Question

The refracting angle of a prism is $A$. The refractive index of the prism is $\cot \frac{A}{2}$. Find angle of minimum deviation.

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

Answer 1

Answer: (C)

${180}^o-2A$

We know that

$\mu =\frac{sin\frac{A+\sin }{2}}{\sin \frac{A}{2}}$

$\mu =\cot \left(\frac{A}{2}\right)$

$\cot \left(\frac{A}{2}\right)\sin \left(\frac{A}{2}\right)=\sin \left(\frac{A+sin}{2}\right)$

$\frac{cos\left(\frac{A}{2}\right)}{sin\left(\frac{A}{2}\right)}\times \sin \left(\frac{A}{2}\right)=\sin \left(\frac{A+sin}{2}\right)$

$\cos \left(\frac{A}{2}\right)=\sin \left(\frac{A+sin}{2}\right)$

$\sin (90-\frac{A}{2})=\sin \left(\frac{A+sin}{2}\right)$

$180-A=A+\sin$

$180-2A=\sin$

Answer C: