\(\frac{1}{ v }+\frac{1}{ u }=\frac{1}{ f }\)

\(\frac{1}{ v }=\frac{1}{ f }-\frac{1}{ u }\)

For concave mirror, focal length is negative. Hence, \(f<0\)

For a virtual object, object distance is positive. Hence \(u _v>0\)

From above, it can be observed that image distance \(v\) is negative when object is virtual. Since image distance is negative, it is formed by real intersection of rays and image is real.

For a real object, object distance is negative. Hence \(u _{ r }<0\)

In this case, image distance \(v\) may be positive or negative depending on the location of object.