You are given prism made of crown glass and flint glass with a wide variety of angles. Suggest a combination of prism which will
(i) deviate a pencil of white light without much dispersion.
(ii) disperse and displace a pencil of white light without much deviation.

Explanation

(a) Let
A = angle of crown glass prism
A. = angle of flint glass prism
`mu_(Y), mu_(V) and mu_(R)=` Corresponding refractive indices of crown glass for yellow, voilet and red lights `mu._(Y), mu._(V) and mu._(R)=` Corresponding refractive indices of flint glass for yellow, voilet and red lights

To produce deviation without dispersion, angular dispersion produced by the two prisms should be zero.
For crown glass prism
Mean deviation, `delta=(mu-1)A`
For flint glass prism
`delta.=(mu.-1)A.`
Angular dispersion,
`delta_(V)-delta_(R)=(mu_(V)-mu_(R))A`
`and delta._(V)-delta._(R)=(mu._(V)-mu._(R))A.`
For no dispersion
`delta_(V)-delta_(R)=delta._(V)-delta._(R)`
`therefore (mu_(V)-mu_(R))A=(mu._(V)-mu.(R))A.`
For flint glass, `(mu._(V)-mu._(R)) gt (mu_(V)-mu_(R))` as that for crown glass.
So, the crown glass prism of larger angle (A) should be combined with a flint glass of smaller angle (A.).
(b) For no deviation
`delta=delta.`
`(mu_(Y)-1)A=(mu._(Y)-1)A.`
`A.=((mu_(Y)-1))/((mu._(Y)-1))A`
This is the required condition.
To disperse the light without deviation, the angle of the flint glass prism should be increased so that deviations due to the two prisms are equal and opposite. The flint glass prism angle will still be smaller than that of crown glass because flint glass has higher refractive index than that of crown glass.