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Question

A transparent solid cylindrical rod has a refractive index of $\frac{2}{3}$ . It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle $θ$ for which the light ray grazes along the wall of the rod is -

40564

A

$sin^{- 1} (\frac{1}{2})$

B

$sin^{- 1} (\frac{3}{2})$

C

$sin^{- 1} (\frac{2}{3})$

D

$sin^{- 1} (\frac{1}{3})$ .

Hard

JEE Mains

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Solution

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Correct option is D)

$I \times sin 90 = \frac{2}{3} sin (90 - α)$
$\Rightarrow cos α = \frac{3}{2}$
So, $sin α = 1 - \frac{3}{4} = \frac{1}{2}$
Now, $1 \times sin θ = \frac{2}{3} sin α = \frac{2}{3} \times \frac{1}{2} = \frac{1}{3}$
$\Rightarrow θ = sin^{- 1} \frac{1}{3}$

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