Page 148 - NCERT Science Class 10 English Medium

The New Cartesian Sign Convention described above is illustrated in
Fig.9.9 for your reference. These sign conventions are applied to obtain
the mirror formula and solve related numerical problems.

9.2.4 Mirror Formula and Magnification

In a spherical mirror, the distance of the
object from its pole is called the object
distance (u). The distance of the image from
the pole of the mirror is called the image
distance (v). You already know that the
distance of the principal focus from the pole
is called the focal length (f). There is a
relationship between these three quantities
given by the mirror formula which is
expressed as
1 1 1
+ = (9.1)
v u f
This formula is valid in all situations for all
spherical mirrors for all positions of the
Figure
Figure 9.9
Figure 9.99.9
Figure
9.9
object. You must use the New Cartesian Sign Figure 9.9
The New Cartesian Sign Convention for spherical mirrors
Convention while substituting numerical
values for u, v, f, and R in the mirror formula
for solving problems.
Magnification
Magnification produced by a spherical mirror gives the relative extent to
which the image of an object is magnified with respect to the object size.
It is expressed as the ratio of the height of the image to the height of the
object. It is usually represented by the letter m.
If h is the height of the object and h′ is the height of the image, then
the magnification m produced by a spherical mirror is given by
h
Height of the image ( ′ )
m =
h
Height of the object ( )
h ′
m = (9.2)
h
The magnification m is also related to the object distance (u) and
image distance (v). It can be expressed as:
′ h v
Magnification (m) = = − (9.3)
h u
You may note that the height of the object is taken to be positive as
the object is usually placed above the principal axis. The height of the
image should be taken as positive for virtual images. However, it is to be
taken as negative for real images. A negative sign in the value of the
magnification indicates that the image is real. A positive sign in the value
of the magnification indicates that the image is virtual.

Light – Reflection and Refraction 143

2024-25