A convex spherical surface with radius r separates a medium with index of refraction 2 from air. As an object is moved toward the surface from far away along the central axis, its image:
A) changes from virtual to real when it is r/2 from the surface
B) changes from virtual to real when it is r from the surface
C) changes from real to virtual when it is r/2 from the surface
D) changes from real to virtual when it is r from the surface
E) remains real

Question

Quizplus · Accepted Answer

When the object is placed at infinity, the rays from it are parallel to the central axis, and they will be converged by the spherical surface to a real image at the focal point F, which is half the radius away from the surface by the lensmaker's formula. As the object is moved toward the surface, the image will move farther away from the surface, and at some point between F and 2F, the image will become virtual due to the intersection of the extended refracted rays. Since the image distance is proportional to the object distance, and the ratio of the distances is negative for a virtual image, the transition from real to virtual happens at r, where the object distance equals 2r, and the image is at infinity. Therefore, choice D is the correct answer.

A Convex Spherical Surface with Radius R Separates a Medium