label":992},"30 cm",{"id":286,"label":994},"5 cm","200 ÷ 40 = 5, so the shadow is 6 × 5 = 30 cm. The distances are both measured from the lamp.",{"itemId":997,"prompt":998,"options":999,"correct":280,"why":1008},"light.understand-q-umbra","You move a screen further away from an object lit by a wide lamp. The umbra:",[1000,1002,1004,1006],{"id":277,"label":1001},"Grows, and the penumbra shrinks",{"id":280,"label":1003},"Shrinks, and the penumbra grows",{"id":283,"label":1005},"Stays exactly the same",{"id":286,"label":1007},"Becomes brighter than the surroundings","Further back, more of the wide source can peep round the object, so the fully dark region shrinks while the grey border widens. Push far enough and the umbra vanishes.",{"itemId":1010,"prompt":1011,"options":1012,"correct":280,"why":1021},"light.understand-q-mirror-height","A 170 cm tall person wants the shortest wall mirror in which they can see all of themselves. It should be:",[1013,1015,1017,1019],{"id":277,"label":1014},"170 cm, and they must stand close",{"id":280,"label":1016},"85 cm, at any distance",{"id":283,"label":1018},"85 cm, but only if they stand 2 m away",{"id":286,"label":1020},"It depends on the width of the room","Rays from head and toes reach the eye from points halfway up, so a mirror half your height is always enough — and, surprisingly, the distance makes no difference at all.",{"itemId":1023,"prompt":1024,"options":1025,"correct":280,"why":1034},"light.understand-q-diffuse","The Moon looks like a softly glowing disc rather than a mirror because its surface:",[1026,1028,1030,1032],{"id":277,"label":1027},"Reflects almost all the light that falls on it",{"id":280,"label":1029},"Is rough, so it scatters sunlight in every direction",{"id":283,"label":1031},"Makes a little light of its own",{"id":286,"label":1033},"Is curved","Diffuse reflection from rough dust and rubble sends some sunlight towards us from every part of the disc. A polished Moon would show one dazzling glint on a black disc.",{"itemId":1036,"prompt":1037,"options":1038,"correct":280,"why":1047},"light.understand-q-two-mirrors","Two plane mirrors at 60° to each other, with a marble between them, give:",[1039,1041,1043,1045],{"id":277,"label":1040},"3 images",{"id":280,"label":1042},"5 images",{"id":283,"label":1044},"6 images",{"id":286,"label":1046},"An infinite number","360 ÷ 60 = 6, minus one for the object, gives 5 images. Only parallel mirrors give an (almost) endless corridor.",{"itemId":1049,"prompt":1050,"options":1051,"correct":277,"why":1060},"light.understand-q-bend-dir","A ray travels from air into glass at a slant. It bends:",[1052,1054,1056,1058],{"id":277,"label":1053},"Towards the normal, because light is slower in glass",{"id":280,"label":1055},"Away from the normal, because light is slower in glass",{"id":283,"label":1057},"Towards the normal, because light is faster in glass",{"id":286,"label":1059},"Not at all","Into a slower material means bending towards the normal. Coming back out into air, it bends away again by the same amount.",{"itemId":1062,"prompt":1063,"options":1064,"correct":283,"why":1073},"light.understand-q-normal-entry","A ray enters a glass block exactly along the normal (0° of incidence). Inside the glass it:",[1065,1067,1069,1071],{"id":277,"label":1066},"Bends towards the normal",{"id":280,"label":1068},"Bends away from the normal",{"id":283,"label":1070},"Travels straight on, but more slowly",{"id":286,"label":1072},"Is completely reflected","Bending needs a slant, so that one edge of the beam slows before the other. At 0° both edges slow together: the light slows down but does not turn.",{"itemId":1075,"prompt":1076,"options":1077,"correct":283,"why":1086},"light.understand-q-depth","A tank of water is 2.0 m deep. Looking down from above, the bottom appears to be about (n for water = 1.33):",[1078,1080,1082,1084],{"id":277,"label":1079},"2.7 m deep",{"id":280,"label":1081},"2.0 m deep",{"id":283,"label":1083},"1.5 m deep",{"id":286,"label":1085},"0.7 m deep","Apparent depth = real depth ÷ n = 2.0 ÷ 1.33 = 1.5 m. Water always looks about three-quarters of its real depth — which is why open water is so dangerous to judge by eye.",{"itemId":1088,"prompt":1089,"options":1090,"correct":283,"why":1099},"light.understand-q-tomato","A tomato looks red in white light because it:",[1091,1093,1095,1097],{"id":277,"label":1092},"Gives out red light of its own",{"id":280,"label":1094},"Absorbs red and reflects the rest",{"id":283,"label":1096},"Reflects red and absorbs the rest",{"id":286,"label":1098},"Bends red light more than other colours","Colour is what an object throws back. The tomato absorbs blue and green and returns red to your eye — so under pure green light it looks black.",{"itemId":1101,"prompt":1102,"options":1103,"correct":280,"why":1112},"light.understand-q-mixing","On a phone screen, a bright yellow patch is actually made of:",[1104,1106,1108,1110],{"id":277,"label":1105},"Yellow lamps",{"id":280,"label":1107},"Red and green lamps lit together",{"id":283,"label":1109},"Red and blue lamps lit together",{"id":286,"label":1111},"All three lamps at half power","Screens mix light additively with red, green and blue only. Red + green arriving together is reported by your eye as yellow; there is no