# 10th Physics | Light | Linear Magnification Produced by Mirrors

## Linear Magnification Produced by Mirrors

The linear magnification produced by a spherical mirror (concave or convex) is defined as the ratio of the height of the image (h¢) to the height of the object (h). It is a pure ratio and has no units. It is denoted by the letter ‘m’ and is given by

$\displaystyle \text{linear}\ \text{magnification}\ (m)=\frac{\text{height}\ \text{of}\ \text{the}\ \text{image}\ \text{({h}')}}{\text{height}\ \text{of}\ \text{the}\ \text{object}\ \text{(h)}}$

or

$\displaystyle m\,\,\,\,=\,\,\,\frac{{{h}'}}{h}\,$

The linear magnification ‘m’ is also related to the object distance (u) and image distance (v). It can be expressed as :

Linear Magnification,         $\displaystyle m=-\frac{v}{u}$

Þ    Linear magnification,         $\displaystyle m\,\,\,\,=\,\,\,\frac{{{h}'}}{h}\,\,\,=\,\,\,-\,\,\frac{v}{u}$

This shows that the linear magnification produced by a mirror is also equal to the ratio of the image distance (v) to the object distance (u) with a minus sign.

### LINEAR MAGNIFICATION IN CASE OF CONCAVE MIRROR

(i) For real and inverted image: According to the New Cartesian Sign Convention, for the real and inverted images formed by a concave mirror,

object height (h) is always +ve

image height (h¢) is always –ve

\    Linear magnification, $\displaystyle m=\frac{{{h}'}}{h}$

$\displaystyle m=\frac{-ve}{+ve}$     or $\displaystyle m=-ve.$

(ii) For virtual and Erect image : According to the new Cartesian sign convention, for the virtual and erect images formed by a concave mirror,

object height (h) is always +ve

image height (h¢) is always +ve.

\    Linear magnification, $\displaystyle m=\frac{{{h}'}}{h}$

$\displaystyle m=\frac{+ve}{+ve}$ or $\displaystyle m=+ve.$

Note: In case of a concave mirror, for the real and inverted images the magnification is always –ve. and for the virtual and erect images the magnification is always +ve.

### LINEAR MAGNIFICATION IN CASE OF CONVEX MIRROR

A convex mirror always forms a virtual and erect image.

(i) For virtual and erect image : According to the New Cartesian Sign Convention, for the virtual and erect images formed by a convex mirror,

Object height (h) is always +ve

Image height (h¢) is always +ve

\    Linear magnification,     $\displaystyle m=\frac{{{h}'}}{h}$

or    $\displaystyle m=\frac{+ve}{+ve}$

or    $\displaystyle m=+ve.$

Note: In case of a convex mirror, which always form virtual and erect images, the magnification is always +ve.

### FOR SPHERICAL MIRRORS IF THE

(i)     Linear magnification, m > 1

the image is enlarged i.e. greater than the object

(ii)    Linear magnification, m = 1

the image is of the same size as the object.

(iii)    Linear magnification, m < 1

The image is diminished i.e. the image is smaller than the object.