If x , y and z denote the object distance, image distance and the radius of curvature respectively of a spherical mirror, which one of the following is the correct relation between them ?

Options

A. Z `= 2 (xy)/(x-y)`
B. `Z= 2(x+y)/(xy)`
C. `Z =2(xy)/(x-y)`
D. `Z = 2(x-y)/(xy)`

Explanation

For a spherical mirror,
`1/f = 1/v + 1/u`
`therefore 2/Z = 1/x + 1/y = (y+x)/(xy) implies Z/2 = (xy)/(x+y)`
`Z = 2(xy)/(x+y)`
Here (a) is the correct answer.