Question

Using Huygen’s wave theory, derive Snell’s law of refraction.

Answer 1

Consider a plane wavefront AB incident on a plane surface XY, separating two media 1 and 2. Medium 1 ∞ rarer & 2 is denser medium. v₁&v₂ be the velocity of light in medium 1 and medium 2 respectively. v₂> v₁

The wave front first strikes at A and then the successive points towards C. according to Huygen’s principle from each point of AC, the secondary wavelets will start growing in the second medium with speed v₂. Let the disturbance take time t to travel from B to C, then BC=v₁t. During the time, the disturbance from B reaches the point C, the secondary wavelets from point A must have spread over a hemi-sphere of radius AD=v₂t in the second medium.

The tangent plane CD drawn from point C over this hemisphere of radius v₂t will be the new refracted wave front

Let the angles of incidence and refraction be i and r respectively,

From right angle triangle, ∆ABC, we get

This constant is called the refractive index of the second medium with respect to I.