Sign Convention for Spherical Lenses
For lenses, we follow sign convention, similar to the one used for spherical mirrors. We apply the rules for signs of distances, except that all measurements are taken from the optical centre of the lens. According to the convention, the focal length of a convex lens is positive and that of a concave lens is negative. You must take care to apply appropriate signs for the values of u, v, f, object height h, and image height h'.
Lens Formula
As we have a formula for spherical mirrors, we also have a formula for spherical lenses. This formula gives the relationship between object- distance (u), image-distance (v), and the focal length (f ). The lens formula is expressed as
\(\frac{1}{v}\,-\,\frac{1}{u}\,=\,\frac{1}{f}\)
The lens formula given above is general and is valid in all situations for any spherical lens. Take proper care of the signs of different quantities, while putting numerical values for solving problems relating to lenses.
Magnification
The magnification produced by a lens, similar to that for spherical mirrors, is defined as the ratio of the height of the image and the height of the object. Magnification is represented by the letter m. If h is the height of the object and h' is the height of the image given by a lens, then the magnification produced by the lens is given by,
\(m\,=\,\frac{Height\,of\,the\,Image}{Height\,of\,the\,Object}\,=\,\frac{h'}{h}\)
Magnification produced by a lens is also related to the object-distance u, and the image-distance v.This relationship is given by
Magnification \((m)=\frac{{{h}'}}{h}\,=\,\frac{v}{u}\)