# Define the Mirror formula,and then prove m=f/f-u

## Question:

Define the Mirror formula,and then prove m=f/f-u

## Mirror

A mirror is reflecting surface such that one side of it is polished, and another side of the mirror reflects the maximum light falling on it. The mirrors are of three types

1. Concave Mirror
2. Convex Mirror
3. Plane Mirror.

The mirror formula is a mathematical relation between the focal length f of the mirror, distance u of the object from the mirror and distance v of the image from the mirror

{eq}\begin{align} \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \end{align} {/eq}........................................(1)

We know that magnification m of a mirror is given by

{eq}\begin{align} m =- \frac{v}{u} \end{align} {/eq}

Now multiplying equation 1 by u

{eq}\begin{align} \frac{u}{f} = \frac{u}{u} + \frac{u}{v} \end{align} {/eq}

{eq}\begin{align} \frac{u}{v}= \frac{u}{f} - 1 \end{align} {/eq}

{eq}\begin{align} \frac{u}{v}= \frac{u-f}{f} \end{align} {/eq}

{eq}\begin{align} \frac{v}{u}= \frac{f}{u-f} \end{align} {/eq}

Now magnification is

{eq}\begin{align} m =- \frac{v}{u} = \frac{-f}{u-f} \end{align} {/eq}

{eq}\begin{align} \color{blue}{\boxed{m = \frac{f}{f-u} }} \end{align} {/eq} 