Ncert Exercises & Solutions

Will the focal length of a lens for red light be more, same or less than that for blue light?

Hint: The focal length of the lens for a particular colour of the light depends on the wavelength of the light.

Step 1: Find the refractive index of the lens for different colours.

As the refractive index for red is less than that for blue, parallel beams of light incident on a lens will be bent more towards the axis for blue light compared to red.
In other words, $μ_{b} > μ_{r}$

Step 2: Find the focal length of the lens for different colours.
By lens maker's formula,

$\frac{1}{f} = (n_{21} - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$
Therefore, $f_{b} < f_{r}$
Thus, the focal length for blue light will be smaller than that for red.

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