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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°. |
Answer» 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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