Question

A short linear object of length $l$ lies along the axis of a concave mirror at a distance $u$ from it. If $v$ is the distance of the image from the mirror, then the size of the image is

• A. $\left(\frac{v}{u}\right)l$
• B. ${\left(\frac{v}{u}\right)}^{2}l$
• C. $\left(\frac{u}{v}\right)l$
• D. ${\left(\frac{u}{v}\right)}^{2}l$

Answer 1

The correct option is B ${\left(\frac{v}{u}\right)}^{2}l$

Longitudinal magnification $\left(m_L\right)$ of a short object is given by,
$m_L=-m^2=\frac{-v^2}{u^2}$
Let $l_o$ and $l_i$ be the size of the object and its image respectively.
$\Rightarrow \frac{l_i}{l_o}=\frac{-v^2}{u^2}$
$\Rightarrow l_i=\left(\frac{-v^2}{u^2}\right)l_o=\left(\frac{-v^2}{u^2}\right)l$
Thus, the size of the image is ${\left(\frac{v}{u}\right)}^{2}l$