At what distance from a concave mirror of focal length $10\text{cm}$ should an object $2\text{cm}$ long be placed in order to get an erect image $6\mathrm{cm}$ tall?

Step 1: Given parameters

The focal length of the concave mirror, $f=-10cm$

Height of the object, $h_o=2cm$

Height of the image, $h_i=6cm$

Step 2: Parameter to be calculated

We need to find the distance of the object

Step 3: Formula used

$m=\frac{h_i}{h_o}$ and $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

Step 4: Calculation

Thus, $m=3cm(erectimage)$

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

We get $v=-3u$

Using the Mirror formula,

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

$\frac{1}{\left(-3u\right)}+\frac{1}{u}=\frac{1}{f}$

Hence, $u=-6.70cm$

Therefore, the object must be placed at $-6.7cm$ concave mirror to get an image of $6\mathrm{cm}$ tall.