Monochramatic light is incident on the pane interface AB between two media of refractive indices `mu_1` and `mu_2(mu_2gtmu_1)` at an angle of incidence theta as shown in figure. The angle theta is infinitesimally greater thannte critical angle for the two media so thast total internal reflection takes place. Now, if a transparent slab DEFG of uniform thickness and of refractive inde `mu_2` is introduced on theinterface (as shown in figure ) , show that for any value of `mu_2` all light will ultimately be reflected back into medium II.

Explanation

We shall use the symbol to mean infinitesimaly greater than. ltbr. When the slab is not inserted `theta bargt theta_c=sin^-1(mu_1/mu_2)`
or `sintheta bargt mu_1/mu_2`.
When the slab is inserted. We have two cases `mu_3lemu_1 and mu_2gtmu_1`.
Case I: mu_2lemu_1`
We have find sintheta bargtmu_1/mu_2bargtmu_3/mu_2`
thus, the light is incident on AB at an angle greater than the criticle angle `sin^-1(mu_3/mu_2). It suffers total interN/Al relfection and goes back to medium II.
Case I `mu_3gtmu_1`
`sintheta bargt mu_1/mu_2ltmu_3/mu_2`
Thus the angel of incidence theta may be smaller than the critical angle `sin^-1 (mu_3/mu_2)` and hence it may enter medium III. The angle of refraction theta is given by ure.
`(sintheta)/(sintheta')=mu_3/mu_2`.............i
`or sintheta'=mu_2/mu_3sintheta`
`bargtmu_2/mu_3.mu_1/mu_2`
Thus sintheta bargtmu_1/mu_3`