How far should an object be placed from a convex lens of focal length 20 cm to obtain its image at a distance of 30 cm from the lens? What will be the height of the image if the object is 6 cm tall?
CBSE OUTSIDE DELHI - SET 1 2010
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$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$\therefore\frac{1}{u } = \frac{1}{v} - \frac{1}{f}$
$= \frac{1}{( + 30)} - \frac{1}{( + 20)}$
$ = \frac{1}{30} - \frac{1}{20} = \frac{2 - 3}{60} = \frac{- 1}{60}$
$\therefore u = - 60 \text{ cm}$
$m = \frac{\text{h}'}{\text{h}} = \frac{v}{u}$
$\therefore \text{h}' = \frac{v}{u}\times \text{h}$
$= \frac{(+ 30)}{( - 60)}\times( + 6)$
$\text{h}' = - 3 \text{ cm}$
$= \frac{1}{( + 30)} - \frac{1}{( + 20)}$
$ = \frac{1}{30} - \frac{1}{20} = \frac{2 - 3}{60} = \frac{- 1}{60}$
$\therefore u = - 60 \text{ cm}$
$m = \frac{\text{h}'}{\text{h}} = \frac{v}{u}$
$\therefore \text{h}' = \frac{v}{u}\times \text{h}$
$= \frac{(+ 30)}{( - 60)}\times( + 6)$
$\text{h}' = - 3 \text{ cm}$
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