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 equation, 1/o + 1/i = 1/f, where o is the object distance, i is the image distance, and f is the focal length. Since the object and image distances are the same (both at point 6), we have 1/o + 1/i = 2/6 = 1/3. We also know that for a concave mirror, the focal length is half the radius of curvature, so f = OC/2. Substituting these values into the mirror equation, we get 1/6 + 1/6 = 1/3 = 1/f = 1/(OC/2), which simplifies to OC = 6. Therefore, the center of curvature is at the point marked 6.

The Figure Shows a Concave Mirror with a Small Object