Question

# Three thin prisms are combined as shown in figure. The refractive indices of the crown glass for red, yellow and violet rays are μr, μy and μv respectively and those for the flint glass are μ′r, μ′y and μ′v respectively. Find A′A for which, there is no net deviation in the yellow light.

A
μy1μy1
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B
2(μy1)μy1
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C
3(μy1)μy1
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D
4(μy1)μy1
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Solution

## The correct option is B 2(μy−1)μ′y−1 The total deviation for the yellow ray produced by the prism combination is, δy=δcy−δfy+δcy=2δcy−δδy Where, δcv=Deviation suffered by the violet light in the crown glass prismδfv=Deviation suffered by the violet light in the flint glass prism As we know, the minimum deviation suffered is, δm=(μ−1)A ⇒δy=2(μy−1)A−(μ′y−1)A′ For net deviation in the yellow ray to be zero, δy=0 ⇒2(μy−1)A−(μ′y−1)A′=0 ∴A′A=2(μy−1)μ′y−1 <!--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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