Write the formula for a lens connecting image distance\[\left( v \right)\] , object distance \[\left( u \right)\] , and focal length\[\left( f \right)\] . How does the lens formula differ from the mirror formula?

Hint: Convex lenses which are also known as converging lenses because the rays converge after falling on the convex lens whereas the concave lenses are known as diverging lenses as the rays diverge after falling on the concave lens. Images that are being formed by these lenses can be real or virtual depending upon their position from the lens and can have a varied size too.


Complete step by step solution:
 The image distance can be estimated with the knowledge of object distance and focal length with the help of the lens formula. In optics, the relationship between the distances of an image \[\left( v \right)\], the distance of an object \[\left( u \right)\], and the focal length \[\left( f \right)\] of the lens is given by the formula called as Lens formula. The lens formula is used for convex as well as concave lenses. These lenses have very little thickness. It is an equation that indicates the relationship between the focal length, image distance, and object distance for a spherical mirror. Lens formula is given by
$\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$
A mirror formula can be referred to as the formula which gives the relationship between the distance of object ‘\[u\] ’, the distance of image ‘\[v\] ’, and the focal length of the mirror ‘\[f\] ’. The mirror formula is used for both, plane mirrors and spherical mirrors (convex and concave mirrors). Now the mirror formula is given by,
$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$
In both the formulae, $u = $ Object distance
$v = $ Image distance
$f = $ Focal length
In mirror formulae, a positive sign exists between the reciprocals of image distance and object distance. In the Lens formula, the negative sign exists between the reciprocals of image distance and object distance.

Note:The distances are measured from the pole of the mirror. According to the conventional method, the negative sign specifies the distance measured in the direction opposite to the incident ray while the positive sign specifies the distance measured in the direction of the incident ray. The distance below the axis is negative while the distance above is positive.