question_answer

The refractive index of the material of a prism is \[\sqrt{2}\] and its refracting angle is \[{{30}^{o}}\]. 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)  \[{{45}^{o}}\]            

B)  \[{{60}^{o}}\]

C)  \[{{0}^{o}}\]               

D)  \[{{30}^{o}}\]  

Correct Answer: A

Solution :

 According to the given condition, the beam light will retrace its path after reflection from BC \[\angle CPQ={{90}^{o}}\] Thus, angle of refraction at surface AC \[\angle PQN=\angle r={{90}^{o}}-{{60}^{o}}={{30}^{o}}\] By Snells law \[\mu =\frac{\sin i}{\sin r}\] \[\Rightarrow \] \[\sqrt{2}=\frac{\sin i}{\sin {{30}^{o}}}\] \[\therefore \] \[\sqrt{2}\times \sin {{30}^{o}}=\sin i\] \[\Rightarrow \] \[\sqrt{2}\times \frac{1}{2}=\sin i\] \[\Rightarrow \] \[i={{45}^{o}}\]