Question

(i) Derive Snells law on the basis of Huygens wave theory when light is travelling from a denser to a rarer medium.
(ii) Draw the sketches to differentiate between plane wavefront and spherical wavefront.

Answer 1

Let the surface separating medium 1 and medium 2, as shown. Let ${\nu }_1$ and ${\nu }_2$ represent the speed of light in medium 1 and medium 2, respectively. We assume a plane wavefront AB propagating in the direction $AC$ incident on the interface at an angle $i$. Let $\tau$ be the time taken by the wavefront to travel the distance BC. Thus,

$BC=v_1\tau$

$\frac{sini}{sinr}=\frac{v_1}{v_2}$

We have $n_1=\frac{c}{v_1}$ and $n_2=\frac{c}{v_2}$

where $n_1,n_2$ are refractive indices of respective media.

Hence $n_{1}sini=n_{2}sinr$