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A ray of light is incident at $60^{0}$ on a prism of refracting angle $30^{0}$ . The emerging ray is at angle $30^{0}$ with incident ray, the value of $μ$ of prism is

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$\frac{\sqrt{3}}{4}$

$\frac{\sqrt{3}}{2}$

$\sqrt{3}$

$2 \sqrt{3}$

answer is C.

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Detailed Solution

$δ = i + e - A \Rightarrow e = δ + A - i$

$∴ e = 30^{0} + 30^{0} - 60^{0} \Rightarrow e = 0^{0}$

$∴ r_{2} = 0^{0}$

$\Rightarrow r_{1} = A = 30^{0}$

Now , $μ_{1} \sin i = μ_{2} \sin r_{1}$

$\sin 60^{0} = μ \sin 30^{0}$

$\frac{\sqrt{3}}{2} = μ \times \frac{1}{2} \Rightarrow μ = \sqrt{3}$

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