Question

A ray incident at a point at an angle of incidence $60$${}^{\circ }$ enters a glass sphere of $\mu =\sqrt{3}$ and is reflected and refracted at the further surface of the sphere. The angle between the reflected and refracted rays at this surface is :

• A. $50$ ${}^{\circ }$
• B. $90$${}^{\circ }$
• C. $60$${}^{\circ }$
• D. $40$${}^{\circ }$

Answer 1

Answer: (B)

Using Snell's Law at point $P$ we get:-

$\frac{sin{60}^o}{sin{r}_1}=\sqrt{3}$

$sin{r}_1=\frac{1}{2}⟹r_1={30}^o$

As we know that $r_1=r_2⟹r_2={30}^o$

Using Snell's Law at point $Q$ we get:-

$\frac{sin{30}^o}{sin{i}_2}=\frac{1}{\sqrt{3}}⟹i_2={60}^o$

Since reflection at point $Q$ occurs

$⟹r_2^{\prime }=r_2={60}^o$

Let angle between the refracted ray and reflected ray be $\alpha$

$\alpha ={180}^o-(r_2^{\prime }+r_2)={90}^o$

Hence option $\left(B\right)$ is correct.