A source of light and screen are separated by a distance of $50 c m$ . A sharp image of the source is produced by lens when placed at two positions between the source and the screen. If the distance of separations of the lens between the two positions is $20 c m$ , find the focal length of the lens.

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Solution

Distance between source and screen $D = 50 c m$
Distance between two positions of lens $d = 20 c m$
Focal length $f = \frac{D^{2} - d^{2}}{4 D}$
So, $f = \frac{50^{2} - 20^{2}}{4 \times 50} = 10.5 c m$

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A source of light and screen are separated by a distance of 50 cm. A sharp image of the source is produced by lens when placed at two positions between the source and the screen. If the distance of separations of the lens between the two positions is 20 cm, find the focal length of the lens.

Distance between source and screen D=50 cmDistance between two positions of lens d=20 cmFocal length f=D2−d24DSo, f=502−2024×50=10.5 cm

Distance between source and screen $D = 50 c m$
Distance between two positions of lens $d = 20 c m$
Focal length $f = \frac{D^{2} - d^{2}}{4 D}$
So, $f = \frac{50^{2} - 20^{2}}{4 \times 50} = 10.5 c m$