If the red light is replaced by a blue light, which of the following…

The correct answer is Option (4) → The focal length of the lens will decrease because the refractive index of blue light is higher than that of red light.

By the lens maker’s formula, \( 1/f = (n - 1)(1/R_1 - 1/R_2) \). By dispersion, n of glass is larger for blue light than for red, so f is smaller for blue light.

Option (1) Focal length will remain the same because it does not depend on the colour of light. — Incorrect. n depends on the colour of light.

Option (2) The focal length of the lens will increase because the refractive index of the blue light is more than that of red light. — Incorrect. A larger n gives a shorter focal length.

Option (3) The focal length of the lens will decrease because the refractive index of red light is higher than that of blue light. — Incorrect. n is higher for blue light, not red.

Option (4) The focal length of the lens will decrease because the refractive index of blue light is higher than that of red light. — Correct. As shown above.

NCERT Exemplar:
Ray Optics and Optical Instruments – “… 9.17 Will the focal length of a lens for red light be more, same or less than that for blue light?”

Ray Optics and Optical Instruments – “… 9.17 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. Thus the focal length for blue light will be smaller than that for red.”