# Lesson Explainer: Concave Mirrors Science

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

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

We can see that the mirror is curved.

We can represent the mirror as it would look viewed from directly above as follows.

The mirror shown has spherical curvature. This means that if it was lengthened while keeping its curvature the same, the ends of the mirror would meet and a circle would be formed as shown in the following figure.

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. This is shown in the following figure.

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 same side as the center of curvature of the mirror.

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 focal point is the point through which all the reflected rays shown pass.

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 Concave 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 concave mirror?

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

### Answer

For a concave mirror, light rays are reflected as shown in the following figure.

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 in the figure below.

We see then that someone on the same side of the mirror as the center of curvature can see reflected light rays from the mirror. This means that they can be an observer. Someone on the other side of the mirror cannot see the reflected light rays and so cannot be an observer.

The correct answer must then be that the center of curvature of a concave mirror will always be on the same side as the observer.

### Example 2: Describing How Parallel Rays Reflect off a Concave Mirror

Which of the following sentences is the correct description of what will happen to parallel rays incident on a concave mirror?

1. They will be focused at the focal point.
2. They will be focused at the center of curvature.
3. They will not be focused at a point at all.
4. They will continue undisturbed.

### Answer

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 concave mirror.

We see that the reflected rays all pass through a point, called the focal point.

The correct answer must then be that they will be focused at the focal point.

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

The radius of curvature of a concave mirror is 5 cm. Which one of the following sentences correctly describes the focal length?

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

### Answer

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

The distance from the back of the mirror to the focal point is half the distance from the back of the mirror to the center of curvature, 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.

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

### Key Points

• A concave 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 concave mirror is on the same side of the mirror as the side that reflects light rays.
• Light rays reflected from a concave mirror focus at a point called the focal point of the mirror.
• The distance from the focal point of a concave mirror to the back of the mirror is half the distance from center of curvature to the back of the mirror.

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