question_answer

A ray falls on a prism ABC W = BC) and   travels as shown in figure. The least value of refractive index of material of the prism,   should be:                    

A) \[1.5\]                                  

B) \[\sqrt{2}\]              

C) \[1.33\]                               

D) \[\sqrt{3}\]

Correct Answer: B

Solution :

\[AB=BC\] \[\therefore \]  \[\angle A=\angle C={{45}^{o}}\] MN is normal drawn at the point of incidence. By geometry \[\angle LMN=45{}^\circ \] The ray is suffering total internal reflection, \[\therefore \]  \[C=45{}^\circ \] So,          \[\mu =\frac{1}{\sin C}\]                 \[=\frac{1}{\sin {{45}^{o}}}=\frac{1}{1/\sqrt{2}}=\sqrt{2}\]