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Numerical

A screen is placed 90 cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. Determine the focal length of the lens.

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#### Solution

Distance between the image (screen) and the object, D = 90 cm

Distance between two locations of the convex lens, d = 20 cm

Focal length of the lens = f

Focal length is related to d and D as:

`"f" = ("D"^2 - "d"^2)/4"D"`

= `((90)^2 - (20)^2)/(4 xx 90)`

= `770/36`

= 21.39 cm

Therefore, the focal length of the convex lens is 21.39 cm.

Concept: Refraction at Spherical Surfaces and Lenses - Refraction by a Lens

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