Question

Arrive at Snell’s law of refraction, using Huygen’s principle for refraction Using Huygens principle for refraction of a plane wave.

Answer 1

Let XY represent the surface separating the medium-I and medium–II. Let V₁ and V₂ be the speed of light in medium-I and medium-II respectively. Consider a plane wave front AB incident in medium-I at an angle i. Let the secondary wavelet from B strike the surface XY at C in a time t, then BC = V₁t Secondary wavelet from A will travel a distance V₂t as radius draw an arc in the medium-II. The tangent from C touches the arc at D. 

Let r be the angle of refraction.

If c represents the speed of light in vacuum then,

This is the Snell’s law of refraction.