Question

On the basis of Huygen's wave theory, prove Snell's law of refraction of light.

Answer 1

Proof of Snell's law of refraction by Huygen's wave theory:
Let speed of light in rarer medium be $v_1$ $m/s$ and in denser medium, be $v_2$ $m/s$.
So, $D{D}^{\prime }=v_{1}t$
In the same time $B{B}^{\prime }=v_{2}t$
In $\Delta BD{D}^{\prime }$ $\sin i=\frac{D{D}^{\prime }}{B{D}^{\prime }}$ ....$\left(1\right)$
In $\Delta B{B}^{\prime }{D}^{\prime }$ $\sin r=\frac{B{B}^{\prime }}{B{D}^{\prime }}$ ......$\left(2\right)$
Dividing equation $\left(1\right)$ by equation $\left(2\right)$, we get
$\frac{sini}{sinr}=\frac{\frac{D{D}^{\prime }}{B{D}^{\prime }}}{\frac{B{B}^{\prime }}{B{D}^{\prime }}}$
$\frac{sini}{sinr}=\frac{D{D}^{\prime }}{B{B}^{\prime }}$
$=\frac{v_{1}t}{v_{2}t}$
$\frac{sini}{sinr}=\frac{v_1}{v_2}{=}_1{\mu }_2$
i.e.,

${}_1{\mu }_2=\frac{sini}{sinr}$

This is called Snell law of refraction. Hence, Snell's law is verified.