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Question

A prism of refractive index 2 has refracting angle 600. In order that a ray suffers minimum deviation it should be incident at an angle:
  1. 450
  2. 900
  3. 300
  4. none

A
300
B
none
C
450
D
900
Solution
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Given: A prism of refractive index 2 has refracting angle 60.
To find the angle of incidence in order that a ray suffers minimum deviation
Solution:
As per the given criteria,
refractive index of the prism, μ=2
Angle of the prism, A=60
For minimum angle of deviation we have angle of incidence is equal to angle of emergence, i.e., i=e
Hence, i=A+δm2, where δm is the minimum deviation angle.
We know,
μ=sin(A+δm2)sinA22=sinisin602sini=2×sin(30)sini=2×12
Multiply and divide by 2, we get
sini=12i=45
In order that a ray suffers minimum deviation it should be incident at an angle 45

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