# Lesson Explainer: Convex Mirrors Science

In this explainer, we will learn how to describe the reflection of light rays from a convex mirror.

The following figure shows a beam of light reflecting from a convex mirror.

We can see that the mirror is curved.

We can represent the mirror as it would look viewed from directly above, as shown below.

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.

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 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.

A ray of light reflected from a spherically curved convex mirror is represented 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.

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.

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.

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.

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.

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 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.

Let us now look at some examples.

### Example 1: Identifying the Location of the Center of Curvature of a Convex Mirror

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?

1. The center of curvature of a convex mirror will always be on the opposite side of the observer.
2. The center of curvature of a convex mirror will always be on the same side as the observer.
3. Depending on the path of the light rays, the center of curvature of a convex mirror can sometimes be on the opposite side of the observer and sometimes on the same side as the observer.

For a convex mirror, light rays are reflected as shown in the figure below.

An observer must be in a position where reflected light rays can reach them.

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.

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.

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.

### Example 2: Describing the Focusing of Rays by a Convex Mirror

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

1. They will continue undisturbed.
2. They will not be focused at a point, but the mirror will still have a focal point.
3. They will be focused at a point, which is called the focal point.
4. They will not be focused at a point and the mirror will have no focal point.

A mirror reflects light rays. Incident rays are reflected rather than continuing undisturbed.

The following figure shows three parallel incident light rays reflected from a convex mirror.

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.

This means that the reflected rays do not focus at a point.

A convex mirror does, however, have a focal point. This is shown in the following figure.

The focal point is the point from which reflected rays appear to originate.

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.

### Example 3: Relating the Positions of the Focal Point and Center of Curvature of a Convex Mirror

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

1. The focal length is 2.5 cm and is the distance from the center of the surface of the mirror to the center of curvature.
2. The focal length is 5 cm and is the distance from the center of the surface of the mirror to the center of curvature.
3. The focal length is 2.5 cm and is the distance from the center of the surface of the mirror to the focal point.
4. The focal length is 5 cm and is the distance from the center of the surface of the mirror to the focal point.

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.

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 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.

Let us now summarize what has been learned in this explainer.

### Key Points

• A convex mirror has a center of curvature.
• For a mirror with spherical curvature, the mirror is curved into a circle. The center of curvature is at the center of the circle.
• The center of curvature of a convex mirror is on the opposite side of the mirror to the side that reflects light rays.
• Light rays reflected from a convex mirror do not focus at a point.
• Light rays reflected from a convex mirror appear to diverge from a point on the opposite side of the mirror to the side that reflects light rays. This is the focal point of the mirror.
• The distance from the focal point of a convex mirror to the front of the mirror is half the distance from center of curvature to the front of the mirror.