Question

The refractive indices of crown glass for blue and red lights are 1.51 and 1.49 respectively and those of the flint glass are 1.51 and 1.49 respectively. An isosceles prism of angle 6 is made of crown glass. A beam of white light is incident at a small angle on this prism. The other flint glass isosceles prism is combine with the crown glass prism such that there is no deviation of the incident light. Determine the angle of the flint glass prism. Calculate the net dispersion of the combined system.

Answer 1

For combination of prisms

net deviation = δ1 + δ2 = (ny -1)A +(n’y-1)A

where δ1 and δ2 are deviations produced by individual prisms.

Net dispersion = (nv - nR) A + (n’v –n’R) A

According to problem net deviation is zero

hence (ny -1)A = -(n’y-1)A’

A’ = - [(ny -1)A /(n’y-1)]

Negative sign implies that second prism is inverted relative to first

ny = (nv + nR)/2, n’y = (n’v –n’R)/2

A’=-[(ny -1)A /(n’y-1)]

ny = (1.51 + 1.49)/2

n’y = (1.77 + 1.73)/2 , A = 6**** on substituting numerical values of ny, n’y, A

we get A’ = -4****

Net dispersion = (nv - nR)A – (n’v - n’R)A’ = 0.04 ans.