Q.What focal length should the reading spectacles have for a person for whom the least distance of distinct vision is 50 cm? What is the nature of the lens? OR An object of size 3.0 cm is placed 14 cm in front of a concave lens of focal length 21 cm. Find the position, nature and size of image.
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Start your 14-day free trial to unlock the full solution →Using the lens formula for object at 25 cm, virtual image at the person's near point 50 cm, gives cm, a convex (converging) lens — this corrects hypermetropia (far-sightedness/long-sightedness).
A person whose least distance of distinct vision (near point) is 50 cm (rather than the normal 25 cm) suffers from hypermetropia — they cannot focus on objects held at the normal reading distance of 25 cm. Reading spectacles must take an object placed at the normal near point (25 cm, where one naturally wants to hold a book) and form a virtual, erect image of it at the person's actual near point (50 cm), where their eye CAN focus.
Taking distances as per the sign convention (object distance and virtual image distance both measured from the lens and taken negative, since both lie on the same side as the incoming light):
(object, the page, held at normal near point)
(virtual image formed at the person's own near point)
Using the thin lens formula: …
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