Question

The refracting angle of a prism is A and refractive index is $\cot(A/2)$. The angle of minimum deviation is

• A. (180??- A)
• B. (180??- 2A)
• C. (90??- A)
• D. (90??- 2A)

Answer 1

Answer: (B)

(180??- 2A)

Answer 2

Here, $u = \cot \frac{A}{2}$ According to prism formula $\mu=\frac{\sin\left(\frac{A +\delta_{m}}{2}\right)}{\sin\left(\frac{A}{2}\right)} \:\:\: \therefore \:\: \cot \frac{A}{2} =\frac{\sin\left(\frac{A+\delta_{m}}{2}\right)}{\sin\left(\frac{A}{2}\right)}$ or $\frac{\cos\left(\frac{A}{2}\right)}{\sin\left(\frac{A}{2}\right)}=\frac{\sin\left(\frac{A+\delta_{m}}{2}\right)}{\sin\left(\frac{A}{2}\right)}$ or $\cos\left(\frac{A}{2}\right) = \sin\left(\frac{A+\delta_{m}}{2}\right)$ or $\sin \left(90^\circ -\frac{A}{2}\right) = \sin\left(\frac{A+\delta_{m}}{2}\right)$ or $90^\circ - \frac{A}{2} =\frac{A+\delta_{m}}{2}$ or $180^\circ = A = A +\delta_{m}$ or $\delta_{m} = 180^\circ - 2A$