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

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Solution

Q.
The refractive index of a prism with apex angle A is cot A/2. The angle of minimum deviation is [2024]

1 $δ_{m} = 180^{o} - 4 A$

2 $δ_{m} = 180^{o} - 3 A$

3 $δ_{m} = 180^{o} - 2 A$

4 $δ_{m} = 180^{o} - A$

Ans.
(3)

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

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

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

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

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