Q: The magnification of an object placed in front of a convex lens of focal length 20 cm is +2. To obtain a magnification of -2, then the image is virtual. Both the image and the object are on the same side of the lens.

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Sol: u = -x ; v = -2 x ; f = + 20

Using , $\large \frac{1}{v} – \frac{1}{u} = \frac{1}{f} $

$\large \frac{1}{-2x} – \frac{1}{-x} = \frac{1}{20} $

or, x = 10 cm.

To have magnification of -2 the image must be real.

u = – y,v = +2y and f = +20

$\large \frac{1}{2y} – \frac{1}{-y} = \frac{1}{20} $

or, y = 30 cm

∴ y-x = 20 cm