Question

If an object is placed at a distance of 20cm from the pole of a concave mirror, the magnification of its real image is 3. If the object is moved away from the mirror by 10cm, then the magnification is -1.

• A. True
• B. False

Answer 1

The correct option is A True

Now magnification is given by:

$M=\frac{-v}{u}$

And mirror formula

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

Multiply by $u$

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

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

We know $M=\frac{-v}{u}$

$\frac{1}{M}=\frac{-u}{v}$

$\frac{u}{v}=\frac{-1}{M}$

Putting in $\left(1\right)$

$\frac{-1}{M}$+$1$=$\frac{u}{f}$

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

So

$M=\frac{f}{f-u}$

Now $u=-20$

$M=\frac{f}{f-(-20)}$ and real image means M is negative

$-3=\frac{f}{f+20}$

$-3f-60=f$

$f=-15cm$

$M=\frac{-15}{-15+30}$

$M=-1$