question_answer

A prism \[(\mu =1.5)\] has the refracting angle of 30°. The deviation of a monochromatic ray incident normally on its one surface will be (sin 48° 36? = 0.75) [MP PMT/PET 1988]

A)            18° 36?                                     

B)            20° 30?

C)            18°

D)            22°1?

Correct Answer: A

Solution :

                   For surface \[AC\frac{1}{\mu }=\frac{\sin 30{}^\circ }{\sin e}\Rightarrow \sin e=\mu \sin 30{}^\circ \] \[\Rightarrow \] \[\sin e=1.5\times \frac{1}{2}=0.75\] \[\Rightarrow \] e = \[{{\sin }^{-1}}(0.75)={{48}^{o}}3{6}'\]                    From figure \[\delta =e-{{30}^{o}}\]            \[={{48}^{o}}\,3{6}'-{{30}^{o}}\]=\[{{18}^{o}}3{6}'\]