Final answer:
The lens is convex with a focal length of 10 cm because it produces a real image with a magnification of 0.5 when an object is placed at 10 cm, beyond its focal length.
Step-by-step explanation:
The student asks about an object placed at 10 cm from a lens that forms a real image with a magnification of 0.5. Given this information, we can determine that the lens is convex because convex lenses are capable of producing real images if the object is placed beyond the focal length of the lens. To find the focal length of the lens, we would use the lens formula 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. Since we have the magnification (m = di/do) and it is 0.5, that implies the image distance (di) is half the object distance (do), which is -5 cm (negative because the image formed is real and inverted).
Now using the lens formula, we get 1/f = 1/do + 1/di = 1/10 + 1/(-5) = 0.1 - 0.2 = -0.1, so the focal length f is -10 cm. Therefore, the lens must have a focal length of 10 cm, but it's a positive 10 cm because convex lenses have positive focal lengths. Hence, the correct answer is that the lens is a convex lens with a focal length of 10 cm.