A double convex lens is made of glass which has refractive index 1.55 for violet rays and 1.50 for red rays. If the focal length for violet rays is 20 cm, the focal length for red rays will be

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20 cm

22 cm

28 cm

9 cm

answer is D.

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Detailed Solution

$\frac{1}{f_{V}} = (μ_{V} - 1) (\frac{1}{R_{1}} + \frac{1}{R_{2}}) \to 1$

$\frac{1}{f_{R}} = (μ_{R} - 1) (\frac{1}{R_{1}} + \frac{1}{R_{2}}) \to 2$

$∴ \frac{2}{1} \to \frac{f_{R}}{f_{V}} = \frac{(μ_{V} - 1)}{(μ_{R} - 1)}$

$\frac{f_{R}}{20} = \frac{(1.55 - 1)}{(1.5 - 1)} \Rightarrow f_{R} = 22 c m$

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