The focal length of a concave mirror is f. A point object is placed beyond the forcal length at a distance xf from the focus. Prove that the image will be formed beyond the focal length at a distanfe `(f)/(x)` from the focus and the magnification of the image will be `-(1)/(x)`.

Explanation

Here, object distance, `u=-(f+xy)`
`"We know", " " (1)/(v)+(1)/(u)=(1)/(f) or, (1)/(-(f+xf))=(1)/(f)`
`or, " " (1)/(v)=(1)/(f+xf)-(1)/(f) or, (1)/(v)=(1)/(f)[(1)/(1+x)-1]=(-x)/(f(1+x))`
`therefore " " v=f(1+x)/(-x)=(f+(f)/(x))`
So, the image is formed beyond the focal lenght at a distance of `(f)/(x)` from the focus.
`therefore " " "Magnification",m=-(v)/(u)=(-f(1+x)/(x))/(-f(1+x))=-(1)/(x)`