question_answer

Find the angle of prism of that rays of light incident normally on face AB of the prism of refractive index \[\mu ,\]come out of the prism along face AC.

A)  \[{{\tan }^{-1}}\left( \frac{1}{{{\mu }^{2}}-1} \right)\]           

B)  \[{{\tan }^{-1}}({{\mu }^{2}}-1)\]

C)  \[{{\tan }^{-1}}\sqrt{{{\mu }^{2}}-1}\]         

D)  \[{{\tan }^{-1}}\left( \frac{1}{\sqrt{{{\mu }^{2}}-1}} \right)\]

Correct Answer: D

Solution :

There is no deviation at P because ray is incident perpendicular to surface AB. Now at Q, By Snell?s Law \[{{\mu }_{1}}\sin {{i}_{1}}\,={{\mu }_{2}}\sin {{i}_{2}}\] \[\mu \,\times \sin A=1\times \sin \,{{90}^{0}}\] \[\sin A=\frac{1}{\mu },\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\tan A=\frac{1}{\sqrt{{{\mu }^{2}}-1}}\] \[A={{\tan }^{-1}}\left[ \frac{1}{\sqrt{{{\mu }^{2}}-1}} \right]\]