A cosmetic "make-up" mirror is designed so that when a person’s face is 25cm in front of the mirror the image appears upright and twice the height of the object.
(a) Determine whether the mirror must be concave, convex, or plane. Provide qualitative reasoning that connects image orientation and size to the choice you make.
(b) Using the given information, calculate the distance of the image from the mirror. Indicate whether this distance is measured in front of or behind the mirror.
(c) Compute the focal length of the mirror and verify that the sign of the focal length is consistent with your answer in part (a).