Question

You are given a prism made of crown glass and flint glass with a variety of angles. Suggest a combination of prisms which will
(a) Deviate a pencil of white light without much dispersion,
(b) Disperse (and displace) a pencil of white light without much deviation.

Answer 1

Hint: crown glass is an optical glass that has a low refractive index and also dispersion is low whereas a flint glass is an optical glass that has high refractive and dispersion is also high for this glass. Crown glass is usually used to make the convex lens and flint glass is usually used to make a concave lens.

Complete answer:
(a) To deviate a pencil of white light without much dispersion, the two prisms should be arranged so that the dispersion produced by one prism should cancel the dispersion produced by the second prism so that no dispersion should take place. Therefore, we can say that the sum of angular dispersion of the crown glass and the flint glass should be zero and is given by
$({\mu _b} - {\mu _r})A + ({\mu _b}^\prime - {\mu _r}^\prime )A' = 0$
Now, the angular dispersion for crown glass is greater than that of the flint glass, therefore
$A' < A$
Hence, the combination of a flint glass of small-angle should combine with a crown glass of large angle to deviate a pencil of white light with much dispersion.
(b) Now, to disperse a pencil of white light without much deviation, the angular dispersion of crown glass and angular deviation of flint glass should be equal and opposite, so that the deviation should be equal and opposite.
$\left( {{\mu _y} - 1} \right)A + \left( {{\mu _y}^\prime - 1} \right)A' = 0$
Now, the refractive index for flint glass ${\mu _y}^\prime $ is greater than that of the refractive index of crown glass. Therefore, the angle of flint glass should be smaller than that of the crown glass.

Note:
When the white light is incident on a prism, the light will get dispersed. Now, when this dispersed light is incident on the other prism, the components of light will recombine and therefore, the white light emerges from the combination of two prisms.
The angular dispersion of crown glass and angular deviation of flint glass should be equal and opposite.