### Video Transcript

Complete the following. The focal length of a spherical mirror is blank the radius of curvature of the
mirror. (A) Double, (B) equal to, or (C) half.

This question is asking us about the relationship between the radius of curvature and
the focal length of a spherical mirror. So, to answer this question, we need to recall the definitions for the radius of
curvature and the focal length.

We call mirrors spherical because of their shape. If we traced out the curve of a spherical mirror, we would find that it is a part of
a larger sphere. Every sphere has a radius. It is the distance from the center to the edge. The radius of the sphere is the same in all directions. So the distances shown here are all equal. The radius of the sphere that we traced out for the mirror is called the radius of
curvature of that mirror.

The focal length of a spherical mirror is the distance between the mirror and the
point where the light rays meet, called the focal point. For convex mirrors, the reflected light rays do not meet. Instead, the focal point is the point where they would meet if we traced the
direction of the reflected light rays back through the mirror, giving us a focal
length.

If we label both the focal length and the radius of curvature on our ray diagram, we
can compare their lengths. We can see that the radius of curvature has a greater length than the focal
length. Hence, the focal length cannot be double its value. So (A) is not the correct answer. Therefore, they are also not equal in length. So (B) is also not the correct answer.

This leaves option (C), half, which by looking at the diagram we can see two focal
lengths equals one radius of curvature. So the correct answer is (C) or that the focal length of a spherical mirror is half
the radius of curvature of the mirror.