Final answer:
A real image can exist without being projected onto a screen; it is formed by the convergence of light rays even if no screen is present. Virtual images appear through divergence but can't be projected; they can still be seen and photographed.
Step-by-step explanation:
The question of whether a real image must be projected onto a screen for it to exist can be answered with option b) No, a real image can exist without being projected. In the context of optics, a real image is one where light rays from an object actually converge and cross at the location of the image. This type of image can be captured on a screen, as in cameras or projected onto film, and it is the same principle that allows our eyes' lenses to project real images onto the retina. However, the existence of a real image does not depend on whether it is projected onto a screen or not; the image is formed by the physical convergence of light rays, irrespective of a screen being present to capture it.
Virtually speaking, a virtual image, in contrast, is one where the light rays do not actually converge but appear to diverge from a common point when seen by an observer. Though virtual images cannot be projected onto a screen, they can be seen and even photographed, as they are what you typically see when looking into a flat mirror. Additional lenses or mirrors can convert a virtual image into a real one that can be projected.