By , 4 months ago

The image is n times the size of the object. Therefore, magnification is -n. The magnification is size of image/size of object. It is negative for a real image and positive for a virtual image. 
Magnification is also -v/u where v is image distance and u is object distance. So, -n = -v/u. So, the image distance v = nu.

But what is u? We can find it by using the mirror formula 1/v + 1/u = 1/f

So, 1/nu + 1/u = -1/f.

I have written -1/f because f will be taken as negative as the focus of a concave mirror is towards the left.

hence, (1+n)/nu = -1/f

Or, nu = -f(1+n)

So, u = -f(1+1/n)

v = image distance = nu = -f(1+n).

The minus sign here indicates that the image is formed to the left of the object - on the real side.

(By sign convention, the object is always placed on the left side of the mirror).