# Magnification

## Magnification

Magnifications of a lens is defined as the ratio of the height of image to the height of object. It is also given in terms of image distance and object distance. It is equal to the ratio of image distance to that of object distance.

$$Magnification(m)\,\,=\,\,\frac{{{h}_{i}}}{{{h}_{o}}}\,\,=\,\,-\frac{v}{u}$$.

Where,

m = Magnification,

hi = Height of Image,

h₀ = Height of Object.

If m is positive then image is erect and if m is negative then image is inverted.

The magnification of a spherical mirror in terms of focal length (f) and the distance of the object from mirror (u):

Magnification is the ratio of the size of the image to the size of the object.

$$Magnification(m)\,\,=\,\,-\frac{v}{u}$$,

Mirror formula:

$$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$$,

Where,

v = Image distance,

u = Object distance,

f = Focal length.

$$\frac{1}{v}\,=\,\frac{1}{f}-\frac{1}{u}$$,

$$v\,=\,\frac{uf}{(u-f)}$$,

$$m=\frac{v}{u}=\frac{uf}{(u-f)u}\,=\,\frac{f}{(u-f)}$$,

∴ $$Magnification(m)\,\,=\,\,\frac{f}{(u-f)}$$.