Question

The refractive index of the material of a prism is $\sqrt{2}$ and its refracting angle is ${30}^0$. 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. ${60}^o$
• B. $0^o$
• C. ${30}^o$
• D. ${45}^o$

Answer 1

Answer: (D)

${45}^o$

According to question from Snell's law,

$1.\sin i=\mu \sin {30}^o\Rightarrow \sin i=\sqrt{2}\times \frac{1}{2}=\frac{1}{\sqrt{2}}$

$\Rightarrow i={45}^o$