How light behaves: rays, angles and rules you can use

In Discover you met the facts: light goes straight, mirrors bounce it, water bends it, a prism splits it.

This 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.

The tool that does nearly all the work is one simple idea: draw light as rays — straight arrows — and follow them.

Physicists explain light with several different pictures, and each is right for a different job. The simplest is the ray model:

• Light travels out from every point of a source in all directions.
• Each path is a ray: a straight line, drawn with an arrowhead to show which way the light is going.
• Rays carry on straight for ever until something absorbs them, reflects them, or refracts them at a boundary between two materials.
• Rays do not interfere with each other. Two beams can cross without either being disturbed.

That 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.

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.

Those rays make two triangles that share the same angle at the lamp — similar triangles. That gives an exact rule:

The shadow is bigger than the object by exactly the ratio of the two distances from the lamp.

That 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.

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.

The 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.

So behind you there are really two regions:

• The umbra: the part of the screen that no part of the source can see. Fully dark.
• 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.

Near 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.

Send a narrow beam at a flat mirror and it bounces off. There is a rule, and it is exact.

First 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.

Then:

1. The angle of incidence (between the incoming ray and the normal) equals the angle of reflection (between the normal and the outgoing ray).
2. The incoming ray, the reflected ray and the normal all lie in the same flat plane.

That 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.

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.

No 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.

Four properties, all testable in a minute with a small mirror:

• Same size as the object, however far away you stand.
• Upright, not upside down.
• As far behind the mirror as the object is in front.
• Laterally inverted: left and right swapped.

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?

Because of what happens to the arrangement of the rays.

A 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.

Paper, 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.

The 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.

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.

Bring 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:

number of images = 360 ÷ angle − 1

At 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.

Light does not have the same speed everywhere. In empty space it is the full 3 × 10⁸ m/s. In water it is about 2.25 × 10⁸ m/s, and in ordinary glass about 2.0 × 10⁸ m/s.

When 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.

That 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.

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.

• A tomato absorbs blue and green light and reflects red. You call it red.
• A leaf absorbs red and blue and reflects green.
• Something that reflects nearly everything looks white.
• 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.

So 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.

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.

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.

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.

Same word, opposite arithmetic. One adds light to darkness; the other takes light away from white.

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.

The 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.

Isaac 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.

Conclusion: white light is a mixture. The prism separates; it does not create.