Question

A ray of light falls on a prism having one silvered surface, at an incident angle of ${45}^0$ as shown in figure. After refraction and reflection it retraces the path, then the refractive index of prism material is :

(prism angle is ${30}^0$)

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

Answer 1

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

Solution :
$givenA={30}^{\circ }$
$i2=0^{\circ }$
because the refracted ray retracts its path
$r2=0^{\circ }$
$r1+r2=A$
$r1+0=A$
$r1={30}^{\circ }$
$\mu =\frac{sini1}{sinr1}$
$\mu =\frac{sin{45}^{\circ }}{sin{30}^{\circ }}$
$\mu =1.414=\sqrt{2}$