PhysicsLAB Amusing Problems

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In this episode, we find Dr. J both in and out of trouble. The CIA has given the infamous part-time agent the distinguished N.Y.S.M. - N.Y.D. (now you see me - now you don't) award for his ability to use mirrors in escaping tight situations. On the other hand, the school administration has taken a dim view of his extra activities outside the classroom. In fact, they have ordered him not to stand in front of any type of mirror while on school property. (They feel it would be a bad reflection on the school.) SAP, in their never-ending quest to reduce Dr. J's image, set out to trick Dr. J into violating the board's order. Attempt after attempt fall flat until they finally get tired. Then it hits them - flat tire! By flattening one of Dr. J's tires in the faculty parking lot, he is forced to look at a freshly-polished hubcap. In other words, SAP cons him into caving in and looking at a mirror. When Dr. J realizes what is happening he quickly flips the hubcap over only to find it has also been highly polished. When he looks into one side of the hubcap, he sees an image of his face 52 cm in back of the hubcap. When he looks into the other side, he sees an image of his face 13 cm in back of the hubcap.
What is the radius of curvature of the hubcap?

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