If the least distance of distinct vision for a person is 50 cm, what…

The correct answer is Option (4) → \( +50\,\mathrm{cm} \)

The person's near point is 50 cm instead of the normal 25 cm, so he has hypermetropia. Reading spectacles must take a book held at the normal near point, 25 cm, and form its virtual image at 50 cm, where he can see it. This needs a converging lens.

Using the lens formula with the sign convention (distances measured from the lens, on the object side negative):

    \( u = -25\,\mathrm{cm} \)
    \( v = -50\,\mathrm{cm} \)

    \( \displaystyle \frac{1}{f} = \frac{1}{v} - \frac{1}{u} = -\frac{1}{50} + \frac{1}{25} = \frac{1}{50} \)

    \( f = +50\,\mathrm{cm} \)

Note: A similar question was also asked in CUET (UG) 2023 on 09-06-2023 (Slot 3).

Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.

NCERT (Pre-rationalised edition, 2022-23):
The Eye – “… Example 9.10 What focal length should the reading spectacles have for a person for whom the least distance of distinct vision is 50 cm? Solution The distance of normal vision is 25 cm. So if a book is at u = –25 cm, its image should be formed at v = –50 cm. Therefore, the desired focal length is given by

    \( \displaystyle \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \quad \text{or} \quad \frac{1}{f} = \frac{1}{-50} - \frac{1}{-25} = \frac{1}{50} \)

or f = + 50 cm (convex lens).”