Reflection and Refraction of Light

Light that bounces and light that bends

Light usually travels in straight lines, which is why shadows have sharp edges. But two things happen when light meets a boundary between materials — say, the surface of a mirror or a pool of water. Some of it bounces back, which we call reflection, and some of it passes through but changes direction, which we call refraction. These two effects explain mirrors, lenses, cameras, your own eyes, rainbows, and the glass cables that carry the internet across oceans. Light itself is a wave — part of the family covered in the electromagnetic spectrum.

Reflection: the law of the bounce

When light hits a smooth surface like a mirror, it bounces off in a perfectly predictable way. To describe it, we first draw a line called the normal — an imaginary line at exactly 90° to the surface at the point where the ray strikes. All angles in optics are measured from this normal, not from the surface.

Law of reflection: the angle of incidence equals the angle of reflection.

The angle of incidence is the angle between the incoming ray and the normal; the angle of reflection is the angle between the outgoing ray and the normal. They are always equal, and both rays lie in the same plane.

This simple law explains why a mirror gives a clear image: every ray bounces off in an orderly, predictable direction, so the pattern of light is preserved. A rough surface like paper also reflects light, but its microscopic bumps scatter the rays in all directions — this is diffuse reflection, which is why you can see this page from any angle but cannot see your face in it.

Refraction: why light bends

Light travels fastest in a vacuum, at about 300,000 km per second. In any material — water, glass, air — it travels more slowly. When a ray of light crosses from one material into another where its speed changes, it bends. This bending is refraction.

Why does a change of speed cause bending? Picture a line of marchers walking from firm ground onto soft mud at an angle. The marchers who reach the mud first slow down while the others are still on firm ground, so the whole line pivots and changes direction. Light does exactly the same: the part of the wavefront that enters the slower medium first gets "held back", swinging the ray to a new angle.

The rule for the direction of bending:

• Light entering a denser, slower medium (air → glass) bends toward the normal.
• Light entering a less dense, faster medium (glass → air) bends away from the normal.

This is why a straw in a glass of water looks broken at the surface, and why a swimming pool always looks shallower than it really is.

Snell's law and the refractive index

We can predict exactly how much light bends using Snell's law:

n₁ sin θ₁ = n₂ sin θ₂

Here θ₁ and θ₂ are the angles to the normal in the two materials, and n is each material's refractive index — a number that tells you how much that material slows light down. The refractive index is defined as:

n = (speed of light in a vacuum) ÷ (speed of light in the material)

A vacuum has n = 1, air is almost exactly 1, water is about 1.33, and ordinary glass is about 1.5. A diamond has a very high index of 2.42, which is why diamonds bend and trap light so dramatically and sparkle.

Worked example. A ray of light travels from air (n₁ = 1.00) into water (n₂ = 1.33), striking the surface at 30° to the normal. What is the angle of refraction inside the water?

n₁ sin θ₁ = n₂ sin θ₂ 1.00 × sin 30° = 1.33 × sin θ₂ 1.00 × 0.500 = 1.33 × sin θ₂ sin θ₂ = 0.500 ÷ 1.33 = 0.376 θ₂ = sin⁻¹(0.376) ≈ 22°

The ray bent toward the normal (from 30° to 22°) as it entered the slower medium, exactly as predicted.

Total internal reflection

Something remarkable happens when light tries to travel from a dense medium into a less dense one — from glass or water into air. As you increase the angle of incidence, the refracted ray bends further and further away from the normal. At a certain angle, called the critical angle, the refracted ray skims right along the surface. Push past that angle, and the light can no longer escape at all — 100% of it reflects back inside. This is total internal reflection.

For water the critical angle is about 49°, and for ordinary glass about 42°. This effect is not a curiosity — it powers fibre-optic cables, the thin glass threads that carry telephone calls, television, and internet data. A light or laser signal fired into the fibre hits the walls beyond the critical angle every time, so it bounces along the inside of the fibre without leaking out, carrying information at enormous speed over thousands of kilometres.

Lenses and rainbows

Refraction is also how lenses work. A convex (bulging) lens refracts parallel rays so they converge to a point — this focuses light in cameras, telescopes, magnifying glasses, and the lens in your own eye. A concave lens spreads rays apart. By carefully shaping glass, we control exactly where light bends and meets.

Refraction also paints the sky. In a rainbow, sunlight enters each raindrop and refracts, reflects off the back of the drop, then refracts again on the way out. Because the refractive index is slightly different for each colour, red light bends a little less than violet, so the colours fan out into the familiar spectrum. To revisit how white light contains all these colours, see the electromagnetic spectrum.

Try it yourself! 🧪

Experiment 1 — The reappearing coin. Place a coin at the bottom of an opaque mug and step back until the rim just hides it from view. Keep still and ask a friend to slowly pour water into the mug. The coin seems to rise into view! No one moved it — the light leaving the coin now refracts (bends) as it crosses the water surface, changing direction enough to reach your eye over the rim. This is refraction made visible.

Experiment 2 — Bend a laser in water. In a darkened room, add a few drops of milk to a clear tank of water so the beam shows up. Shine a laser pointer down into the water at an angle and watch the beam kink at the surface, bending toward the normal as it slows in the water. Now aim the laser from inside the water (or use a tank with a flat side) up toward the surface at a shallow, glancing angle — past the critical angle the beam stops escaping and reflects entirely back into the water. You have just demonstrated both Snell's law and total internal reflection, the very effect that runs the internet. (Never point a laser at anyone's eyes.)