What must be the distance between an object and a converging lens of focal length 20cm to produce an erect image two times the object height?

This is a question related to optics and the use of converging lenses. When an object is placed in front of a converging lens, it forms an image on the other side of the lens. The distance between the lens and the object affects the properties of the image formed. The formula to determine the distance between the object and the lens is: 1/f = 1/di + 1/do where f is the focal length of the lens, di is the distance between the image and the lens, and do is the distance between the object and the lens. Since we want to produce an image that is two times the height of the object and the image is erect (upright), the image distance (di) is positive, and the magnification (M) is 2. Therefore: M = -di/do = 2 Solving for di, we get: di = -2do Substituting this value of di in the lens formula: 1/f = 1/di + 1/do 1/20 = 1/(-2do) + 1/do Multiplying both sides by -2do, we get: -2 + 20/do = -1 Solving for do, we get: do = 10cm Therefore, the distance between the object and the lens must be 10cm to produce an erect image that is two times the height of the object. The correct option is: 10cm.