The center of curvature of a spherical mirror is the point that is the same distance from every part of the mirror, as shown below.

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The focal length is equal to half the distance from the center of curvature to the point on the mirror nearest to the focal point, as shown below.

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We see that these reflected light rays do not cross each other. This is true for any two reflected light rays from a convex mirror.

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It is important to understand that the reflected light rays do not start at the focal point. The reflected light rays actually all start at different points on the mirror, as shown in the following figure.

An observer who can see light reflected from the mirror cannot also see the center of curvature of the mirror, as the mirror blocks the line of sight to that point.

We see then that there is no way that someone on the same side of the mirror as the center of curvature can see any reflected light rays. This means that they cannot be an observer.

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Another important point is on the same side of the mirror as the center of curvature. This point is called the focal point, and it is shown in the following figure.

The distance from the front of the mirror to the focal point is half the distance from the front of the mirror to the center of curvature, as shown in the following figure.

The radius of curvature of the mirror is 5 cm, which means that the front of the mirror is 5 cm from the center of curvature. This is shown in the following figure.

Convex mirrorray diagram

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The correct answer must then be that reflected rays will not be focused at a point, but the mirror will still have a focal point.

Which one of the following sentences is the correct description for what happens to parallel rays incident on a convex mirror?

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For any spherical mirror, the distance between the center of curvature and the center of the surface is just the radius of that sphere. Which one of the following sentences correctly describes the location of the center of curvature of a convex mirror?

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There is a point called the center of curvature of the mirror. For a spherically curved mirror, this point is at the same distance from every part of the surface of the mirror, as shown below.

The correct answer is then that the focal length is 2.5 cm and is the distance from the center of the surface of the mirror to the focal point.

Concavemirror

It is important to understand that the distances between the ends of reflected rays increase the further these rays extend from the mirror. This means that these rays will not actually focus at a point. The focal point of the mirror is only the point that reflected light rays seem to have started at.

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The distance from the center of curvature of a spherically curved mirror to the mirror is equal to the radius of a circle centered on the center of curvature, as shown in the following figure.

We see that the light reflected from the mirror is on the opposite side of the mirror to the center of curvature of the mirror.

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The radius of curvature of a convex mirror is 5 cm. Which one of the following sentences about the focal length is correct?

The correct answer must then be that the center of curvature of a convex mirror will always be on the opposite side to the observer.

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The distance from the focal point to the nearest point on the mirror is called the focal length. This is shown in the following figure.

The mirror shown has spherical curvature. This means that if the mirror was lengthened while keeping its curvature the same, its ends would meet and a circle would be formed, as we can see below.