question_answer

What should be the minimum value of refractive index of the material of the prism for the reflections to take place as shown in the figure?                                                                                      [BHU M-2003]

A)  \[1.7\]                                 

B)  \[1.4\]

C)  \[1.2\]                                 

D)  \[2.7\]

Correct Answer: B

Solution :

                 The ray diagram is as follows                                 \[\angle A=\angle C={{45}^{\circ }}\]                 \[\therefore \]                  \[i={{45}^{\circ }}\] At both the faces \[AB\] and\[BC\]. For total internal reflections at faces, we have                                                 \[\sin \,\,i>\frac{1}{n}\] Or           \[n>\frac{1}{\sin \,\,i}>\frac{1}{\sin \,\,{{45}^{\circ }}}>\sqrt{2}\] The minimum value of \[n\] should be \[\sqrt{2}\left( =1.414 \right).\]