Question

The refracting angle of a prism is A and the refractive index is $cot\left(\frac{A}{2}\right)$. The angle of minimum deviation is

• A. ${180}^o-A$
• B. ${180}^o-2A$
• C. ${180}^o-3A$
• D. ${180}^o-4A$

Answer 1

The correct option is B ${180}^o-2A$

We know refractive index
$\mu =\frac{sin\left(\frac{A+{\delta }_m}{2}\right)}{sin\left(\frac{A}{2}\right)}$
Given, $\mu =cot\left(\frac{A}{2}\right)$
Thus, $cot\left(\frac{A}{2}\right)=\frac{sin\left(\frac{A+{\delta }_m}{2}\right)}{sin\left(\frac{A}{2}\right)}$
or $cos\left(\frac{A}{2}\right)=sin\left(\frac{A+{\delta }_m}{2}\right)$
$sin({90}^o-\frac{A}{2})=sin\left(\frac{A+{\delta }_m}{2}\right)$
which gives $\frac{A+{\delta }_m}{2}={90}^o-\frac{A}{2}$
or ${\delta }_m={180}^o-2A$