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 of violet rays is 20cm, the focal length of red rays (in cm) is ______

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answer is 22.

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Detailed Solution

$\frac{1}{f} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$\Rightarrow \frac{1}{f} = (μ - 1) (\frac{2}{R})$

For violet rays, $\frac{1}{20} = (1.55 - 1) (\frac{2}{R})$

For red rays, $\frac{1}{f_{v}} = (1.50 - 1) (\frac{2}{R})$

$\Rightarrow \frac{1}{f_{v}} = (0.5) (\frac{1}{20 \times 0.55})$

$\Rightarrow f_{v} = 22 cm$

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