A convex lens of focal length 25 cm produces images of the same...

For the given convex lens, focal length, $f = 25cm$

Magnification of lens in terms of $u$ and $f$ is given by,

$m = \dfrac{f}{f + u} = \dfrac{25}{25 + u}... \left(i\right)$

When the image is real, then $m = - 2$ and $u = - {x}_{1}$

$∴$ From Eq. $( i )$, $- 2 = \dfrac{25}{25 - {x}_{1}}$⇒ {x}_{1} = $\dfrac{75}{2}$

Again, when the image is virtual, then $m = 2$ and $u = - {x}_{2}$

$∴$ From Eq. $( i )$, $2 = \dfrac{25}{25 - {x}_{2}}$⇒ {x}_{2} = $\dfrac{25}{2}$

Hence, the ratio of ${x}_{2}$ and ${x}_{1}$ is

$∴ \dfrac{x2}{x1} = \dfrac{25 / 2}{75 / 2} = \dfrac{1}{3}$