In this explainer, we will learn how to draw diagrams of light rays interacting with convex mirrors.
Before starting to draw ray diagrams, it will be useful to first consider a convex mirror as a three-dimensional solid object.
A convex mirror is a hollow curved object, like a bowl.
The following figure shows a convex mirror and its optical axis.
The optical axis of a concave mirror is an imaginary line that passes through the point at the front of the mirror.
The optical axis of a spherical mirror is equidistant from surface of the mirror in every direction perpendicular to this axis. This means that the red and blue lines shown in the following figure are actually the same length.
If the mirror is viewed looking along the optical axis, it is clearer to see that the mirror is symmetrical around this axis.
An incident light ray can travel along the optical axis of the mirror. This is shown in the following figure.
We can see that an incident light ray that travels along the optical axis of the mirror will hit the point at the front of the mirror and be reflected back along its incoming path.
Only rays that travel along the optical axis of a convex mirror are reflected back along their incoming path. Any other path that a ray travels along results in the ray being reflected on a different path than its incoming path.
The following figure shows how we can represent a cross section of a convex mirror with a curve in a two-dimensional drawing.
The following figure shows light rays incident on a curve representing a convex mirror cross section.
Of the incident light rays shown, only the ray shown in pink will reflect along its incoming path. The rays shown in black will reflect along different paths to their incoming paths.
The following figure shows a magnified view of the part of the mirror where one of the rays shown in black hits the mirror.
We see that where the ray hits the mirror, there is a line normal to the surface of that point on the mirror.
The following figure shows the law of reflection determining how this incident ray would reflect from the mirror.
If we recall the law of reflection, the incident angle equals the reflection angle. Each of these angles is between a light ray and the line normal to the surface of the mirror.
Two incident rays traveling in different directions that hit the same point on the mirror are not reflected in the same direction. This is shown in the following figure.
Let us now consider the reflection of parallel incident rays.
We see that incident rays traveling in the same direction are reflected in different directions. The reflected rays diverge.
We can see that the distances between the reflected rays increase the farther they travel from the mirror.
This means that if we draw lines inside the mirror that extend from the reflected rays, the distances between these lines must decrease.
The following figure shows that these lines, when extended, meet at a point.
The point at which the extensions of these lines meet is called the focal point of the mirror.
Diverging light rays do not produce a real image that can be projected onto a screen. A human eye can, however, focus the diverging rays from a convex mirror. We say that a convex mirror produces a virtual image.
The figure below shows the image produced by a convex mirror.
The following figure shows how a virtual image is produced by a convex mirror.
We see that the image produced is smaller than the object.
We see that the incident light ray from the top of the object is reflected to become the reflected ray from the top of the image.
We also see that the incident light ray from the bottom of the object is reflected to become the reflected ray from the bottom of the image.
This means that the image is the same way up as the object.
If the object is placed very close to the mirror, the image will still be upright and smaller than the object. This is shown in the following figure.
Let us now look at two example questions.
Example 1: Identifying the Maximum Size of an Image Produced by a Convex Mirror
Can the image produced by a convex mirror be larger than the imaged object?
Answer
A convex mirror produces a virtual image. The top of the virtual image is at a point on a straight line that crosses the center of curvature of the mirror and the top of the object.
The image is closer to the center of curvature than the object, so the size of the image must be less than the size of the object. An image cannot be larger than the object.
Example 2: Classifying the Orientation of an Image Produced by a Convex Mirror
Can the image produced by a convex mirror be inverted?
Answer
A convex mirror produces a virtual image.
When this image is formed, the incident light ray from the top of the object is reflected to become the reflected ray from the top of the image. The incident light ray from the bottom of the object is reflected to become the reflected ray from the bottom of the image.
The object and image must be the same way up, so the image cannot be inverted.
Let us now summarize what has been learned in this explainer.
Key Points
- A convex mirror reflects parallel incident light rays so that these rays diverge.
- Reflected light rays from a convex mirror form a virtual image.
- The virtual image formed by a convex mirror is always smaller than the object.
- The virtual image formed by a convex mirror is always the same way up as the object.
