See the diagram.
I guess your query is only about real images and it is not about virtual images formed behind the concave mirror on the other side between pole P and focus (f = R/2).
Concave mirror is a small piece of a spherical surface and it is cut off from the surface. Its height could be around 5 cm total. Let us call the center of curvature C and radius of curvature R = radius of sphere from which it is cut.
When an object is more than R distance away, a real inverted image is formed between focus F (at R/2) and center C (at R) from pole of mirror. When the object is in between C and F, a real and inverted image is formed after C. That is more than distance R.
All these images can be caught on screen. Since object is above principal axis and image is below the axis, there is no problem in catching the image on a screen.
For the image to be formed a small piece of the mirror is enough. That reflects the rays coming from the object. The image will be fainter. For a bigger mirror the image is brighter as more rays converge to image.
The image is formed in air. If you have smoke at the location, where image is formed, due to reflection from smoke particles, you can see the image. If you put paper you can see the image on it. We do not see the image until some thing reflects the rays from the image into our eyes. So if there is no screen, image is formed and is hanging in the air. But we do not see that.
If the query or confusion is about the virtual image formed, when the object is placed within the focal length in front of mirror :
The rays reflected from mirror do not converge and they diverge. The seem to come from a location behind mirror between P and F behind mirror. This virtual image is erect. This image is not hanging in air. It is only seen by the eye and directly. The eye calculates 3-d distances from the rays and imagines the image to be there.