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 location separated by `20 cm`. Determine the focal length of the lens.

Options

A. `42.8 cm`
B. `21.4 cm`
C. `10.7 cm`
D. `5.5 cm`

Answer

B

Explanation

The image of the object can be located on the screen for two positions of convex lens such that u and v are exchanged.
The separation between two positions of the lens is
`d = 20 cm`
From the figure,
`u_(1) + v_(1) = 90 cm`
`v_(1) - u_(1) = 20 cm`
Solving
`v_(1) = 55 cm, u_(1) = 35 cm`
From lens formula
`1/v - 1/u = 1/f`
`1/55 - 1/(-35) = 1/f` or `1/55 + 1/35 = 1/f rArr f = (55 xx 35)/(90) = 21.4 cm`