A convex lens produces an inverted image magnified three times of an object placed at a distance of 15 cm from it. Calculate focal length of the lens.

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Solution

Given:
Object distance, u = $-$ 15 cm
Magnification, m = $-$ 3 (Image is inverted.)
Applying magnification formula, we get:
m = v/u = $-$ 3
or, v/( $-$ 15) = $-$ 3
or, v = 45 cm
Applying lens formula, we get:
1/v $-$ 1/u = 1/f
1/45 $-$ 1/( $-$ 15) = 1/f
1/f = ( 1+3 )/45
1/f = 4/45
or f = 11.2 cm
Hence, focal length of the lens is 11.2 cm.

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