Question

Solve Numerical example.

From the given data set, determine angular dispersion by the prism and dispersive power of its material for extreme colours. n_R = 1.62 n_V = 1.66, δ_R = 3.1°

Answer 1

Given: n_R = 1.62, n_V = 1.66, δ_R = 3.1°

To find: i. Angular dispersion (δ_VR)
ii. Dispersive power (ω_VR)

Formula: i. δ = A (n − 1)
ii. δ_VR = δ_V − δ_R
iii. ω = ${\displaystyle \frac{{\delta }_{\text{V}}-{\delta }_{\text{R}}}{\left(\frac{{\delta }_{\text{V}}+{\delta }_{\text{R}}}{2}\right)}}$

Calculation: From formula (i),
δ_R = A(n_R − 1)
∴ A = ${\displaystyle \frac{{\delta }_{\text{R}}}{({\text{n}}_{\text{R}}-1)}=\frac{3.1}{(1.62-1)}=\frac{3.1}{0.62}}$

∴ δ_V = A(n_V − 1) = 5 × (1.66 − 1) = 3.3°
From formula (ii),
δ_VR = 3.3 − 3.1 = 0.2°
From formula (iii),
ω_VR = ${\displaystyle \frac{3.3-3.1}{\left(\frac{3.3+3.1}{2}\right)}=\frac{0.2}{6.4}\times 2=\frac{0.2}{3.2}=\frac{1}{16}}$
= 0.0625

1. Angular dispersion by prism is 0.2°
2. Dispersive power of material of prism is 0.0625.