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. `xy`
B. `sqrt(xy)`
C. `x+y`
D. `sqrt((x)/(y))`

Answer

B

Explanation

`u=-(f+x),v=-(f+y),f=-f`
`(1)/(v)+(1)/(u)=(1)/(f)implies(1)/(-(f+y))+(1)/(-(f+x))=(1)/(-f)`
`(2f+x+y)/((f+y)(f+x))=(1)/(f)`
`2f^2+f(x+y)=f^2+f(x+y)=xy`
`f^2=xy`
`f=sqrt(xy)`