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Question

A ray of light enters a medium of refractive index $$\mu_m$$. It is observed that the angle of refraction is half the angle of incidence. Then, the angle of incidence will be :


A
cos1μ
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B
2cos1μ2
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C
2cos1μ
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D
cos1μ3
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Solution

The correct option is B $$2\cos^{-1}\displaystyle\frac{\mu}{2}$$
From Snell's Law, $$\mu=\displaystyle\frac{\sin i}{\sin r}$$

As $$\displaystyle r=\frac{i}{2}$$

So, $$\displaystyle \mu=\frac{\sin i}{\sin \displaystyle\frac{i}{2}}=\frac{2\sin\displaystyle\frac{i}{2}\cos\frac{i}{2}}{\sin\displaystyle\frac{i}{2}}$$

$$=2\cos \displaystyle\frac{i}{2}$$

$$\Rightarrow \cos\displaystyle\frac{i}{2}=\frac{\mu}{2}$$

$$\Rightarrow \displaystyle\frac{i}{2}=\cos^{-1}\frac{\mu}{2}$$

$$\Rightarrow \displaystyle i=2\cos^{-1}\frac{\mu}{2}$$.

Physics

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