Question

A concave mirror has a radius of curvature of $20\, cm$. The image of a object formed in mirror is $2.50$ times the size of the object. How far is the mirror from the object?

• A. $5.5\, cm$
• B. $40 \,cm$
• C. $6\, cm$
• D. $10 \,cm$

Answer 1

Answer: (A)

For spherical mirror, $f=\frac{R}{2}$
here, $ R=20 \, cm , m=2.5$
$\therefore f=\frac{R}{2}=\frac{20}{2}=10 \, cm$
Now, $ \frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
and magnification $m=\frac{-v}{u}$ or $v=-m u$
$\therefore \frac{1}{f}=\frac{1}{u}-\frac{1}{m u}$
$ \Rightarrow u=f\left(1-\frac{1}{m}\right)$
$=10\left(1-\frac{1}{2.5}\right)=6 \,cm$