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)`
`(2 f + d_1 + d_2)/((f + d_1)(f + d_2))=(1)/(f)`
or `2f^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)`.