Shown in the figure is a prism of refracting angle ${30}^{\circ }$  and refractive index ${\mu }_p(=\sqrt{3}).$ The face AC of the prism is covered with a thin film of refractive index  ${\mu }_f(=2.2).A$ monochromatic light of wavelength $\lambda =550nm$ falls on the face AB at an angle of incidence of  ${60}^0$. 

The minimum value of thickness “t” of the coated film so that the intensity of the emergent ray is maximum is 

a) applying snell’s Law, we get $\sin i_1=\mu \sin r_1$

$\Rightarrow \sin \left({60}^{\circ }\right)=\sqrt{3}\sin r_1\Rightarrow \sin r_1=\frac{1}{2}\Rightarrow r_1={30}^{\circ }$

Since,  $r_1+r_2=A$

$\Rightarrow r_2=A-r_1={30}^{\circ }-{30}^{\circ }=0^{\circ }$

Therefore, ray of light falls normally one the face AC  and angle of emergence  $e=i_2=0^{\circ }$
b) Multiple reflection occurs between surfaces of film.
Intensity will be maximum if interference takes place in the transmitted wave.
For maximum thickness, we have $\Delta x=2\mu t=\lambda$
Where  t is the thickness of coated film
$\Rightarrow t=\frac{\lambda }{2\mu }=\frac{550}{2\times 2.2}=125nm$