Question

A concave mirror has a radius of curvature of $ 35\, cm $ . It is positioned so that the (upright) image of an object is $ 2.5 $ times, the size of the object. How far is the mirror from the object?

• A. $ 10.5\, cm $
• B. $ 9.2 \,cm $
• C. $ 8.7 \,cm $
• D. $ 6.7\, cm $

Answer 1

Answer: (A)

Here, focal length $f=\frac{R}{2}=\frac{35}{2}=17.5$
As it is a concave mirror focal length will be negative $f=-17.5$
Now $m=-\frac{v}{u}=2.5$
$\Rightarrow v=-2.5\,u$
Using mirror formula
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
$-\frac{1}{17.5}=-\frac{1}{2.5\,u}+\frac{1}{u}$
$\Rightarrow u=-10.5\,cm$