For each of the following cases, use a ray diagram to show that the angular sizes of the image and the object are identical if both angles are measured from the center of the lens.
(a) A convex lens with the object outside the focal length.
(b) A convex lens with the object inside the focal length.
(c) A concave lens with the object outside the focal length.
(d) Given that the angular size does not change, how does a simple magnifier work? Explain.