A convex lens of focal length 25 cm produces images of the same magnification 2 , when an object is kept at two positions x 1 and x 2 x 1 x 2 from the lens. The ratio of x 2 and x 1 is

Question

A convex lens of focal length 25 cm produces images of the same magnification 2 , when an object is kept at two positions x 1 and x 2 x 1 > x 2 from the lens. The ratio of x 2 and x 1 is

TestHub · Accepted Answer

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

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

$m = \frac{f}{f + u} = \frac{25}{25 + u} . . . (i)$

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

$∴$ From Eq. $(i)$ , $- 2 = \frac{25}{25 - x_{1}} \Rightarrow x_{1} = \frac{75}{2}$

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

$∴$ From Eq. $(i)$ , $2 = \frac{25}{25 - x_{2}} \Rightarrow x_{2} = \frac{25}{2}$

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

$∴ \frac{x_{2}}{x_{1}} = \frac{25 / 2}{75 / 2} = \frac{1}{3}$

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