Optics 4 Question 18

19. A monochromatic beam of light is incident at 60 on one face of an equilateral prism of refractive index n and emerges from the opposite face making an

angle θ(n) with the normal (see figure). For n=3 the value of θ is 60 and dθdn=m. The value of m is

(2015 Adv.)

Analytical & Descriptive Questions

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Solution:

  1. Applying Snell’s law at M and N,

sin60=nsinrsinθ=nsin(60r)

Differentiating we get

cosθdθdn=ncos(60r)drdn+sin(60r)

Differentiating Eq. (i),

ncosrdrdn+sinr=0 or drdn=sinrncosr=tanrncosθdθdn=ncos(60r)tanrn+sin(60r)dθdn=1cosθ[cos(60r)tanr+sin(60r)]

Form Eq. (i), r=30 for n=3

dθdn=1cos60(cos30×tan30+sin30)=212+12=2



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