Sign convention for reflection by spherical mirrors

Reflection of light by spherical mirrors follow a set of sign conventions called the New Cartesian Sign Convention. In this convention, the pole (P) of the mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis (X’X) of the coordinate system. The conventions are as follows –

The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.

All distances parallel to the principal axis are measured from the pole of the mirror.

All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along – x-axis) are taken as negative.

Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.

Distances measured perpendicular to and below the principal axis (along –y-axis) are taken as negative.

These new Cartesian sign convention for spherical mirrors are shown below in the figure

Mirror formula and magnification

Mirror formula:-

It gives the relationship between image distance (v) , object distance (u) and the focal length (f) of the mirror and is written as
\(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\)
Where
v is the distance of image from the mirror, u is the distance of object from the mirror and f is the focal length of the mirror. This formula is valid in all situations for all spherical mirrors for all positions of the object.

Magnification

agnification 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. So,
or,
\(m = \frac{{{h_1}}}{{{h_2}}}\)
The magnification m is also related to the object distance (u) and image distance (v) and is given as
\(m = \frac{{{h_1}}}{{{h_2}}} = - \frac{v}{u}\)