Question

The focal length of a concave mirror is f and the distance from the object to the principal focus is x. The ratio of the size of the image to the size of the object is

• A. $\frac{f+x}{f}$
• B. $\frac{f}{x}$
• C. $\sqrt{\frac{f}{x}}$
• D. $\frac{f^2}{x^2}$

Answer 1

The correct option is B $\frac{f}{x}$

We know that
$magnification\left(m\right)=\frac{h^{\prime }}{h}=-\frac{v}{u}$
where
$h^{\prime }=heightoftheimageh=heightoftheobjectv=dis\tan ceofimagefrommirroru=dis\tan ceofobjectfrommirror$

$\Rightarrow v=\frac{h^{\prime }u}{h}$


$u=f+x\left(asshown\right)$
Using mirror equation,
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
Putting value of $v$ in mirror equation
$\frac{1}{f}=\frac{1}{\left(\frac{h^{\prime }u}{h}\right)}+\frac{1}{u}$
Multiplying whole equation by $u$
$\frac{u}{f}=\frac{h}{h^{\prime }}+1\Rightarrow \frac{h^{\prime }}{h}=\frac{f}{x}$