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 (δ) is given by

δ = δ_c + δ_f

= (μ_c - 1)A + (μ_f – 1)A

= (μ_c + μ_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°.