A concave mirror has a focal length of 20 cm. If an object is placed at a distance of 30 cm from the pole of the mirror then the image distance and transverse magnification are respectively

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50 cm, 2

60 cm, 3

50 cm, 3

60 cm, 2

answer is A.

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Detailed Solution

$f = - 20 c m, u = - 30 c m, v = ?$

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

$\frac{- 1}{20} = \frac{- 1}{30} + \frac{1}{v}$

$\frac{1}{v} = \frac{- 1}{20} + \frac{1}{30}$

$\frac{1}{v} = \frac{- 3 + 2}{60}$

$\frac{1}{v} = \frac{- 1}{60}$

$v = - 60 c m (i m a g e d i s \tan c e)$

$m = \frac{- v}{u}$

$m = \frac{v}{u}$

$m = \frac{- 60}{30} (o r) m = \frac{- (- 60)}{- 30} = - 2 (o r)$ $m = - 2$

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