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Question
The focal length of a concave lens is 20 cm. At what distance from the lens should a 5 cm tall object be placed so that its image is formed at a distance of 15 cm from the lens? Also calculate the size of the image formed.
Solution
Focal length of concave lens, f = −20 cm
Distance of the image from the lens, v = -15 cm
Using the lens formula, we get:
`1/f=1/v - 1/u`
`1/-20= 1/-15 - 1/u`
`1/u=1/-15-1/-20`
`1/u=(-4+3)/60 = (-1)/60`
`u=-60 "cm"`
To find the size of the image formed (h′), use the magnification formula, where magnification (m) = `h^'/h = v/u` and h is the height of the object.
h=5 cm, and we have v = -15 cm and u = -60 cm
`m = (-15)/-60=1/4`
`h^' = mxxh = 1/4xx5 =1.25`
Hence, the size of the image is 1.25 cm.
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