A rectangular slab ABCD, of refractive index `n_1` , is immersed in water of refractive index `n_2(n_1 lt n_2)`. A ray of light is incident at the surface AB of the slab as shown in Fig. Find the maximum value of angle of incidence `alpha_(max)`, such that the ray comes out only from the other surface CD.

Explanation

For a maximum angle of incidence at surface AB there will be a maximum angle of incidence at the surface AD. A ray to pass through the face CD as it should not pass beyond AD.i.e. it should not refract at AD. Hence, the angle `theta` should be the critical angle.
By Snell's law,
`sintheta = n_(2)/n_(1)`
`n_(2) sin alpha_(max)=n_(1)sin(90-theta)`
`sin alpha_(max)=n_(1)/n_(2) costheta rArr alpha_(max)=sin^(-1)[n_(1)/n_(2)cos ("sin"^(-1)n_(2)/n_(1))]`