A dedicated sports car enthusiast polishes the inside and outside surfaces of a hubcap that is a section of a sphere. When he looks into one side of the hubcap, he sees an image of his face 30.0 cm in back of it. He then turns the hubcap over, keeping it the same distance from his face. He now sees an image of his face 10.0 cm in back of the hubcap. (a) How far is his face from the hubcap? (b) What is the radius of curvature of the hubcap?

I will hazard a guess at 10cm for both answers. To prove: draw a semi-circle 10cm radius, draw an eye 10cm from left hand side of circle. This is face 1, when you rotate the hubcap, the image will be 30cm. Seems a rather easy answer. But it looks right if you draw it.

This sounds like a homework problem in optics with a concave and a convex lens of the same r and in the same position with respect to the original object.

jenan41, have you tried the problem?