Ray Tracing and Image Formation in Plane Mirrors

Guide 26-1. Ray Tracing and Image Formation in Plane Mirrors

See Figure 26-6a (p. 873) in the text for an example of how ray tracing is used to locate the image of an object for a plane mirror. While every point of the object emits light rays in all directions, two rays are sufficient to locate the image point corresponding to each object point. In the figure, these rays are drawn in such a way as to reach the eye of the observer. Note that although the object in Figure 26-6a is parallel to the mirror, that is simply a special case. The object can have any orientation.

View this applet to see the image of an object constructed ray-by-ray. Once the image is constructed, you can then change position coordinates of the object to see the corresponding change in the rays and the image.

Although the rays in the applet and in Figure 26-6a are drawn in such a way as to reflect to the eye of the observer, any ray that is drawn from an object point and that reflects according to the law of reflection can be used to help locate the corresponding image point.

View this applet to see how to construct the image of the object without reference to an observer.

The principles to apply in drawing rays and images are the following:

Light rays travel in straight lines.
The law of reflection governs what path a ray of light will take from an object point to the eye of the observer.
If the reflected ray is extended backward behind the mirror, the light from the object appears to come from a point on this extension.

With those principles, rays can be traced and the positions of images determined. Here are also a few conventions to use when drawing rays.

Indicate with an arrow the direction of the incident ray from the object to the mirror and of the reflected ray from the mirror to the observer. The arrows indicate the direction that light travels. This is based on the known fact that we see because of light that reaches our eyes from what we're looking at.
Indicate with an arrow the direction from which the light seems to come from the image. Our optical processors seem to assume that light always travels in straight lines, even when its direction is changed through reflection.

With these things in mind, let's look at a ray tracing construction. Click here to open the construction in a new window. Here are things to note about the construction:

All the lines on the reflecting side are solid while those on the image side (back of the mirror) are dashed. A solid ray indicates the path of an actual light ray, while a dashed line is the path of an apparent light ray. Light appears to travel but doesn't actually travel to the observer along apparent rays.
The object is represented by a red arrow. An arrow is used to distinguish the two ends of the object.
At least two rays from each object point must be traced in order to find the corresponding image point. Note how the two blue rays diverge after reflecting, but their extensions behind the mirror converge. The point where they cross is where the light appears to come from. The observer, by the way, is not shown but would be in a position to see the reflected rays.
In a similar way, two rays drawn from the tip of the object are used to locate the corresponding image point. For a straight-line object, it is sufficient to locate the image points of the two ends of the line.
The choice of incident rays drawn from an object point is arbitrary as long as they strike the mirror surface. All corresponding reflected rays, when extended backward behind the mirror, will converge to a single point to within the accuracy of the construction.

Once the image is located, it's important to note its characteristics. These include i) the type of image (real or virtual), ii) the orientation (inverted or upright) of the image, and iii) the size (reduced, unchanged, enlarged) of the image. For the example shown above, the image is virtual, upright, and unchanged in size from the object. By virtual, we mean that light appears to come from the image but doesn't actually do so. Later, we'll find that curved mirrors can form real images where real light rays converge. By upright, we mean that the image has the same orientation as the object. Had the arrow tip been on the other end of the image, it would have been called inverted.

As it turns out, all images created by plane mirrors are virtual and are the same size as the object. For a single plane mirror, the image will also be upright.