Question
You are given prisms made of crown glass and flint glass with a wide variety of angles. Suggest a combination of prisms which will
(i) deviate a pencil of white light without much dispersion.
(ii) disperse (and displace) a pencil of white light without much deviation.
Solution
(i) Angular dispersion produced by two prisms should be zero so that, no dispersion take place.
The sum of angular dispersion by crown glass prism and angular dispersion by flint glass prism is equal to zero.
i.e., (μb – μr)A + (μb’ – μr’)A’ = 0.
Since (μb’ – μr’) for flint glass is more than that for crown glass, therefore,
A'< A
Hence, the combination of prism is such that the, flint glass prism of smaller angle has to be suitably combined with crown glass prism of larger angle.
(ii) For almost no deviation,
(μy – 1) A’ + (μy’ – 1)A’ = 0
To disperse without deviation, we need flint glass prism of greater so that the deviation due to two prisms are equal and opposite. In the final combination however, angle of flint glass prism will be smaller than the angle of crown glass prism because the refractive index is more for flint glass as compared to the refractive index of crown glass.
The sum of angular dispersion by crown glass prism and angular dispersion by flint glass prism is equal to zero.
i.e., (μb – μr)A + (μb’ – μr’)A’ = 0.
Since (μb’ – μr’) for flint glass is more than that for crown glass, therefore,
A'< A
Hence, the combination of prism is such that the, flint glass prism of smaller angle has to be suitably combined with crown glass prism of larger angle.
(ii) For almost no deviation,
(μy – 1) A’ + (μy’ – 1)A’ = 0
To disperse without deviation, we need flint glass prism of greater so that the deviation due to two prisms are equal and opposite. In the final combination however, angle of flint glass prism will be smaller than the angle of crown glass prism because the refractive index is more for flint glass as compared to the refractive index of crown glass.
