A rectangular glass slab ABCD of refractive index n_1 is immersed in water of refractive index n_2(n_1 gt n_2) A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence a_(max) such that the ray comes out only from the other surface CD, is given by

A rectangular glass slab ABCD of refractive index n_1 is immersed in w

1.	A rectangular glass slab ABCD of refractive index n_1 is immersed in water of refractive index n_2(n_1 gt n_2) A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence a_(max) such that the ray comes out only from the other surface CD, is given by
Answer» Solution :`r_1+r_2=90^@, therefore r_1=90^@-r_2` `(r_1) _(MAX)=90^@-(r_2)_min` `and (r_2)_min= theta_c` (for total internal reflection at AD) where `sin theta_c= n_2/n_1 or theta_c= sin^-1(n_2/n_1)` `therefore (r_1)_(max)=90^@- theta_c` Now applying Snell.s LAW at FACE AB, `n_1/n_2= (sin a_max)/(sin (r_1)_max)=(sin a_(max))/(sin (90^@- theta_c))= (sin a_max)/(COS theta_c)` or `sina_max=n_1/n_2 cos theta_c` `therefore a_max= sin^-1\|n_1/n_2 cos theta_c\|= sin^-1 [n_1/n_2 cos { sin^-1 (n_2/n_1)}]`