An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 12cm .The size of the images in two situations are in the ratio 4 : 1. What is the distance between the screen and the object?

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12 cm

36 cm

18 cm

24 cm

answer is D.

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Detailed Solution

$\begin{array}{l} | m_{1} | = \frac{x_{2}}{x_{1}} \\ | m_{2} | = \frac{x_{1}}{x_{2}} \\ \frac{m_{1}}{m_{2}} = {(\frac{x_{2}}{x_{1}})}^{2} \Rightarrow {(\frac{x_{2}}{x_{1}})}^{2} = \frac{4}{1} \Rightarrow \frac{x_{2}}{x_{1}} = \frac{2}{1} \\ x_{2} - x_{1} = 12 c m \\ 2 x_{1} - x_{1} = 12 + 24 = 36 c m \end{array}$

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