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AB and CD are two slabs, the medium between the slabs has refractive index 2. The minimum angle of incidence at Q, so that the ray is totally reflected by both the slabs is $\frac{π}{x}$ , then x is_____

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answer is 3.

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Detailed Solution

Critical angle at 1

$θ_{C_{2}} = S i n^{- 1} (\frac{μ_{3}}{μ_{2}}) = S i n^{- 1} (\frac{\sqrt{3}}{2}) = 60^{0}$

Critical angle at 2

$θ_{C_{3}} = S i n^{- 1} (\frac{μ_{3}}{μ_{2}}) = S i n^{- 1} (\frac{\sqrt{3}}{2}) = 60^{0}$

$∴ i_{\min} = 60^{0} = \frac{π}{3} [G i v e n, \frac{π}{x}]$

$x = 3$

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