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

Using `(1)/(v)+(1)/(u)=(1)/(f)`
Given `u=f+d_(1)" "v=f+d_(2)`
`f=(uv)/(u+v)=((f-d_(1))(f+d_(2)))/((f+d_(1))+(f+d_(2)))`
On solving `f=sqrt(d_(1)d_(2))`