In an experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an an angle of 45⁰ with the x-axis meets the experimental curve at P. The coordinates of P will be:

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$(f, f)$

$(4 f, 4 f)$

$(\frac{f}{2}, \frac{f}{2})$

$(2 f, 2 f)$

answer is D.

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Detailed Solution

From U-V graph

$slope = \tan 45^{o} = \frac{V}{u} \Rightarrow v = u$

$\Rightarrow \frac{1}{f} = \frac{1}{v} - \frac{1}{u}$

$\Rightarrow \frac{1}{f} = \frac{1}{v} - \frac{1}{- v}$

$\Rightarrow v = 2 f = u$

$\Rightarrow P \equiv (2 f, 2 f)$

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