First slide

Ray optics

Question

When a parallel beam of white light passes through a convex lens, red, yellow and violet colours are focussed at 20.5 cm, 20 cm and 19.5 cm respectively. Then dispersive power of material of the lens is

Moderate

A

0.195
B

0.200
C

0.205
D

none of these

Solution

(4)
$\begin{array}{l} \frac{1}{f} = (μ - 1) (\frac{1}{R_{1} + R_{2}}) \Rightarrow μ = 1 + \frac{k}{f} w h e r e k = \frac{R_{1} R_{2}}{R_{1} + R_{2}} \\ ∴ μ_{r} = 1 + \frac{k}{20.5}, μ_{v} = 1 + \frac{k}{19.5} a n d μ_{Y} = 1 + \frac{k}{20} \\ ∴ ω = \frac{μ_{v} - μ_{r}}{μ_{Y - 1}} = \frac{\frac{k}{19.5} - \frac{k}{20.5}}{k / 20} = \frac{20 \times 1}{19.5 \times 20.5} = 0.05 \end{array}$

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