Question

As shown in the figure, a light ray is incident on face $AB$ of prism $ABC$ . The second prism is then arranged in such a manner that emergent ray from prism $ABC$ is falling normally on face $A^{\prime }{B}^{\prime }$ of prism $A^{\prime }{B}^{\prime }{C}^{\prime }$ . What is the net deviation produced by the optical system of the two prisms?

• A. $48^{\circ }$
• B. $112^{\circ }$
• C. $32^{\circ }$
• D. $18^{\circ }$

Answer 1

Answer: (A)

From prism 1 :
$sini=\mu sinr\Rightarrow sin53^{\circ }=\frac{4}{3}\times sinr\Rightarrow sinr=\frac{3}{4}\times \frac{4}{5}=\frac{3}{5}\Rightarrow r=37^{\circ }Totaldeviation=16^{\circ }onbothends=32^{\circ }Inprism2:\frac{{\delta }_1}{A_1}=\frac{{\delta }_2}{A_2}\Rightarrow {\delta }_2=\frac{37}{74}\times 32^{\circ }=16^{\circ }Totaldeviation={\delta }_1+{\delta }_2=32+16=48^{\circ }$