The refractive index of a prism with apex angle A is cot A/2. The angle of minimum deviation is:

Question

The refractive index of a prism with apex angle A is cot $\frac{A}{2}$ . The angle of minimum deviation is:

Smart Achievers · Accepted Answer

(4)

$μ = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin \frac{A}{2}}$

$\frac{\cos \frac{A}{2}}{\sin \frac{A}{2}} = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin \frac{A}{2}}$

$\sin (\frac{π}{2} - \frac{A}{2}) = \sin (\frac{A + δ_{m}}{2})$

$\frac{π}{2} - \frac{A}{2} = \frac{A}{2} + \frac{δ_{m}}{2}$

$δ_{m} = π - 2 A$

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