Question

The refracting angle of prism is A and refractive index of material of prism is cot $\frac{A}{2}$ The angle of minimum deviation is

• A. ${180}^{\circ }-3A$
• B. ${180}^{\circ }+2A$
• C. ${90}^{\circ }-A$
• D. ${180}^{\circ }-2A$

Answer 1

The correct option is D ${180}^{\circ }-2A$

By using $\mu =\frac{sin\frac{A+{\delta }_m}{2}}{sin\frac{A}{2}}\Rightarrow cot\frac{A}{2}=\frac{sin\frac{A+{\delta }_m}{2}}{sin\frac{A}{2}}$
$\Rightarrow \frac{cos\frac{A}{2}}{sin\frac{A}{2}}=\frac{sin\frac{A+{\delta }_m}{2}}{sin\frac{A}{2}}\Rightarrow sin({90}^{\circ }-\frac{A}{2})=sin\left(\frac{A+{\delta }_m}{2}\right)\Rightarrow {\delta }_m=180-2A$