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Question

Three thin prisms are combined as shown in figure. The refractive indices of the crown glass for red, yellow and violet lights are μr, μy and μv respectively and those for the flint glass are μr, μy and μv respectively. Find the AA for which, there is no net angular dispersion.


A
μvμrμvμr
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B
2(μvμrμvμr)
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C
μvμrμvμr
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D
2(μvμrμvμr)
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Solution

The correct option is B 2(μvμrμvμr)
Total deviation suffered by the violet light by these prisms combination is,

δv=δcvδfv+δcv

Where, δcv=Deviation suffered by the violet light in the crown glass prismδfv=Deviation suffered by the violet light in the flint glass prism

δv=2δcvδfv

As we know, the minimum deviation suffered is,

δm=(μ1)A

δv=2A(μv1)A(μv1)

Similarly, the deviation suffered by the red light is,

δr=2A(μr1)A(μr1)

For net angular dispersion to be zero,

δvδr=0

2A(μv1)A(μv1)[2A(μr1)A(μr1)]=0

2A(μvμr)=A(μvμr)

AA=2(μvμr)(μvμr)

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (B) is the correct answer.
Why this question ?

Note: If the second prism in the question is also made up of the crown glass instead of flint glass and if (A=A), then the combination of three prisms will behave as a single prism.


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