The focal length of a concave mirror is f . What will be the magnification of an object at a distance x from the principal focus (given, object distance `gt` f)? For what value of x will the size of the object and the image be the same?

Explanation

Object distance with respect to the pole, u = f + x
`(1)/(v) + (1)/(u) = (1)/(f) or, (1)/(v) = (1)/(f) - (1)/(u)`
`or, " " (u)/(v) = (u)/(f) -1 = (f+x)/(f) - 1 = (x)/(f)`
`therefore` Magnification of the image, `m = (v)/(u) = (f)/(x)`
[taken mod value of m]
If size of the object and the image is same then , m = 1
i.e., `(f)/(x) = 1 or, x = f`