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**Mirror Equation**:

The object distance in a spherical mirror is the distance between the object and its pole (\(u\)).

The image distance is the distance between the image and the mirror's pole (\(v\)).

As you already know, the focal length (\(f\)) is the distance between the principal focus and the pole.

The mirror formula, which is expressed as shows a relationship between these three quantities.

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

This formula holds true in all situations for all spherical mirrors and all object positions.

You must use the New Cartesian Sign Convention when substituting numerical values for \(u\), \(v\), \(f\) and \(R\) in the mirror formula.

Linear Magnification (\(m\)):

Magnification produced by a spherical mirror gives the relative extent to which the image of an object is magnified with respect to the object's size. It is expressed as the ratio of the height of the image (${h}^{\prime}$) to the height of the object (${h}_{o}$). It is usually represented by the letter \(m\).

It is expressed as,

$m=\frac{{h}^{\prime}}{{h}_{o}}$

The magnification can be related to object distance (\(u\)) and the image distance (\(v\)).

$m=-\frac{v}{u}$

(or)

$m=\frac{{h}^{\prime}}{{h}_{o}}=-\frac{v}{u}$

Important!

The presence of a negative sign in the magnification value indicates that the image is real.

The presence of a positive sign in the magnification value indicates that the image is virtual.

\(m>1\) \(-\) The image formed is enlarged.

\(m<1\) \(-\) The image formed is diminished.