Question

Derive Snell’s law of refraction using Huygens’s wave theory.

Answer 1

AB - Incident wavefront

A'B' - Refracted wavefront

i = ∠CAN = ∠BAA'

r = ∠NA'a' = ∠AA'B'

${\displaystyle \therefore \frac{\text{sin i}}{\text{sin r}}=\frac{\text{BA′}}{\text{AB′}}}$

BA' = V₁ t ; AB = V₂t

${\displaystyle \therefore \frac{\text{sin i}}{\text{sin r}}=\frac{{\text{V}}_1}{{\text{V}}_2}}$

${\displaystyle \frac{{\text{V}}_1}{{\text{V}}_2}}$ is called refractive index, it's constant for two particular optical medium.

∴ ${\displaystyle \frac{\text{sin i}}{\text{sin r}}=\text{constant}}$