Refraction · Grade 8
Light changes speed when it passes from one material into another, and unless it hits along the normal, this makes it change direction – refraction. It is why pools look shallower than they are and straws look bent. Snell’s law predicts the angles, and above the critical angle light is totally internally reflected, which is how optical fibres carry the internet.
Key facts
- Entering a denser material (air → glass), light slows and bends towards the normal; leaving, it bends away.
- Refractive index n = c ÷ v (c = 3.0 × 10⁸ m/s); water 1.33, glass about 1.5, diamond 2.42.
- Snell’s law: n = sin i ÷ sin r (from air), or n₁ sin θ₁ = n₂ sin θ₂.
- Critical angle: sin c = 1 ÷ n (into air), or sin c = n₂ ÷ n₁.
- Total internal reflection: from denser to less dense, with angle of incidence greater than c.
- Frequency stays the same; wavelength in the material is λ ÷ n. Apparent depth = real depth ÷ n.
Worked examples
Example 1
Light enters glass (n = 1.50) from air at 40° to the normal. Find the angle of refraction.
Answer: 25.4°
Example 2
Find the critical angle for water (n = 1.33), and decide whether light hitting the surface from below at 55° escapes.
Answer: c = 48.8°; it does not escape (total internal reflection)
Example 3
An optical fibre has a core of n = 1.52 and cladding of n = 1.46. Find the critical angle and the speed of light in the core.
Answer: 73.8°; 1.97 × 10⁸ m/s