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
B
2cos1μ2
C
2cos1μ
D
cos1μ3

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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