Refraction and Snell's Law — Why Light Bends

High School⏱ 9 min readOptics

Snell's law of refraction: n₁sinθ₁ = n₂sinθ₂. Learn why light bends at boundaries, how lenses work, and why pools look shallower than they are.

Quick answer

Snell's law describes how light bends when crossing between materials: n₁sinθ₁ = n₂sinθ₂. Light slows in denser media (higher n), and the ray bends toward the normal entering glass — away from it leaving.

$n_1\sin\theta_1 = n_2\sin\theta_2$

Unit: Angles in degrees; n is unitless

Example: Light enters water (n = 1.33) from air (n = 1.00) at 45° to the normal. It refracts to about 32° — bent toward the normal because water is optically denser.

What you will learn

State Snell's law and define refractive index
Predict bend direction when light enters denser or rarer media
Calculate refraction angles with n₁sinθ₁ = n₂sinθ₂
Explain apparent depth in water
Connect refraction to lens action

The bent straw and why it happens

Push a straw into a glass of water and it appears to snap at the surface. It has not broken — the light carrying its image bent on the way out. This bending is refraction, and it rules everything from eyeglasses to fiber-optic internet.

Light travels at $c$ in vacuum but slower in matter — about $c/1.33$ in water, $c/1.5$ in glass. When a wavefront crosses the boundary at an angle, one side slows first and the ray pivots. The refractive index $n = c/v$ measures how much a material slows light.

Snell's law

Willebrord Snellius found the exact relationship around 1621:

n_1\sin\theta_1 = n_2\sin\theta_2

n₁, n₂ = refractive indices; θ₁, θ₂ = angles from the normal in each medium

Which way does it bend?

Entering a denser medium (higher n): toward the normal. Leaving to a rarer medium (lower n): away from the normal. Air → glass bends in; glass → air bends out.

Working Snell's law

Worked example. Light travels from air ( $n_1 = 1.00$ ) into water ( $n_2 = 1.33$ ) at $\theta_1 = 45°$ from the normal. Find $\theta_2$ .

$\sin\theta_2 = \frac{n_1}{n_2}\sin\theta_1 = \frac{1.00}{1.33} \times \sin 45°$

$\sin\theta_2 = 0.752 \times 0.707 = 0.532 \quad\Rightarrow\quad \theta_2 \approx 32.1°$

The ray bends toward the normal, from 45° to about 32° — exactly why submerged objects look displaced.

From bending to lenses

A lens is just refraction, engineered. Each curved glass surface bends rays by Snell's law; the two surfaces of a convex lens cooperate to converge parallel rays to a focal point. Concave lenses do the opposite, spreading rays apart.

Your eye is a living lens system: the cornea does most of the refracting, the crystalline lens fine-tunes focus. Glasses add a second lens in front to pre-correct the bending — converging for farsightedness, diverging for nearsightedness.

When light cannot escape

Push refraction to its limit and something dramatic happens. Going from glass to air, the ray bends away from the normal — and beyond the critical angle, $\sin\theta_2$ would exceed 1, which is impossible. The light cannot escape at all: it reflects perfectly inside. This total internal reflection traps signals in fiber-optic cables and makes diamonds blaze.

Same law, extreme consequence — the subject of its own article.

Variables and units

Symbol	Name	Unit	Meaning
$n₁$	Index 1	unitless	Refractive index of first medium
$n₂$	Index 2	unitless	Refractive index of second medium
$θ₁$	Incident angle	degrees	Angle in medium 1, from the normal
$θ₂$	Refracted angle	degrees	Angle in medium 2, from the normal

Common mistakes

✗ Light bends because it slows down and gets 'tired.'

Bending comes from the speed change across the boundary, not from tiredness. One edge of the wavefront slows before the other, pivoting the whole ray — like a car turning when one wheel hits gravel.

✗ The angle in Snell's law is measured from the surface.

Like reflection, refraction angles are measured from the normal. Using the surface angle flips sines and cosines and gives wrong answers.

✗ Refraction only happens going into denser media.

It happens at every boundary between different media, in both directions. Going from glass to air, light bends away from the normal — and past the critical angle it cannot escape at all (total internal reflection).

Real-world applications

Eyeglasses: lenses bend light by refraction to correct nearsightedness and farsightedness.
Fiber optics: total internal reflection (refraction's extreme case) carries internet data across oceans.
Swimming pools: refraction makes pools look shallower than they are — light bends away from the normal leaving water.
Atmospheric optics: mirages, rainbows, and the twinkling of stars are all refraction in air of varying density.

Frequently asked questions

What is refraction?

Refraction is the bending of light as it passes from one medium into another of different optical density. The speed of light changes (slower in glass than air), and the wavefront pivots — like a marching band hitting mud at an angle.

What is Snell's law?

n₁sinθ₁ = n₂sinθ₂, where n is each medium's refractive index and θ is measured from the normal. It predicts the exact bend angle at any boundary.

Why does a pool look shallower than it really is?

Because light leaving water bends away from the normal, your brain traces the rays back along straight lines to a shallower apparent position. The real bottom can be a third deeper than it looks — which is why diving into unfamiliar water is dangerous.

Who discovered Snell's law?

Willebrord Snellius discovered the sine relationship around 1621 (it was unpublished; Descartes later published it). The law is sometimes called the Snell-Descartes law.