Given,
ω=0.03 ; ω′=0.05
μy=1.517 ; μ′y=1.621
Where,
ω ,ω′=Dispersive powers of crown and flint prisms respectively
μy ,μ′y=R.I. of the yellow light for crown and flint prisms respectively
Let, the angle of the crown and flint prism needed is
A and
A′ respectively.
Dispersive power is,
ω=μv−μrμy−1
μv−μr=(μy−1)ω
The angular dispersion produced by the crown prism is,
(μv−μr)A=(μy−1)ωA
Similarly, the angular dispersion produced by the flint prism is,
(μ′v−μ′r)A′=(μ′y−1)ω′A′
For achromatic combination, the net dispersion should be zero. Thus,
(μy−1)ωA=(μ′y−1)ω′A′
A′A=(μy−1)ω(μ′y−1)ω′=0.517×0.030.621×0.05
A′A=0.5 .......(1)
The deviation in the yellow ray produced by the crown prism is,
δ=(μy−1)A
And by the flint prism is,
δ′=(μ′y−1)A′
The net deviation produced by the combination is,
δ−δ′=(μy−1)A−(μ′y−1)A′
1∘=0.517A−0.621A′ ......(2)
Solving
(1) and
(2) we get,
A=4.8∘ and
A′=2.4∘
Thus, the crown prism should have its refracting angle
4.8∘ and that of the flint prism should be
2.4∘.
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Hence,
(D) is the correct answer.
Why this question ?
Note: Achromatic combination means that colours of the white light are not separated by the combination of prisms. Therefore, achromatic combination refers to the deviation without dispersion. |