How is it possible to see a virtual image formed by a convex mirror if that image cannot be focussed on a screen?
Images are created by any lens when light rays created by an object cross.
Light rays can cross in one of two ways: the rays of light can trace out a path and the path actually cross in space, or the rays of light trace out a path which does not actually cross in space but instead appear to originate from some location at which they did cross.
The first case represents the formation of a real image. That is, the rays trace paths that really do cross in real space and therefore if you place a screen or photographic film at the location of intersection you will see an image appear.
The second case represents the formation of a virtual image. The path the rays actually follow as the pass through the lens never really cross in real space. However, as the rays pass through the lens they are bent away from the principle axis going through the center of the lens. If one traces the rays backwards, through the lens and extrapolate them without allowing them to bend at the lens the extrapolated traces will eventually cross "behind" the lens. The real rays not only do not actually cross there, they do not even exist there. Therefore, if you put a screen or a piece of photographic film where the extrapolated rays appear to cross there will be no image.
The only way to actually see the virtual image created by a convex lens is to arrange the eye of the observer so that it is on the side of the lens opposite to the virtual image and to look back through the lens to where the rays appear to cross. Because the eye does not see the real rays bending at the lens, they perceive the rays as though they are coming from the point where they appear to cross. Consequently it "sees" the virtual image even though it isn't really there.