P22.  Ray Tracing and Image Formation in Plane Mirrors

While this is an exercise in ray tracing and image formation in plane mirrors, the principles and methods apply to curved mirrors also.  Here are the main things to remember.

  1. Light rays travel in straight lines.

  2. The law of reflection governs what path a ray of light will take from an object point to the eye of the observer.

  3. If the reflected ray is extended behind the mirror, the light from the object appears to come from a point on this extension.

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

  1. 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 coming to our eyes from what we're looking at.  (There was a time when people thought that they saw by emitting light from their eyes.)

  2. 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:

  1. 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.

  2. The object is represented by a red arrow.  An arrow is used to distinguish the two ends of the object.

  3. 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.

  4. In a similar way, two rays drawn from the tip of the object are used to locate the corresponding image point.  For a line object, it is sufficient to locate the image points of the two ends of the line.

  5. 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 type of image (real or virtual), orientation (inverted or upright), and size (reduced, unchanged, enlarged).  For the example shown, 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 the same size as the object.  For a single plane mirror, the image will also be upright.  For the configuration you're about to investigate, however, you'll find that the image is inverted.  The configuration is that of two plane mirrors placed at right angles to each other.  Example 26-2 is about this situation.  Examine that example now.  Note that when an incident ray bounces off both mirrors, the outgoing ray is parallel to the incident ray.  This fact may aid you in the construction you're about to do.

Click here to open the template for the construction.  Print it in landscape orientation.  You'll draw your construction on the print.  One ray is already traced for you.  You need to select rays that reflect from both mirrors.  The reflected ray that you extend backwards behind the mirror is the second reflected ray.  Go ahead now and construct three other rays in order to determine the locations of the tip and tail of the image.  Use a straight edge and be sure to make your incident and reflected rays obey the law of reflection.  When you extend reflected rays behind the mirror, line your straightedge up carefully with the reflected ray.  If you're careful, you'll get good results.  However, a small deviation in angle can result in large errors.  By the way, you don't need a protractor in order to get angles equal.  Just count squares in the rise and run of a line.  Be sure to add arrows to the rays.

When you're finished, you should see that the image is inverted.  This is an interesting thing to test if you have two mirrors that you can hold at right angles.  First try a single mirror.  Hold your hand in front of the mirror and note how the orientation of your hand compares to its image.  Then try the same thing with two mirrors at right angles.  In this case, it's important to view from a position where you're looking into the intersection of the mirrors rather than at one mirror or the other.  Another thing to try is to hold written material up to the mirrors.  You'll be able to read it normally.

Fax your construction when done.