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The refractive index of prism is $$\mu = \sqrt{3}$$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _______.
Correct Answer: 60
For minimum deviation: $$\mu = \frac{\sin\frac{A+\delta_m}{2}}{\sin\frac{A}{2}}$$. Given $$\delta_m = A$$:
$$\sqrt{3} = \frac{\sin A}{\sin(A/2)} = \frac{2\sin(A/2)\cos(A/2)}{\sin(A/2)} = 2\cos(A/2)$$.
$$\cos(A/2) = \frac{\sqrt{3}}{2} \Rightarrow A/2 = 30° \Rightarrow A = 60°$$.
The answer is 60.
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