Question

Write the Lens Makers’ Formula and explain the terms in it.

Answer 1

Hint : The lens maker’s formula states that the focal length of a lens depends upon the refractive index of the material of the lens and the radii of curvatures of the two surfaces. It is used by lens manufacturers to make the lenses of particular power from the glass of a given refractive index.

Formula Used: The formulae used in the solution are given here-
 $ \dfrac{1}{f} = \left( {n - 1} \right)\left( {\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}}} \right) $ .
where is the focal length of the mirror, is the refractive index, is the radius of curvature of the lens surface closer to the light source, is the radius of curvature of the lens surface farther from the light source.

Complete step by step answer
Lenses have two faces and allow light to pass through either face, no matter from which direction the light comes from.
Lens maker’s formula is the relation between the focal length of a lens to the refractive index of its material and the radii of curvature of its two surfaces. Lens maker formula is used to construct a lens with the specified focal length. A lens has two curved surfaces, but these are not exactly the same. If we know the refractive index and the radius of the curvature of both the surface, then we can determine the focal length of the lens by using the given lens maker’s formula:
 $ \dfrac{1}{f} = \left( {n - 1} \right)\left( {\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}}} \right) $ where $ f $ is the focal length of the mirror, $ n $ is the refractive index, $ {R_1} $ is the radius of curvature of the lens surface closer to the light source, $ {R_2} $ is the radius of curvature of the lens surface farther from the light source.
Here, $ n = \dfrac{{{n_2}}}{{{n_1}}} $ where the refractive indices of the surrounding medium and the lens material be $ {n_1} $ and $ {n_2} $ respectively.
The terms in the Lens Makers’ formula have been explained below:
The refractive index of a lens, represented by $ n $ is the relative measure, i.e. is the ratio of velocities of light in two mediums. It is dependent upon the relative refractive index of the surrounding medium where it is measured.
A lens is constructed by two spherical surfaces with different centres, thus they are part of different spheres with different radii. Thus the radius of curvature of each spherical surface is represented by $ {R_1} $ and $ {R_2} $ .
Focal point, F of the lens is a point at which parallel light rays incident on the lens converge. There are two focal points on either side of the lens. The distance from the centre of the lens (C) to the focal point (F) is the focal length (represented by f).

Note
 It is to be remembered that,
 $ \dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f} $ where $ f $ is the focal length, $ v $ is the image distance and $ u $ is the object distance.
This is another relation by which focal length could be found out.