Snell's Law — Light Escaping Diamond (Worked Example)

Given

• n₁ = 2.42 (diamond)

• n₂ = 1.00 (air)

• θ₁ = 30°

Find

Whether refraction is possible; the critical angle.

Principle

Snell's law n₁sinθ₁ = n₂sinθ₂: if sinθ₂ > 1, no refraction exists — total internal reflection. The critical angle is θc = arcsin(n₂/n₁).

Formula

Solution

1. Try Snell: $\sin\theta_2 = (n_1/n_2)\sin\theta_1 = 2.42 \times \sin30° = 2.42 \times 0.5 = 1.21$

2. Since $1.21 > 1$, no real θ₂ exists — total internal reflection occurs

3. Critical angle: $\theta_c = \arcsin(1/2.42) = \arcsin(0.413) = 24.4°$

4. Because 30° > 24.4°, the ray reflects entirely

Unit check

Angles in degrees throughout — consistent.

What this means physically

Total internal reflection — this light-trapping is why diamonds sparkle: rays bounce around inside instead of leaking out, exiting only through the top facets.