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Two objects A and B when placed in front of a concave mirror of focal length 7.5 cm, give images of equal size. If A is three times the size of B and is placed 30 cm from the mirror, what is the distance of B from the mirror ?

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12.5 cm

15 cm

17.5 cm

10 cm

answer is C.

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Detailed Solution

$∵ m = \frac{h_{i}}{h_{0}} ∴ m_{A} = \frac{m_{B}}{3} also m = \frac{f}{f - u}$

$So, \frac{f}{f - u_{A}} = \frac{1}{3} (\frac{f}{f - u_{B}})$

$\Rightarrow u_{B} = \frac{2}{3} f + \frac{1}{3} u_{A} = - 15 cm$

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