Final answer:
Real images are formed by converging lenses or concave mirrors when the object is placed beyond the focal distance (do > f), and virtual images are formed when the object is within the focal length (do < f) or for any positive object distance with diverging lenses or convex mirrors.
Step-by-step explanation:
For converging lenses and concave mirrors, real images are formed when the object distance, do, is greater than the focal distance, f. Specifically, for an f of 10 or 15 cm, real images form when do > f. If the object is placed beyond twice the focal distance (do > 2f), the image is diminished and real. For diverging lenses and convex mirrors, any positive object distance results in a virtual image, as indicated by the negative image distance, di.
Regarding virtual images, with a converging lens or a concave mirror, they occur when an object is within the focal length (do < f). Here, f is 10 cm or 15 cm as per the supplied values. For a diverging lens or a convex mirror, the virtual image is formed regardless of the object distance, as long as it is positive.
A virtual image is seen because it cannot be projected onto a screen; it can be seen directly through the lens or reflected in the mirror. A real image, on the other hand, can be projected onto a screen because the light rays actually converge.