Question

The focal length of a converging lens are f_v and f_r for violet and red light respectively.

Options

• f_v > f_r

• f_v = f_r

• f_v < f_r

• Any of the three is possible depending on the value of the average refractive index μ.

Answer 1

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:-

\[f \propto \frac{1}{\lambda^2}...........\left( \because    \lambda_r  <  \lambda_v \right)\]

∴ f_v < f_r