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A convex lens of focal length 20cm produces images of the same magnification 2 when an object is kept at two distance $x_{1}$ and $x_{2} (x_{1} > x_{2})$ from the lens. The ratio of $x_{1}$ and $x_{2}$ is

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3:1

4 :3

5:3

2 :1

answer is D.

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Detailed Solution

Magnification $= \frac{v}{u} = \pm 2$ …(i) $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ …(ii)

From equation (i) and (ii), we get $x_{1}, x_{2}$

$\begin{aligned} x_{1} = \frac{3 f}{2}, x_{2} = \frac{f}{2} \\ \Rightarrow \frac{x_{1}}{x_{2}} = \frac{3}{1} \end{aligned}$

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