A parallel sides slab ABCD of refractive index 2 is sandwiched between two slabs of refractive indices 2 and 3 as shown in the Fig. The minimum value of angle θ (in degrees) such that the ray PQ suffers total internal reflection at both the surfaces AB and CD is

Refer to Fig.For total internal reflection at surface AB, angle θ must be greater than or equal to the critical angle i1 given bysin⁡i1=μ2μ1=22=12which gives i1=45∘For total internal reflection at surface CD, angle θ must be greater than or equal to the critical angle i2 given bysin⁡i2=μ3μ1=32which gives i2=60∘Hence, for total internal reflection at both the surfaces AB and CD, the minimum value of θ = 60°.