Mirrors and lenses present some unique problems as far as terminology and sign convention is concerned. The only way to be sure you have it all correct in your head is to work with the text or instructor notes you are using and work problems. On this page we will stick to some basics.

Images viewed in plane mirrors appear to be behind the mirror. This image is called a virtual image. The virtual image is the same distance behind the mirror as the real object is in front of the mirror.

Real images are ones where the light from the image really comes from the image. Virtual images are ones where the light appears to come from somewhere other than the image.

For spherically shaped mirrors the focus of the mirror is at one-half the distance to the center of curvature. Light rays from infinity are all reflected so as to pass through the focus.

The magnification of a mirror is defined as the image height over the object height. The magnification is also the image distance over the object distance with a negative magnification indicating the image is inverted.

The object distance, image distance and focus are related by

The location of images by drawing rays can be confusing if not approached in a logical manner. The following four rules should help in drawing images.

Rules for locating mirror images by drawing rays:

1. A ray initially parallel reflects through the focus.

2. A ray through the focus and to the mirror is then reflected parallel.

3. A ray reflected at the central axis does so symmetrically.

4. A ray through the center of curvature is reflected back along itself.

The application of these rules for drawing rays to locate mirror images is illustrated in the problems.

Additionally there is a sign convention for mirrors. The following rules will keep the signs correct.

Sign rules for mirrors:

1. f is positive if the center of curvature is in front of the mirror.

2. f is negative if the center of curvature is in back of the mirror.

3. o is positive for an object in front of the mirror.

4. o is negative for an object in back of the mirror.

5. i is positive if the image is in front of the mirror.

6. i is negative if the image is in back of the mirror.

These rules look to be a bit much to memorize, and they are. However as we will show in the problems, drawing the rays to locate images is a lot easier than it sounds. The same is true of determining whether the image is upright or inverted.

Lenses are either converging or diverging. Lenses formed by smoothing the surfaces of two prisms placed base-to-base are converging lenses. Rays from infinity are refracted on entrance and exit from the lens so that they are focused at one spot, the focus of the lens. Lenses formed by smoothing the surfaces of two prisms placed point-to-point are diverging lenses.

For lenses, real images are ones formed on the side opposite the object and virtual images are ones formed on the same side as the object. The same formula relating object and image distances and focus for mirrors is also valid for lenses. The ray drawing rules for locating images is different for lenses than for mirrors.

Rules for locating lens images by drawing rays:

1. A ray parallel on one side passes through the focus on the other side.

2. A ray through the focus will emerge parallel on the other side.

3. A ray through the center is not diverted.

The application of these rules for drawing rays to locate lens images is illustrated in the problems.

Additionally there is a sign convention for lenses. The following rules will keep the signs correct.

Sign rules for lenses:

1. f is positive for a converging lens.

2. f is negative for a diverging lens.

3. o is positive for an object in front of the lens.

4. o is negative for an object in back of the lens.

5. i is positive if the image is in back of the lens.

6. i is negative if the image is in front of the lens.

Again, do not be put off from mirror and lens problems by these rules. Locating and characterizing images is not as difficult as it at first seems.

More complete discussions of mirrors and lenses, including  more completely worked problems, are presented in the books How to Solve Physics Problems and Physics for the Utterly Confused. Review and ordering information, including sample pages, is available by following the links to either of these books. Alternatively, clicking on the appropriate icon will take you directly to our book at the online bookstore.