Question

A convex mirror has a length of $20$ cm find the position or position of an object for which the image size is double the object size.

Answer 1

Given magnification $m=\frac{-v}{u}=2$

Thus $v=-2u$---------(A)

Given focal length $f=20cm$

Now from mirror formula we get,

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$----------(B)

Substituting the values of A in B we get,

$\frac{1}{-2u}=\frac{1}{f}-\frac{1}{u}$

$\frac{1}{-2u}-\frac{1}{-u}=\frac{1}{-20}$

$-(\frac{1}{2u}+\frac{1}{u})=-\left(\frac{1}{20}\right)$

$u=30cm$

Here v=image distance, u=object distance and f = focal length.