Question

The refractive index of the material of a prism is $\sqrt{2}$ and its angle is $30^{\circ }.$ One of the refracting surfaces of the prism is made a mirror inwards. A beam of monochromatic light entering the prism from the other face will retrace its path after reflection from the mirrored surface if its angle of incidence on the prism is

• A. $60^{\circ }$
• B. $0^{\circ }$
• C. $30^{\circ }$
• D. $45^{\circ }$

Answer 1

Answer: (D)

If the ray retraces its path, means the light ray hits the mirrored surface normally.
$\Rightarrow r_2=0$
$A=r_1+r_2$
$\Rightarrow 30^{\circ }=r_1+0$
$\frac{\sin i}{\sin r_1}=\mu$ or $\frac{\sin i}{\sin 30^{\circ }}=\sqrt{2}$
$\Rightarrow \sin i=\frac{1}{\sqrt{2}}$ or $i=45^{\circ }$