Question

A ray of light falls on a prism having one silvered surface, at an incident angle of 45 as shown in figure. After refraction and reflection it retraces the path, then the refractive index of prism material is (prism angle is 30) ;

• A. $\sqrt{2}$
• B. $2$
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\sqrt{2}$

$n_1=1;n_2=?;{\theta }_1={45}^0;{\theta }_2={30}^0$ (by using geometry)
we know
$n_{1}sin{\theta }_1=n_{2}sin{\theta }_2$
$n_2=\frac{sin{\theta }_1}{sin{\theta }_2}=\frac{sin{45}^0}{sin{30}^0}$
$n_2=1.414=\sqrt{2}$
hence, the refractive index of prism material is $\sqrt{2}$