yellow lamp at all.",{"itemId":1114,"prompt":1115,"options":1116,"correct":280,"why":1125},"light.understand-q-newton","Newton passed a single colour from a spectrum through a second prism. It bent further but did not split. This shows that:",[1117,1119,1121,1123],{"id":277,"label":1118},"Prisms add colour to white light",{"id":280,"label":1120},"White light is a mixture of colours already present",{"id":283,"label":1122},"Colour is only in the eye",{"id":286,"label":1124},"Glass is coloured","If the prism created colour, the second prism would have created more. Instead the single colour survived unchanged — so the first prism had separated, not manufactured. A reversed prism then recombined the fan into white.",{"id":1127,"type":1128,"title":1129,"points":1130},"cheat-understand","summary","Cheat sheet",[1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143],"**Ray model:** light leaves every point of a source in all directions, travels in straight lines, and only changes direction when it reflects or refracts. Draw rays with a ruler; dot the imaginary parts.","**Shadow size:** shadow = object × D ÷ d, both distances measured from the lamp. Halfway gives ×2; touching the screen gives ×1.","**Umbra and penumbra:** a source with size gives a fully dark umbra and a grey penumbra. Bigger source or further screen means less umbra, more penumbra — which is why high-flying birds cast no shadow.","**Law of reflection:** angle of incidence = angle of reflection, both measured **from the normal**, with both rays and the normal in one plane.","**Tilt a mirror by θ and the reflected beam swings by 2θ.**","**Plane mirror image:** same size, upright, as far behind as the object is in front, laterally inverted, virtual. A mirror half your height shows all of you, from any distance.","**Regular vs diffuse:** smooth surfaces keep rays in formation and give images; rough ones scatter them and give an even glow. Both obey the same law.","**Two mirrors at angle θ:** number of images = 360 ÷ θ − 1. Parallel mirrors give a fading corridor.","**Refraction:** light has different speeds in different materials. At a slant, it bends — **towards** the normal going slower, **away** going faster, and not at all at 0°.","**Refractive index** n = speed in vacuum ÷ speed in material. Water 1.33, glass 1.5, diamond 2.42. Apparent depth = real depth ÷ n, so a 1.2 m pool looks 0.90 m.","**Colour of objects:** what they reflect, not what they absorb. Change the light and you change the colour; under pure green light a red object is black.","**Two kinds of mixing:** light adds (primaries red, green, blue; all three make white) and pigment subtracts (primaries cyan, magenta, yellow; all three make near-black).","**Dispersion:** glass bends violet slightly more than red, so a prism fans white light into a spectrum. Newton showed the prism separates rather than creates.",{"id":1145,"type":291,"conceptId":1146,"relation":293,"explanation":1147},"u-conn-angles","angles","Every rule in this lesson is measured in degrees from a normal. Knowing acute, obtuse and complementary angles makes ray diagrams much easier to read.",{"id":1149,"type":291,"conceptId":1150,"relation":1151,"explanation":1152},"u-conn-eye","human-body-anatomy","applied_in","The eye is refraction put to work: a curved cornea and a lens bend light to a point on the retina, making a real, inverted image.",{"id":1154,"type":1155,"sourceIds":1156},"sources-understand","sources",[1157,1158,1159,1160,1161,1162],"light-ncert-curiosity-7-light","light-physicsclassroom-reflection","light-physicsclassroom-refraction","light-britannica-light","light-nasa-visible","light-hyperphysics-rainbow",[1157,1158,1159,1160,1161,1162],"needs_review",{"generatedBy":1166,"notes":1167},"claude-code","Draft generated locally; every number computed and asserted in scratchpad\u002Flight\u002Fnumbers.py. Pending owner review.","6d6eaa0403d39cc11021f8aa2e970787a04ab4ea5edb8f46e21ec8fc0a01dabc",{"component:shadow-lab@1":1170,"component:light-ray@1":1171,"logic:practice":1172,"component:match-pairs@1":1173,"component:prism-lab@1":1174,"source:light-britannica-light":1175,"source:light-hyperphysics-rainbow":1176,"source:light-nasa-visible":1177,"source:light-ncert-curiosity-7-light":1178,"source:light-physicsclassroom-reflection":1179,"source:light-physicsclassroom-refraction":1180},"7476ef546fdb1f398a07393483e549c923f9568dc1bb1c2561191bf47862c475","d66d44021dc28328ce2ea82e0d6cefc9466b5dc65dbb93c92b05b88161725be6","3d6b0fe1b15255975a32b0fcd94e8019bc959ad45cbf12e136e86149549c6878","2a8ee4ac87460b4e1175a4bb13c96b03d577db06dde95670eb7fcfe4ad787899","835c8ba7fd707c60ded46494f4b672aa095199ba9a2628409905335d0b3434a9","0e76ba316118067e955dbaf8cbbabc23d388ad0bf547c518be84bcc95923d376","dce907528f01e833f82d68150b423cc68c60d1c9c88673a96a84eb269bbbd3ce","711ba457ef893111775bd5fd9bfd09632c8ef20e5e7708971e06754f5ef7f4bd","9517f5bdb40f9f891f26ae78e97ff552db5602c4da5cf91f3eb3265a44a62860","e66dbe6283e14f7619d6e497882b26fbe0ae3a0632f7bd1202b67fe8f02bfe7b","43e2d25a3db005014fd7d491471e9e47242ce863ec6c79370b74a25bfe96acfb",{"state":1182,"reviewer":1183,"selfReview":322,"reviewedAt":1184,"method":1185},"approved","The library owner","2026-09-20T10:18:37.581Z","owner_bulk","preview-7e1cbbcc4f",1789899597168]