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Q.

A short linear object of length ‘b’ lies along the axis of a concave mirror of focal length ‘f’ at a distance ‘u’ from the pole of the mirror. The size of the image is approximately equal to

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a

$b {(\frac{u - f}{f})}^{1 / 2}$

b

$b {(\frac{f}{u - f})}^{1 / 2}$

c

$b (\frac{u - f}{f})$

d

$b {(\frac{f}{u - f})}^{2}$

answer is D.

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Detailed Solution

From mirror formula,

$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ ........ (1)

$\Rightarrow | dv | = |\frac{v^{2}}{u^{2}} du| = |\frac{v^{2}}{u^{2}}| |du|$ ........ (2)

Using mirror formula,

$\frac{u}{v} + 1 = \frac{u}{f}$

$\Rightarrow \frac{v^{2}}{u^{2}} = {(\frac{f}{u - f})}^{2}$

from eqn (2),

$\Rightarrow | dv | = b {(\frac{f}{u - f})}^{2}$

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A short linear object of length ‘b’ lies along the axis of a concave mirror of focal length ‘f’ at a distance ‘u’ from the pole of the mirror. The size of the image is approximately equal to