A ray of light passes from vacuum into a medium of refractive index $μ$ ,the angle of incidence is found to be twice the angle of refraction. Then the angle of incidence is

c o s^{- 1} (\frac{μ}{2})

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2 c o s^{- 1} (\frac{μ}{2})

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2 s i n^{- 1} (μ)

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2 s i n^{- 1} (\frac{μ}{2})

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Solution

The correct option is B $2 c o s^{- 1} (\frac{μ}{2})$
By using $μ = \frac{s i n i}{s i n r} \Rightarrow μ = \frac{s i n 2 r}{s i n r} = \frac{2 s i n r c o s r}{s i n r}$
$\Rightarrow r = c o s^{- 1} (\frac{μ}{2}) . S o, i = 2 r = 2 c o s^{- 1} (\frac{μ}{2})$

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The correct option is B $2 c o s^{- 1} (\frac{μ}{2})$
By using $μ = \frac{s i n i}{s i n r} \Rightarrow μ = \frac{s i n 2 r}{s i n r} = \frac{2 s i n r c o s r}{s i n r}$
$\Rightarrow r = c o s^{- 1} (\frac{μ}{2}) . S o, i = 2 r = 2 c o s^{- 1} (\frac{μ}{2})$