Refraction of Light

Refraction is the bending of light when it crosses a boundary between two transparent materials (like air to glass). It happens because light changes speed in different materials.

Key terms

• Normal: a line drawn at right angles (90°) to the boundary where the light hits.
• Angle of incidence ($i$): the angle between the incoming ray and the normal.
• Angle of refraction ($r$): the angle between the refracted (bent) ray and the normal.

How light bends

• Into a slower medium (e.g. air → glass): bends towards the normal.
• Into a faster medium (e.g. glass → air): bends away from the normal.
• The ray only bends at the boundary. Inside a uniform block it travels straight.
• Through a rectangular block, the emerging ray is parallel to the incident ray.

Refractive index and Snell’s law

The refractive index, $n$, compares speeds: $$n = \frac{\text{speed in air}}{\text{speed in material}}$$ For light going from air into a material: $$n = \frac{\sin i}{\sin r}$$ A larger $n$ means light slows down more in that material.

Frequency stays the same when light changes medium; speed and wavelength change.

Critical angle and total internal reflection (TIR)

When light tries to go from a denser medium to a less dense one (e.g. glass → air), there is a special angle in the denser medium called the critical angle, $c$. If $i > c$, all the light is reflected inside: total internal reflection.

For a material to air: $$\sin c = \frac{1}{n}$$

Use: optical fibres guide light by repeated TIR, useful in telecommunications and medical endoscopes.

Simple experiment

Place a glass block on paper and draw its outline. Shine a narrow light ray at one side. Draw the normal at the entry point. Mark the incident, refracted, and emergent rays. Measure $i$ and $r$ with a protractor. Repeat for different $i$. Plot $\sin i$ against $\sin r$; the gradient gives $n$.

Common misconceptions

• “Light bends inside a material.” It bends only at boundaries; between them it travels straight.
• “Angles are to the surface.” Angles are to the normal.