Question

A real image of magnification $2$ is obtained when an object of height $h$ is placed at $x\text{cm}$ distance from a concave mirror of focal length $10\text{cm}$, then the value of $|x|$ is.

Answer 1

Given:
$|m|=2;f=10\text{cm};u=x\text{cm}$

We know that, magnification $m=\frac{-v}{u}$

For a real image, object distance $u>f$ and the image formed is inverted. So we take the magnification to be negative.

Substituting the given data,
$-2=\frac{-v}{x}\Rightarrow v=2x$

Using mirror formula,

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

we get,

$\frac{1}{2x}+\frac{1}{x}=\frac{1}{-10}\Rightarrow \frac{2+1}{2x}=\frac{-1}{10}$

$\Rightarrow \frac{3}{2x}=\frac{-1}{10}$

$\Rightarrow x=-15\text{cm}$

$\therefore |x|=15$