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A crown glass prism of angle 5 is to be combined with a flint glass prism in such a way that the mean ray passes undeviated. The angle of flint glass prism is A and angular deviation produced by the combination when white light goes through it is δ. Refractive indices for red, yellow and violet light are 1.514, 1.517 and 1.523 respectively for crown glass and 1.613, 1.620 and 1.632 for flint glass. Then :

A
A=8.4
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B
A=4.2
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C
δ=0.0348
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D
δ=0.0137
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Solution

The correct option is C δ=0.0348
Given:-
A=5; μr=1.514; μy=1.517; μv=1.523
μr=1.613; μy=1.620; μv=1.632

The deviation produced by crown prism is :
δ=(μy1)A

The deviation produced by flint prism is:
δ=(μy1)A

Net deviation is given by :
D=δδ=(μy1)A(μy1)A

If the net deviation is zero :

(μy1)A(μy1)A=0

A=(μy1)(μy1)A

A=(1.5171)(1.6201)×5=4.2

Angular dispersion produced by the crown prism :

θ=δvδr=(μvμr)A

Angular dispersion produced by flint prism :

θ=δvδr=(μvμr)A

The net angular dispersion is :
δ=(μvμr)A(μvμr)A

=(1.5231.514)×5(1.6321.613)×4.2=0.0348

The magnitude of angular dispersion is 0.0348.

Hence, options (B) and (C) are the correct answers.
Why this question :
In this type of questions where two prisms are involved, put the values of the refractive index and angle of the prism carefully.

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