Question

Magnification produced by a convex mirror is $\frac{1}{3}$, then distance of the object from mirror is

• A. $\frac{f}{3}$
• B. $\frac{2f}{3}$
• C. $1f$
• D. $2f$

Answer 1

The correct option is D $2f$

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$, multiply using by u

$\Rightarrow \frac{u}{f}=\frac{u}{v}-\frac{u}{u}=\frac{u}{v}-1$

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

$\Rightarrow \frac{v}{u}=\frac{f}{f+u}\Rightarrow m|\frac{-v}{u}|=\frac{f}{f+u}$

given that $m=\frac{1}{3}$

So $\frac{1}{3}=\frac{f}{f+u}\Rightarrow f+u=3f$

$\Rightarrow u=2f$