Refraction and lenses

Light changes speed when it passes from one material to another, which makes it bend: refraction. Lenses use refraction to focus light.

Key facts

  • Into a denser material (slower): bends towards the normal.
  • Refractive index n = speed in vacuum ÷ speed in material.
  • Snell’s law: n = sin i / sin r.
  • Total internal reflection happens beyond the critical angle: sin c = 1/n.
  • Convex lenses converge light; concave lenses spread it out.

Worked examples

Example 1

Light enters glass (n = 1.5) at 40° to the normal. Find the angle of refraction.

  1. sin r = sin 40° ÷ 1.5 = 0.4285
  2. r ≈ 25.4°

Answer: 25.4°

Example 2

Find the critical angle for water (n = 1.33).

  1. c = sin⁻¹(1 ÷ 1.33) ≈ 48.8°

Answer: 48.8°