How can an INVERTED and VIRTUAL image can be formed on the concave side of a spoon.
There is no need to think of a screen at all - you are not looking at the image produced by the reflected light on a screen - there is no screen. The light is upended by the reflecting concave surface, squeezes through the focal point and then fans out. Your eye intercepts some of this fan and forces the diverging rays to converge on your retina. Notice that the image you see of yourself ( upside down) stays in focus no matter how far you are from the spoon ( except if you get inside the focal length when its hard to see anything as not enough light gets into the space available (or is that just because I have such a big nose?)). That staying in focus is the give away - your eye lens is doing the work to keep the image sharp without you realising it.
This is what makes optics rather hard to describe, since we rely on a variable optical system to actually make any observations.
You are very right to worry about this....the books and teachers just stick with simple experiments and come up with "rules" that only make sense if our eyes are not involved.