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'B' of prism A'B'C'. What is the net deviation produced by the optical system of the two prisms?

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48^o

112^o

32^o

18^o

answer is A.

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Detailed Solution

From prism 1 :

$\sin i = μ \sin r$

$\Rightarrow \sin 53^{\circ} = \frac{4}{3} \times \sin r$

$\Rightarrow \sin r = \frac{3}{4} \times \frac{4}{5} = \frac{3}{5}$

$\Rightarrow r = 37^{\circ}$

Total deviation = 16^o

on both ends = 32^o

In prism 2 :

$\frac{δ_{1}}{A_{1}} = \frac{δ_{2}}{A_{2}} \Rightarrow δ_{2} = \frac{37}{74} \times 32^{\circ}$

$= 16^{\circ}$

$Total deviation = δ_{1} + δ_{2} = 32 + 16 = 48^{o}$

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