Snell’s Law Formula – Practice
n₁sinθ₁ = n₂sinθ₂ — Snell’s law (refraction)
At an interface, n₁sinθ₁ = n₂sinθ₂. Problems here often give sinθ values so you focus on the product rule.
Guide — how to use this formula
- 1. Identify n₁ with the incident ray (θ₁).
- 2. sinθ₂ = n₁sinθ₁/n₂; rearrange for n or sinθ₁.
- 3. Keep sinθ ≤ 1 for a real refracted ray.
- 4. Equal n → equal sin → no bending.
Derivation
From wavefront continuity (or Fermat), the sines of the angles link to refractive indices:
- Snell’s law:
n_1\sin\theta_1 = n_2\sin\theta_2 - Solve for sinθ₂:
\sin\theta_2 = \frac{n_1\sin\theta_1}{n_2}
If sinθ₂ would exceed 1, total internal reflection occurs.
Examples
Example: air → glass
n₁=1, sinθ₁=0.5, n₂=1.5 → sinθ₂≈0.333.
Example: find n₂
n₂ = n₁sinθ₁/sinθ₂.