# 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.

# 10th Physics | Light | Sign Convention for Reflection by Spherical Mirrors and Mirror Formula

## Sign Convention for Reflection by Spherical Mirrors

The new Cartesian sign convention is used for measuring the various distances in the ray-diagrams of spherical mirrors.

According to the new Cartesian sign convention (figure 1) :

(i) The pole ‘P’ of the mirror is taken as the origin and the principal axis of the mirror is taken as the x-axis of the coordinate system.

(ii) The object is always placed to the left of the mirror i.e. the light (incident rays) from the object falls on the mirror from the left hand side.

(iii) All the distances parallel to the principal axis of the spherical mirrors are measured from the pole ‘P’ of the mirror.

(iv) All the distances measured to the right of the origin (along +ve x-axis) are taken as positive.

(v) All the distances measured to the left of the origin (along –ve x-axis) are taken as negative.

(vi) The distances (heights) measured upwards (i.e. above the x-axis) and perpendicular to the principal axis of the mirror are taken as positive

(vii) the distances (heights) measured downwards (i.e. below the x-axis) and perpendicular to the principal axis of the mirror are taken as negative.

The following fig. 32 illustrates all the points of the new cartesian sign convention stated above.

Figure 1

## Mirror Formula

Let us first know about the terms used in the mirror formula of spherical mirrors.

(i) Object distance (u) : The distance of the object from the pole ‘P’ of the spherical mirror is called the object distance. It is denoted by the letter ‘u’

(ii) Image Distance (v) : The distance of the image from the pole ‘P’ of the spherical mirror is called the image distance. It is denoted by the letter ‘v’.

(iii) Focal length (f) : The distance of the principal focus (F) from the pole (P) of the spherical mirror is called the focal length. It is denoted by the letter ‘f ‘.

The relationship between the image distance (v), object distance (u) and focal length (f ) of a spherical mirror is known as the mirror formula. The Mirror formula can be written as :

$\displaystyle \frac{1}{\text{Image }\ \text{distance}}+\frac{1}{\text{object}\ \text{distance}}=\frac{1}{\text{focal}\ \text{length}}$

symbolically        $\displaystyle \frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

where the symbols have their usual meaning.