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