A ray is incident at an angle of incidence on one surface of a prism of small angle A and emerges normally from the opposite surface. If the refractive index of the material of the prism is μ, the angle of incidence i is nearly equal to :
A
A/μ
B
A/2μ
C
μ/A
D
μA
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Solution
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Given data:
The angle of incidence =i
The angle of the prism =A
The angle of emergence =e
the refractive index of the material of the prism is μ.
For a small angle prism, angle of deviation, δ=(μ−1)A .......(i)
Since, the ray emerges normally, ∴e=0
By the relation,
A+δ=i+e
We have, i=A+δ
or δ=(i−A) .........(ii)
From Eqs. (i) and (ii)
(i−A)=(μ−1)A
⇒i=μA.
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