Question

On the basis of Huygens’s wave theory, prove Snell’s law of refraction of light. Draw a neat and labelled diagram. (Postulates of Huygens’s wave theory not required)

Answer 1

We focus our attention on the instant ray 1 strikes the surface and subsequent time interval. Until ray 2 strikes the surface. During this time interval, the wave at A send out a Huygens’s wavelet towards D. In the same time interval, the wave at B sends out Huygens’s wavelet towards C. Since two wavelets travel through different mediums, thus radii of the two wavelets are different.

Let radius of wavelet from A is AD = V₂Δt, where V₂ is the speed of light in second medium.

The radius of wavelet from B is BC = V₁Δt, where V₁ is the speed of light in first medium.

Now, from ΔABC and ADC, we find

Dividing the above two equations, we have