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/f = 1/v + 1/u where f is the focal length, v is the distance of the image from the mirror, and u is the distance of the object from the mirror. Since the image is formed at the same distance as the object, v = u. Therefore, 1/f = 1/u + 1/u = 2/u. Solving for u, we get u = 6. The center of curvature is at a distance of 2u from the mirror, which is 12. Therefore, the best choice is C.

The Figure Shows a Concave Mirror with a Small Object