# A convex mirror is needed to produce an image that is nine-tenths the size of an object and...

## Question:

A convex mirror is needed to produce an image that is nine-tenths the size of an object and located {eq}21 \ cm {/eq} behind the mirror.

What focal length should be specified?

## Convex mirror:

The image formed by the convex mirror is behind the mirror that is virtual image. And the size of the image is also smaller than the object. That's why these mirrors are used for the vehicles.

Given Data

Magnification of the mirror {eq}(m) = \dfrac{9}{10} {/eq}

Distance of the image {eq}(v) = -21 \ cm {/eq}

Now, the magnification can be written as

{eq}m = \dfrac{-v}{u} \\ \dfrac{9}{10} = \dfrac{-(-21)}{u} \\ u = 23.33 \ cm {/eq}

Now, using the mirror formula

{eq}\dfrac{1}{u} + \dfrac{1}{v} = \dfrac{1}{f} \\ \dfrac{1}{23.33} + \dfrac{1}{-21} = \dfrac{1}{f} \\ f = - 210 \ cm {/eq}