In a concave mirror, an object is placed at a distance `d_1` from the focus and the real image is formed aat a distance `d_2` from the focus. Then the focal length of the mirror is :

Options

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

Answer

A

Explanation

Here, `u = -(f + d_(1))` and `v = -(f + d_(2))`
From `(1)/(u) + (1)/(v) = (1)/(f)`
`(1)/(-(f + d_(1))) + (1)/(-(f + d_(2))) = (1)/(-f)`
`(2f + d_(1) + d_(2))/((f + d_(1)) + (f + d_(2))) = (1)/(f)`
or `2 f^(2) + (d_(1) + d_(2)) f = f^(2) + d_(1) f + d_(2) f + d_(1)d_(2)`
`f^(2) = d_(1) d_(2)`
or `f = sqrt(d_(1) d_(2))`