Calculate the information about the lenses available in an optical shop. Find out how the focal length of a lens may be determined by the given power of the lens.

Hint: An optical lens can be defined as a transparent optical device used to converge or diverge light rays emanating from an object. The refracted light rays then form a real or virtual image of the object. Lenses are a good example of optical components that pass or transmit light. Lenses are available in a variety of shapes including biconvex, biconcave, Plano-convex, Plano-concave, as well as those having a positive meniscus and negative meniscus.

Complete solution:
Lenses can be broadly classified as: positive (or converging) and negative (or diverging) lenses. Converging lenses converge or focus a collimated beam of light to a point behind the lens, with the assumption that the beam travels parallel to the lens axis and passes through the lens. Diverging lenses, on the other hand, cause a collimated light beam to diverge and spread behind the lens. The two types of concave lenses — biconcave and Plano-concave — are negative. Meniscus lenses form a third type broadly referred to as convex-concave lenses and can be either positive or negative, depending on the radius of curvature of the sides of the lens. The power of a given lens is the reciprocal of its focal length expressed in metres. Therefore, if we have to calculate the focal length from the given power of a lens, all we need to do is take its reciprocal, that \[{\text{focal length(in metres) = }}\dfrac{1}{{{\text{power of the lens(in dioptres)}}}}\]

Note: We must know that the interconversion between power and focal length can be done only after we’ve converted the given power in dioptres or the focal length of the given lens in metres. People suffering from astigmatism have trouble because they cannot focus correctly on the objects in all directions. They are advised to use bifocal lenses, also available in optical shops.