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

linear magnification (m) = height of the image(h')/ height of the object(h)

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 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, m = h'/h

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