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1)

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 

932021722_p5.PNG


A) 3

B) 2

C) 1

D) 0

Answer:

Option B

Explanation:

Appluing Snell's law at M and N,

  sin600=nsinr          ............(i)

    sinθ=πsin(60r)     ............(ii)

 Differentiating we get

         cosθdθdn=ncos(60r)drdn+sin(60r)

 932021355_p3.PNG

Differentiating Eq.(i),

  ncosrdrdn+sinr=0

or         drdn=sinrncosr=tanrn

                  cosθdθdn=ncos(600r)[tanrn]+sin(600r)

                dθdn=1cosθ[cos(600r)tanr+sin(600r)]

  From Eq.(i)  , r =30°  for n=3

                      dθdn=1cos60(cos30×tan30+sin30)

                         =2(12+12)=2