Refraction of Light

Refraction is the bending of light as it passes from one medium to another. The bending occurs because light travels at different speeds in different materials.

Why Does Light Bend?

Light travels at different speeds in different materials. When it crosses the boundary between two materials at an angle, the change in speed causes it to change direction — this is refraction.

Light bends toward the normal when entering a denser medium (air → glass).

Snell's Law

n_1 \sin\theta_1 = n_2 \sin\theta_2

n = refractive index (dimensionless), θ = angle from the normal.

Refractive Index

The refractive index $n$ of a material describes how much slower light travels compared to vacuum:

$n = \frac{c}{v} \quad \text{where } c = 3 \times 10^8 \text{ m/s}$

Material	Refractive Index
Vacuum	1.00
Air	1.00
Water	1.33
Glass	~1.50
Diamond	2.42

Bending Direction

Into denser medium (larger $n$ ): light bends toward the normal ( $\theta_2 < \theta_1$ )
Into less dense medium (smaller $n$ ): light bends away from the normal ( $\theta_2 > \theta_1$ )

Note A straw in a glass of water appears bent — this is refraction at the water–air boundary.

Light goes from air (n=1.0) into glass (n=1.5) at θ₁ = 30°. Find θ₂.

$1.0 \times \sin 30° = 1.5 \times \sin\theta_2$

$\sin\theta_2 = \frac{0.5}{1.5} = 0.333 \implies \theta_2 \approx 19.5°$

Real world: A straw appears bent in a glass of water

Place a straight straw in a glass of water and look from the side — it appears to be broken or bent at the water surface. Light from the submerged part travels from water (n = 1.33) into air (n = 1.00) and bends away from the normal, so your eye traces the ray back in a straight line to the wrong position.

Real world: Swimming pool looks shallower than it is

A swimming pool that is 2 m deep may appear to be only about 1.5 m deep when you look straight down into it. Light from the bottom travels from water into air and refracts away from the normal, making the pool floor appear closer to the surface than it really is.

Real world: Mirages on a hot road

On a very hot day, the road ahead appears wet and shiny — this is a mirage. Air near the hot tarmac is much less dense than the cooler air above. Light from the sky bends gradually (refracts) as it passes through layers of air with different temperatures, eventually curving upward into your eye — creating the illusion of water on the road.

Tip Where do you see this in real life? Straws in drinks, shallow-looking pools, fish appearing in the wrong position when you try to spear them, and mirages on hot roads are all caused by refraction!

Practice Problems

Does light bend toward or away from the normal when going from water into air?

Show answer

Away from the normal, because air is less dense (smaller n).

Why do diamonds sparkle so much?

Show answer

Diamond has a very high refractive index (2.42), causing strong bending and total internal reflection that splits and reflects light.