Question

# If the angle of incidence is twice the angle of refraction in a medium of refractive index $$\mu$$, then the angle of incidence is :

A
2cos1μ2
B
2sin1μ2
C
2cos1μ
D
2sin1μ

Solution

## The correct option is B $$2\, cos ^{-1}\dfrac{\mu}{2}$$According to Snell's law,$$\mu =\dfrac {sin\, i}{sin \, r}$$Given :  $$i= 2r$$$$\mu =\dfrac {sin\,2r}{sin \, r}$$ $$\Rightarrow \mu =\dfrac {2sin \, r \, cos \, r}{sin \, r}$$$$cos^{-1} \dfrac {\mu}{2}=r = \dfrac{i}{2}$$$$\implies \ i=2\, cos ^{-1}\dfrac{\mu}{2}$$Physics

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