Question

Answer the following question in detail.

Obtain angular dispersion expression for a thin prism. Relate it with the refractive indices of the material of the prism for corresponding colours.

Answer 1

1. For any two-component colours, angular dispersion is given by,
   δ₂₁ = δ₂ − δ₁
2. For white light, we consider two extreme colours viz., red and violet.
   ∴ δ_VR = δ_V − δ_R
3. For thin prism,
   δ = A(n −1)
   ∴ δ₂₁ = δ₂ − δ₁
   = A(n₂ − 1) − A(n₁ − 1) = A(n₂ − n₁)
   where n₁ and n₂ are refractive indices for the two colours.
4. For white light,
   δ_VR = δ_V − δ_R
   = A(n_V − 1) − A(n_R − 1) = A(n_V − n_R).