Question

# 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 μ′r=1.613; μ′y=1.620; μ′v=1.632 The deviation produced by crown prism is : δ=(μy−1)A The deviation produced by flint prism is: δ′=(μ′y−1)A′ Net deviation is given by : D=δ−δ′=(μy−1)A−(μ′y−1)A′ If the net deviation is zero : ⇒(μy−1)A−(μ′y−1)A=0′ A′=(μy−1)(μ′y−1)A ⇒A′=(1.517−1)(1.620−1)×5=4.2∘ Angular dispersion produced by the crown prism : θ=δv−δr=(μv−μr)A Angular dispersion produced by flint prism : θ′=δ′v−δ′r=(μ′v−μ′r)A′ The net angular dispersion is : δ=(μv−μr)A−(μ′v−μ′r)A′ =(1.523−1.514)×5∘−(1.632−1.613)×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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