Question

A 10 cm tall image is projected on a screen 50 cm away from a convex lens of focal length20 cm. Find the position, and size of the object

Answer 1

The given quantities are  

Height of the object h = 50 cm

Height of the image formed h’ = -20 cm

Image distance v = 10 cm

The image distance is the distance between the position of convex lens and the position where the image is formed.

The ‘focal length’ of a convex lens can be found using the below formula

Here f is the focal length, v is the image distance which is known to us and u is the object distance.

The object distance is the distance between the ‘object position’ and the lens position. To determine the focal length, first we should find the object distance.

From the magnification equation, we know that

Thus,

So, the object distance will be

So the focal length will be

Thus the focal length of the convex lens is 7.14 cm

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