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A small linear object of length b is placed at a distance u from the pole of the concave mirror along the axis the focal length of mirror is f. The length of image will be

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a

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

b

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

c

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

d

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

answer is D.

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Detailed Solution

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u} \frac{- 1}{f} = \frac{1}{v} - \frac{1}{u} ∣ \frac{1}{v} = \frac{1}{u} - \frac{1}{f} \frac{1}{v} = \frac{f - u}{uf} \frac{u}{v} = \frac{f - u}{f} \frac{v}{u} = \frac{f}{f - u} \frac{leng th of image}{leng th of object} = \frac{f}{f - u} Length of image = b (\frac{f}{f - u})$

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