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# AB and CD are two slabs. The medium between the slabs has refractive index 2. Find the minimum angle of incidence (in degrees) at Q so that the ray is totally reflected by both the slabs.

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#### Let the minimum angle be αFor first surface to completely reflect, 2Sinα⩾√2Sin90 => sinα⩾1/√2 =>α⩾45∘For second surface to completely reflect, 2Sinα⩾√3Sin90 => sinα⩾√3/2=> $\alpha \geqslant 60^\circ$So $\alpha \geqslant 60^\circ$ satisfies both conditionAnswer. Minimum angle of incidence so as to totally reflect from both surface is α=60∘

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