Question

A ray of light is incident at an angle of 60${}^{\circ }$on one of the faces of a prism which has an angle of 30${}^{\circ }$. The ray emerging out of prism makes an angle of 30${}^{\circ }$ with the incident ray. The refractive index of material is

• A. $1.1$
• B. $1.33$
• C. $1.5$
• D. $1.732$

Answer 1

The correct option is D $1.732$

$\delta ={30}^{\circ }A={30}^{\circ }$ $i_1={60}^{\circ }$

$\delta =(i_1+i_2)-A$

$30=60+i_2-30$

$\Rightarrow i_2=0$

$\Rightarrow r_2=0$

$r_1=30$

$\mu \times sin{r}_1=sini$

$\mu \times \frac{1}{2}=\frac{\sqrt{3}}{2}$

$\mu =1.732$