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If the focal lengths of a lens for red and violet light rays are f_R and f_V respectively, then which of the following is the true relationship?

Asked in GUJCET 2016 · Dispersion and scattering

Answer: (2) f_R>f_V

Step-by-step solution

Idea: a lens is a piece of a dispersive material, and its focal length follows the refractive index through 1/f=(n-1)(1/(R₁)-1/(R₂)).

In any normal dispersive medium violet light has the larger index: n_V>n_R.

A larger n makes (n-1) larger, so 1/f is larger and f is smaller.

Therefore f_V<f_R, which is the same statement as f_R>f_V.

This colour-by-colour difference in focal length is chromatic aberration, the coloured fringe seen at the edge of an image formed by a single lens.

Why the other options are wrong

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