A prism `(mu_(P)=sqrt(3))` has an angle of prism `A=30^(@)`.A thin film `(mu_(f)=2.2)` is coated on face `AC` as shown in the figure.Light of wavelength `550nm` is incident on the face `AB`at`60^(@)`angle of incidence,find
(I)the angle of its emergence from the face`AC`and

(ii)the minimum thickness (in mn) of the film for which the emerging light is of maximum possible intensity.

Explanation

a. Given, `i_(1) = 60^(@), A = 30^(@), mu_("prism") = sqrt 3`
From Snell's law,
`mu_(1) sin i_(1) = (1)/(sqrt 3) xx sin 60^(@) = (1)/(sqrt 3) xx (sqrt 3 )/(2) = (1)/(2) s`
`r_(1) = 30^(@)`
Also, `r_(1)+r_(2)=A rArr r_(2)=A-r_(1)=30^(@)-30^(@)=0^(@)`
That is, the ray is incident normally on face `AC` and angle of emergence `i_(2) = 0^(@)`
(b) For maximum intensity, the thickness of coated film must satisfy the condition of maxima in transmitted light, i.e.,
`2mu t cos r=(2n-1)lamda//2`
`rArr t=((2n-1)lamda)/(4 mu cos r)`
For normal incidence, `r=0`. So, `cos r=1` and for minimum thickness, `n=1`
`:. t_(min)=(lamda)/(4 mu)=(6600 Å)/(4 xx 2.2)=750 Å`
.