A convex lens forms a real and inverted image at a distance of 40 cm from it. If the size of the image is equal to the size of the object, what is the focal length of the lens?
Correct: B
For a convex lens, when a real and inverted image is formed, and its size is equal to the object's size, the object must be placed at 2F, and the image is also formed at 2F on the other side of the lens. Since the image distance (v) is 40 cm (positive for real image formed by convex lens), then 2F = 40 cm. Therefore, the focal length F = 40 cm / 2 = 20 cm.
Alternatively, using the lens formula: 1/f = 1/v - 1/u. Since the image is real, inverted, and same size, m=-1. For lenses, m = v/u, so -1 = v/u, which means u = -v. Given v = +40 cm, then u = -40 cm.
1/f = 1/40 - 1/(-40) = 1/40 + 1/40 = 2/40 = 1/20.
So, f = +20 cm.