When the object is at distance `u_(1)`and`u_(2)`the images formed by the same lens are real and virtual respectively and of the same size.Then focal length of the lens is:

Options

A. `(1)/(2)sqrt(u_(1)u_(2))`
B. `(u_(1) + u_(2))/(2)`
C. `sqrt(u_(1)u_(2))`
D. `sqrt((u_(1) + u_(2)))`

Answer

B

Explanation

`m_(1) = (1)/(u_(1)-f) m_(2) = (1)/(u_(2)-f), (m_(1))/(m_(2)) = -1`
`implies u_(2) - f = -(u_(1)-f) implies u_(1)+u_(2) = 2f`
`implies f = (u_(1) + u_(2))/(2)`