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.

Answer 1

(c) f_v < f_r

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