A screen is placed at a distance of 100cm from an object. The image of the object is formed on the screen by a convex lens for two different locations of a lens seperated by 20cm. Calculate the focal length of the lens used.

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Solution

You can use the relation f=(D^2−X^2)/4D to solve such kind of problem
in this formula f is the focal length of the convex lens
D distance between the object and the screen
x is the distance between the two position of the lens..
f=(100^2−20^2)/4x100
=9600/400=24 cm

the eqation v-u= 20 is obtained when you consider the image formed by the lens at its first location as object

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