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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
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B
2sin1μ2
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C
2cos1μ
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D
2sin1μ
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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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