The refractive indices of the material of the prism for red and yellow colour are 1.620 and 1.635 respectively. Calculate the angular dispersion and dispersive power, if refracting angle is 8°.
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Given: nR = 1.620, nY = 1.635, A = 8°
To find:
i. Angular dispersion (δV – δR)
ii. Dispersive power (ω)
Formulae:
i. δv – δr = A(nV – nR)
ii. ω = \(\frac{n_V-n_R}{n_Y-1}\)
Calculation: Since, nY = \(\frac{n_V+n_R}{2}\)
∴ nV = 2nY – nR
nV = 2 × 1.635 – 1.620 = 3.27 – 1.620
∴ nV = 1.65
From formula (i),
δV – δR = 8(1.65 – 1.620)
= 8 × 0.03 = 0.24°
∴ δV – δR = 0.24°
From formula (ii),
ω = \(\frac{1.65-1.620}{1.635-1}=\frac{0.03}{0.635}\) = 0.0472
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