Question

What focal length should the reading spectacles have for a person for whom the least distance of distinct vision is 50 cm?

Answer 1

A concave lens diverges a straight light beam from the source, resulting in a reduced, upright virtual picture. It has the ability to create both real and virtual pictures. At least one inner surface of concave lenses is curved. Because it is curved round inwards at the centre and bulges outwards through the edges, causing the light to diverge, a concave lens is also known as a diverging lens. They're used to cure myopia since they make remote objects appear smaller.
$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}\;$

Complete answer:
The focal length of an optical system is the inverse of the system's optical power; it measures how strongly the system converges or diverges light. A system with a positive focus length converges light, whereas one with a negative focal length diverges light. A system with a shorter focal length bends the rays more sharply, bringing them closer to the focus or diverging them faster. The focal length of a more generic optical system has no intuitive meaning; it is just the inverse of the optical power of the system. The focal length of a narrow lens in air is the distance between the lens's centre and its primary foci (or focus points). The focal length of a converging lens (for example, a convex lens) is positive, and it is the distance at which a collimated light beam will be concentrated to a single spot. The focal length of a diverging lens (such as a concave lens) is negative, and it is the distance from which a collimated beam seems to be diverging after passing through the lens.
Now using the question
Let focal length is f
U = −50
V = −25
$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}\;$
$\dfrac{1}{f} = \dfrac{1}{{ - 25}} + \dfrac{1}{{50}}\;$
$\Rightarrow \dfrac{1}{f} = \dfrac{1}{{ - 50}}$ D.

Note:
The sign convention of focal length must be memorised carefully. The focal length of a concave lens is more difficult to determine. The focal length of such a lens is defined as the point where the spreading light beams would meet if the lens were not present. The focal length must be measured by sending light (for example, a laser beam) through the lens, measuring how much that light becomes dispersed/ bent, and tracing the beam of light backwards to the lens's focal point.