question_answer

What should be the minimum value of refractive index of the material of the prism for the reflection to take place as shown in the figure?

A)  1.7                  

B)  1.4

C)  1.2                    

D)  2.7

Correct Answer: A

Solution :

 The ray diagram is as follow \[\angle A=\angle C={{45}^{o}}\] \[i={{45}^{o}}\] At both the faces AB and BC. For total internal reflection at three faces. \[\sin \,i>\frac{1}{n}\] \[n>\frac{l}{\sin \,i}\Rightarrow \frac{l}{\sin {{45}^{o}}}>\sqrt{2}\] \[n=1.1717\]