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.

Answer

A, B

Explanation

(a) Using Snell's law at surface AB
`mu_(air)sin60^circ=mu_(p)sinrimplies(sqrt3)/(2)=sqrt3sinrimpliesr30^circ`
Now, `NN^(`)` is the normal to surface AB.
`:'``angleAMN=90^circ`
But `angle QMN=30^circimpliesangleAMQ=60^circ`
In `triangleAMQ`
``angleAQM=180^circ-(60^circ+30^circ)=90^circ`
The refracted ray inside the prism hits the other face `90^circ`, hence deviation produced by this face is zero andhence angle of emergence is zero.
(b) Multiple reflections occur in the film for minimum thickness.
The intensity of emergent ray will be maximum if transmitted waves undergo constructive interference. `:'` For minimum thickness,
`trianglex=lamda`
`impliesx=2mut=lamda`,
Where `t=thickness `implies``t=(lamda)/(2mu)=125nm`