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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 μ′r, μ′y and μ′v respectively. Find the A′A 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(μv−μrμ′v−μ′r) Total deviation suffered by the violet light by these prisms combination is, δv=δcv−δfv+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=2δcv−δfv As we know, the minimum deviation suffered is, δm=(μ−1)A ⇒ δv=2A(μv−1)−A′(μ′v−1) Similarly, the deviation suffered by the red light is, δr=2A(μr−1)−A′(μ′r−1) For net angular dispersion to be zero, δv−δr=0 ⇒2A(μv−1)−A′(μ′v−1)−[2A(μr−1)−A′(μ′r−1)]=0 ⇒2A(μv−μr)=A′(μ′v−μ′r) ⇒A′A=2(μv−μr)(μ′v−μ′r) <!--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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