See Light Bend: Refraction and Snell's Law

How to use this simulation

1. Drag the light source (the yellow dot) or move the slider to change the angle of incidence.
2. Pick the two media. In the denser one the wavefronts bunch up and slow down, which is why the ray bends.
3. Press "Swap the media" so the light goes from glass into air, then raise the angle past the critical angle.
4. Beyond it the refracted ray vanishes and all the light comes back: total internal reflection.

Why does a straw look broken in a glass of water?

Put a straw or a pencil into a glass of water, tilted, and look at it from the side. Right at the water surface it seems to snap, as if the part under water had shifted. Pull it out and it is perfectly straight. Nothing happened to the pencil. Something happened to the light coming from it.

You have probably noticed other odd things too. A swimming pool looks shallower than it really is. A coin at the bottom of a cup seems to float up when you pour water in. On a hot day, a road far ahead looks wet and shiny. All of these come from one simple fact: when light crosses from one material into another, it can change direction.

That change of direction is called refraction. On this page we will build it up from nothing: why light bends, how much it bends, how to calculate it, and the surprising moment when light stops escaping altogether and gets trapped inside.

Starting from zero: why light bends at all

The first thing to know is that light does not travel at the same speed everywhere. In a vacuum it moves at about 3 × 10⁸ m/s, in air almost as fast, in water noticeably slower, in glass slower still and in diamond slowest of all. A material in which light travels slowly is called optically denser; one in which it travels faster is optically rarer.

Now picture a shopping trolley rolling across a smooth floor onto a carpet. If it meets the carpet head-on, both front wheels reach the carpet together and slow down together, so the trolley just slows and keeps its direction. If it meets the carpet at a slant, one wheel hits the carpet first and slows while the other is still rolling fast on the floor. The trolley swings round a little. It has changed direction simply because one side slowed before the other.

Light does exactly this. The part of a wavefront that enters the denser material first slows down first, while the rest is still moving quickly, so the whole wavefront pivots and the ray changes direction. That is also why light hitting the boundary straight on (at 0°) does not bend: every part of the wavefront slows at the same moment.

A line of marching soldiers stepping from a road into mud at an angle behaves the same way, and the simulation shows it directly. Keep "moving wavefronts" switched on and watch them crowd together and slow down in the denser medium.

• Rarer to denser (air → water): light slows, the ray bends towards the normal, so the angle of refraction is smaller than the angle of incidence.
• Denser to rarer (water → air): light speeds up, the ray bends away from the normal, so the angle of refraction is larger.
• Straight on (angle of incidence 0°): the speed changes but the direction does not.

Words you need to know

These terms come up in every refraction question. Read them once carefully and the rest of the page becomes much easier.

The laws of refraction and Snell's law

Refraction is not random. It always follows two rules, called the laws of refraction.

Critical angle and total internal reflection

Now send the light the other way, from a denser medium into a rarer one, such as from water into air. It now bends away from the normal, so the angle of refraction is always bigger than the angle of incidence. Keep increasing the angle of incidence and the refracted ray leans closer and closer to the surface.

At one particular angle of incidence the refracted ray skims exactly along the boundary: the angle of refraction is 90°. That special angle of incidence is the critical angle. Putting θ₂ = 90° into Snell’s law, and using sin 90° = 1, gives sinθc = n₂/n₁. When the rarer medium is air this becomes simply sinθc = 1/n.

What happens beyond the critical angle? Snell’s law would then need sinθ₂ to be bigger than 1, which no angle can give. So the light cannot enter the second medium at all, and all of it reflects back into the first. This is total internal reflection. An ordinary mirror absorbs some light, but total internal reflection returns almost all of it, which makes it a better mirror than a mirror.

• Condition 1: light must travel from the denser medium towards the rarer one.
• Condition 2: the angle of incidence must be greater than the critical angle.
• Going from rarer to denser, total internal reflection never happens, whatever the angle.

Try it yourself in the simulation

Reading about refraction helps, but moving the controls yourself makes it stick. Work through these experiments with the animation above.

Experiment 1: set the first medium to air and the second to glass. Put the angle of incidence at 0° and notice the ray does not bend at all. Now raise the angle slowly: the angle of refraction rises too, but always stays smaller.

Experiment 2: keep the same angle and change the second medium from glass to water, then to diamond. Diamond bends the ray the most because its refractive index is the largest. Check v₂ in the readings panel: light is slowest in diamond.

Experiment 3: press "Swap the media" so the light travels from glass into air. Increase the angle until you pass the red dashed critical-angle line. The refracted ray disappears and the "total internal reflection" badge appears.

Experiment 4: watch the brightness of the reflected ray. At small angles it is faint, because most of the light gets through, but it grows brighter as you approach the critical angle, just as it does in real life.

Worked examples, step by step

Let’s solve some problems. In each one, write down what you know, then the formula, then substitute. Written this way, an answer earns full credit even if you slip on the arithmetic.

Mistakes students often make

A handful of errors come up again and again. Knowing them in advance saves easy marks.

• Measuring angles from the surface. Angles of incidence and refraction are always measured from the normal.
• Saying light speeds up in a denser medium. It is the opposite: light slows down, which is why n is larger.
• Looking for a critical angle when light goes from rarer to denser. There is none in that direction.
• Giving the refractive index a unit. n is a ratio of two speeds, so it has no unit.
• Thinking the frequency changes. It does not; the speed and the wavelength change, the frequency stays the same.
• Leaving the calculator in radians. Check it is in degree mode before taking a sine.

Refraction in everyday life

Refraction is not just a textbook topic; it is happening around you all the time.

• Optical fibres: light bounces along a glass thread thinner than a hair by total internal reflection. Internet data and medical endoscopes both rely on it.
• Diamond sparkle: diamond’s tiny critical angle traps light inside, so it reflects many times and leaves through the top, which is why cut diamonds glitter.
• Mirages: on a hot road, layers of hot air bend light gradually until it totally internally reflects, and you see a reflection of the sky that looks like water.
• A bent pencil in water, a pool that looks shallow, a coin that seems to rise in a cup: all refraction.
• Spectacles, cameras and microscopes use lenses, which work by refracting light to a focus.
• Rainbows: refraction and internal reflection inside raindrops, with each colour bending by a slightly different amount, spread sunlight into its colours.

Exam corner

These are the question types that come up most often, with the key point each answer needs.

Quick revision summary

The night before a test, this table is the whole topic on one screen.

Frequently asked questions