Answer to Question #159774 in Optics for ashton

Question

if the focus of a concave mirror is 12 cm from the mirror where is the centre of the curvature

Answer 1

By the definition of the radius of curvature of the mirror, we have:

$$f=\dfrac{R}{2},$$ $$R=2f=2\cdot12\ cm=24\ cm.$$

So, the center of curvature lies 24 cm to the left from the vertex of the concave mirror.

From the other hand, we can say that the center of curvature lies 12 cm to the left from the focus of the concave mirror - it is also the right answer.