Question

when an object is placed at a distance of 50 cm from a concave mirror the magnification produced is -1 by 2 where should an object be placed to get a magnification of minus 1 by 5​

Answer 1

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Answer 2

Given info : when an object is placed at a distance of 50 cm from a concave mirror the magnification produced is -1/2.

To find : where should an object be placed to get a magnification of -1/5 ?

solution : here, object distance, u = - 50cm

we know, magnification, m = -v/u

⇒ -1/2 = -v/-50

⇒ v = -25 cm

now using mirror formula, $\frac{1}{v} +\frac{1}{u} =\frac{1}{f}$

⇒ $\frac{1}{-25}+\frac{1}{-50}=\frac{1}{f}$

⇒ f = -50/3 cm

now, when magnification is -1/5

⇒ -1/5 = -v/u

⇒ v = u/5

now, using mirror formula, $\frac{1}{v} +\frac{1}{u} =\frac{1}{f}$

⇒ $\frac{1}{u/5} +\frac{1}{u} =\frac{1}{-50/3}$

⇒ $\frac{6}{u}=-\frac{3}{50}$

⇒ u = -100cm

therefore the position of the object should be 100cm from the mirror to get a magnification of -1/5.