Optics 4 Question 1

1. A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is 3, then the angle of incidence is

(2019 Main, 11 Jan II)

(a) 45

(b) 90

(c) 60

(d) 30

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Solution:

  1. Given, refractive index of material of prism n=3, prism angle A=60

Method 1

Using prism formula,

n=sinA+δ2sinA2sin60+δ2=32sin60+δ2=sin6060+δ2=60

or angle of minimum deviation δ=60

Incident angle, i=60+δ2=60

Method 2 For minimum deviation, ray should pass symmetrically (i.e. parallel to the base of the equilateral prism) From geometry of given figure, we have, r=30

Using Snell’s law,

n=sinisinrsini=nsinr=3sin30sini=32 or i=60



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