A prism is made up of material of refractive index $\sqrt{3}$. The angle of the prism is $Ã…$. If the angle…

A prism is made up of material of refractive index $\sqrt{3}$. The angle of the prism is $Ã…$. If the angle of minimum deviation is equal to the angle of the prism, then the value of $A$ is:
  1. $30^{\circ}$
  2. $45^{\circ}$
  3. $60^{\circ}$
  4. $75^{\circ}$

Solution

$\begin{aligned} & \mu=\sqrt{3}, \delta_m=A \\ & \text { For prism } \mu=\frac{\sin \frac{A+\delta_m}{2}}{\sin \frac{A}{2}} \\ & \sqrt{3}=\frac{\sin \frac{A+A}{2}}{\sin \frac{A}{2}} \\ & \sqrt{3}=\frac{\sin A}{\sin \frac{A}{2}} \Rightarrow \sqrt{3}=\frac{2 \sin \frac{A}{2} \cos \frac{A}{2}}{\sin \frac{A}{2}} \\ & \cos \frac{A}{2}=\frac{\sqrt{3}}{2} \\ & \Rightarrow \quad \cos \frac{A}{2}=\cos 30^{\circ} \\ & \therefore \quad \frac{A}{2}=30^{\circ} \Rightarrow A=60^{\circ} \\ & \end{aligned}$

Asked in: AP EAMCET 2002

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