question_answer

A ray of light is incident normally on one of the faces of a prism of apex angle \[30{}^\circ \]and refractive index \[\sqrt{2}\]The angle of deviation of the ray is

A) \[0{}^\circ \]   

B) \[12.5{}^\circ \]

C) \[15{}^\circ \]              

D) \[22.5{}^\circ \]

Correct Answer: C

Solution :

[c]: For normal incidence, \[i={{0}^{o}},{{r}_{1}}={{0}^{o}}\] As\[{{r}_{1}}+{{r}_{2}}=A\] \[\therefore \]\[{{r}_{2}}=A-{{r}_{1}}={{30}^{o}}\] As\[\mu =\frac{\sin e}{\sin {{r}_{2}}}\] \[\therefore \]\[\sin e=\mu \sin {{r}_{2}}\] \[=\sqrt{2}\sin {{30}^{o}}=\frac{1}{\sqrt{2}}\]            \[E={{45}^{o}}\] \[\delta =i+e-A={{0}^{o}}+{{45}^{o}}-{{30}^{o}}={{15}^{o}}\].