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Refracting Telescope

The focal len...

Question

The focal length of a converging lens are f_v and f_r for violet and red light respectively.
(a) f_v > f_r
(b) f_v = f_r
(c) f_v < f_r
(d) Any of the three is possible depending on the value of the average refractive index μ.

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Solution

(c) f_v < f_r

Focal length is inversely proportional to refractive index and refractive index is inversely proportional to $λ^{2}$ . So, keeping other parameters the same, we can say:
$f \propto \frac{1}{λ^{2}} (∵ λ_{r} < λ_{v})$
∴ f_v < f_r

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