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Question

A monochromatic beam of light is incident at 60o 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. For n=3 the value of θ is 60o and dθdn=m. The value of m is
351923.png

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Solution

From the geometry we have r1+r2=60o
Using Snells law at the left side we have sin60osinr1=n
or
sinr1=32n
Using Snells law at the right end
sinr2sinθ=1n
or
sinθ=nsinr2
=nxin(60or1)
=n(32cosr112sinr1)
or
=n(321sin2r112sinr1)
or
=n(32134n21232n)
Solving we get
sinθ=344n2334
Differentiating
cosθdθ=34×124n23×8ndn
or
dθdn=3n4n23×1cosθ
=3×34×33×11/2
=2
324597_351923_ans.png

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