Question

State the lens formula and write it mathematically.

Answer 1

To solve the problem we have to know what the lens is. We know that the lens is a transparent refracting medium bounded by either two spherical surfaces or one surface spherical and another surface plane. We know that lenses are of two kinds. One is convex or convergent and the other one is concave or divergent. We can say, A plane surface can be treated as a spherical surface of infinite radius of curvature.

Complete answer:
We know that, the equation relating the distance of object which is u, the distance of image which is v, and the focal length of a lens is called lens formula. It is the same for both concave and convex lenses. Now, the mathematical formula is,
$\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}$

Note: We can get confused between the signs of the elements. We know that, in numerical the known values are substituted with their proper sign and then the unknown quantity is obtained with its proper sign. We know that, according to the sign convention for the convex lens, u is always negative, f is always positive, v is positive for the real image and v is negative for virtual image. But for a concave lens we know that, u, v and f all are negative. And then the numerical value of u is always greater than v. from this formula we can also get to know about linear magnification. We denote this linear magnification by m.