A student obtained a sharp image of the grill of a window on a screen, using a convex lens. For getting better results, the teacher suggested focussing of a distant tree instead of the grill. In which direction should the lens be moved for this purpose?

Away from the screen

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Very far away from the screen

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Behind the screen

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Towards the screen

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Solution

The correct option is D Towards the screen
Let $u_{1}, v_{1}$ be the object and image positions when grill is focused.
Let $u_{2}, v_{2}$ be the object and image positions when tree is focused.
$\frac{1}{v_{1}} - \frac{1}{u_{1}} = \frac{1}{f}$
$\frac{1}{v_{2}} - \frac{1}{u_{2}} = \frac{1}{f}$
Therefore, $\frac{1}{v_{2}} - \frac{1}{v_{1}} = \frac{1}{u_{2}} - \frac{1}{u_{1}}$
Since the grill is nearer, $| u_{1} | < | u_{2} |$
But $u_{1}, u_{2} < 0$ ,
$⟹ \frac{1}{u_{2}} > \frac{1}{u_{1}}$
$⟹ \frac{1}{v_{2}} > \frac{1}{v_{1}}$
$⟹ v_{1} > v_{2}$
Hence the distance between lens and image reduces.
Therefore the lens is moved towards the screen.

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