An object is placed 10 cm in front of a lens. The image formed is real, inverted and of same size as the object. What is the focal length and nature of the lens?

For a lens to form a real and inverted image, it must be a converging (convex) lens, as diverging (concave) lenses only produce virtual, erect, and diminished images. According to the principles of geometrical optics, a real, inverted image of the same size as the object (magnification m = -1) is formed only when the object is placed at a distance equal to twice the focal length (u = 2f). In this case, the object is placed 10 cm in front of the lens. Therefore, 2f = 10 cm, which implies the focal length (f) is 5 cm. Using the lens formula 1/f = 1/v - 1/u, where u = -10 cm and v = +10 cm (for same size real image), we get 1/f = 1/10 - (-1/10) = 2/10, confirming f = 5 cm. Thus, the lens is a converging lens with a focal length of 5 cm.