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Question

AB and CD are surfaces of two slabs as shown in Fig. The medium between the slabs has refractive index 2. Refractive index of the slab above AB is 2 and below CD is 3. The minimum angle of incidence at Q is (x×12) in degree, so that the ray is totally reflected by both the slabs. The value of x is:
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Solution
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Let θ be the angle of incidence at face AB, then for total internal reflection at face AB.
sinθ>C1=μ1μ2=22
sinθ>12 or sinθ>sin45oθ>45o
For total internal reflection at face CD,
sinθ>sinC2=μ3μ2=32sinθ>32
or sinθ>sin60 or θ>60o
Therefore, for total internal reflection at both the surfaces,
θmin=60o.

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