Ray Optics and Optical Instruments - Result Question 55
57. The refracting angle of a prism is ’ $A$ ‘, and refractive index of the material of the prism is $\cot (A / 2)$. The angle of minimum deviation is :
[2015]
(a) $180^{\circ}-2 A$
(b) $90^{\circ}-A$
(c) $180^{\circ}+2 A$
(d) $180^{\circ}-3 A$
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Answer:
Correct Answer: 57. (a)
Solution:
- (a) As we know, the refractive index of the material of the prism
$ \mu=\frac{\sin (\frac{\delta_m+A}{2})}{\sin (A / 2)} $
$ \begin{aligned} & \cot A / 2=\frac{\sin (\frac{A+\delta_m}{2})}{\sin A / 2}=\frac{\cos (A / 2)}{\sin (A / 2)} \\ & {[\because \mu=\cot (A / 2)]} \end{aligned} $
$\Rightarrow \quad \sin (\frac{\delta_m+A}{2})=\sin (90^{\circ}+A / 2)$
$\Rightarrow \delta _{\text{min }}=180^{\circ}-2 A$
