The figure shows a concave mirror with a small object located at the point marked 6. If the image is also at this point, then the center of curvature of the mirror is at the point marked:
A) 3
B) 4
C) 6
D) 9
E) 12

Question

The figure shows a concave mirror with a small object located at the point marked 6. If the image is also at this point, then the center of curvature of the mirror is at the point marked: 
A) 3 
B) 4 
C) 6 
D) 9 
E) 12

Quizplus · Accepted Answer

According to the mirror formula, 1/v + 1/u = 1/f, where v is the distance of the image from the mirror, u is the distance of the object from the mirror, and f is the focal length of the mirror. In this case, since the image is at the same distance from the mirror as the object, the magnification is 1. Therefore, u = -v. Substituting these values in the mirror formula, we get 1/v - 1/v = 0, which means the focal length is infinite. For a concave mirror, the center of curvature is located at twice the focal length away from the mirror. Since the focal length is infinite, the center of curvature must be at infinity as well. However, in the options given, the closest choice is point 6, which is where the object and image are located. Therefore, the best choice is C.

The Figure Shows a Concave Mirror with a Small Object