Question

A real object is placed at a distance $\frac{f}{2}$ in front of a concave mirror having focal length $f$. If object is shifted by a distance $\frac{f}{4}$ away from the mirror. Find the ratio of final magnification to initial magnification.

• A. $4$
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. $2$

Answer 1

The correct option is D $2$

Initially u$=-\frac{f}{2}$ ; $f=-f$

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

or, $\frac{1}{v}-\frac{2}{f}=-\frac{1}{f}$

or, $\frac{1}{v}=\frac{2}{f}-\frac{1}{f}$

or, $\frac{1}{v}=\frac{1}{f}$

or, $v=f$

Initial magnification is $-\frac{v}{u}=\frac{f}{\left(f/2\right)}$= 2

After displacing $u=-\frac{3f}{4};f=-f$

So, $\frac{1}{v}-\frac{4}{3f}=-\frac{1}{f}$

or, $v=3f$

Final magnification is $-\frac{v}{u}=\frac{3f}{\left(3f/4\right)}=4$

Ratio of final to initial magnification is: $\frac{4}{2}=2$