# Linear Magnification Produced By Mirrors

## Light of Class 10

### 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

or m = 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, m = -v/u

⇒ Linear magnification, m = h'/h = - 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.

### 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, m = h'/h

m = -ve/+ve or 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, m = h'/h

m = +ve/+ve or m = +ve

• 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.

### IN CASE OF CONVEX MIRROR:

A convex mirror always forms a virtual and erect image.

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, m = h'/h

m = +ve/+ve or m = +ve

• In case of a convex mirror, which always forms virtual and erect image, the magnification is always +ve.

### FOR SPHERICAL MIRRORS IF THE:

1. Linear magnification, m > 1, the image is enlarged i.e. greater than the object
2. Linear magnification, m = 1,the image is of the same size as the object.
3. Linear magnification, m < 1.the image is diminished i.e. the image is smaller than the object.