The refractive indices of the material of the prism for red and yellow colour are 1.620 and 1.635 respectively.
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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