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A linear object AB is placed along optical axis of a concave mirror of focal length 20cm as shown in the figure.

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a

If AB = 5 mm, the size of image is nearly 20 mm

b

If AB = 5 cm, the size of image is 20 mm

c

If AB = 5 cm, the size of image is 13.33 cm

d

If AB = 5 cm, the size of image is 20 cm

answer is A, B.

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Detailed Solution

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$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
$\frac{1}{- 20} = \frac{1}{v_{1}} + \frac{1}{- 30} \Rightarrow v_{1} = - 60 c m$
$\frac{1}{- 20} = \frac{1}{v_{2}} + \frac{1}{- 35} \Rightarrow v_{2} = \frac{- 140}{3} c m$
$Δ v = 60 - \frac{140}{3} = 13.33 c m$
$m = - \frac{v}{u} \Rightarrow m = - 2$
$Δ v = m_{L} \times Δ u$
$Δ v = 2^{2} \times 5 = 20 m m$

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