AB and CD are surfaces ot two slabs as shown in Figure . The medium between the slabs has refractive indes 2. Refractive indes of the slab above Ab is `sqrt(2)` and below CD is `sqrt(3)` . Find the minimum angle of incidence at Q, so that the ray is totally reflected by both the slabs.

Explanation

Let `theta` be the angle of incidence at face AB, then for total internal reflection at face AB
`sin theta gt C_(1)=(mu_(1))/(mu_(2))=(sqrt(2))/(2)`
`rArr sintheta gt (1)/(sqrt(2))` or `sintheta gt sin45^@rArr theta lt 45^@`
(i) For total internal reflection at face CD,
`sintheta gt sinC_(2)=(mu_(3))/(mu_(2))=(sqrt(3))/(2)rArrsintheta gt (sqrt(3))/(2)`
or `sintheta gt sin60^@` or `theta gt 60^@`
(ii) Therefore, the total internal reflection at both the surfaces,
` theta_(min)=60^@` .