Question

A thin prism of crown glass (μ_r = 1.515, μ_v = 1.525) and a thin prism of flint glass (μ_r = 1.612, μ_v = 1.632) are placed in contact with each other. Their refracting angles are 5.0° each and are similarly directed. Calculate the angular dispersion produced by the combination.

Answer 1

For crown glass, we have:
Refractive index for red colour, μ_cr = 1.515
Refractive index for violet colour, μ_cv = 1.525
For flint glass, we have:
Refractive index for red colour, μ_fr = 1.612
Refractive index for violet colour,μ_fv = 1.632
Refracting angle, A = 5°
Let:
δ_c = Angle of deviation for crown glass
δ_f = Angle of deviation for flint glass
As prisms are similarly directed and placed in contact with each other, the total deviation produced $\left(\delta \right)$ is given by
δ = δ_c + δ_f
= (${\mu }_c$ – 1)A + (${\mu }_f$ – 1)A
= (${\mu }_c$ + ${\mu }_f$ – 2)A
For violet light, δ_v = (μ_cv + μ_fv – 2)A
For red light, δ_r = (μ_cr + μ_fr – 2)A
Now, we have:
Angular dispersion of the combination:
δ_v – δ_r = (μ_cv + μ_fv – 2)A – (μ_cr + μ_fr – 2)A
= (μ_cv + μ_fv – μ_cr – μ_fr) A
= (1.525 + 1.632 – 1.515 – 1.612)5
= 0.15°
So, the angular dispersion produced by the combination is 0.15°.