Chapter 10.3, Problem 1cT

Observers at M and N arc looking at an image of the pin in the mirror.

1. Suppose that all but a small portion of the mirror were covered as shown at right.

How, if at all, would this change affect what the observers at M and N see? Explain.

Determine the region in which an observer must be located in order to see an image of the pin. Discuss your reasoning with your partners.

Would two observers at different locations in this region agree on the approximate location of the image? Explain.

2. Suppose that all but a small portion of the mirror near the center were covered, as shown at right.

Determine the region in which an observer must be located in order to see an image of the pin.

Would two observers at different locations in this region agree on the approximate location of the image? If so, find the approximate image location. If not, explain how you can tell.

Check your answers experimentally.

While the image location is independent of observer location in certain cases (e.g., Plane mirrors), in general it is not. In many cases, however, it is possible to identify a limited range of locations for which the image location is essentially independent of the observer location. An example is when both the object and the observer lie very nearly along the axis of a cylindrical or spherical mirror. In this situation, all rays are said to be paraxial, that is, they make small angles with the axis of the mirror. Ray diagrams often specify the location of an image but not the observer’s location. For such a diagram, it should be assumed that the image location is independent of the observer’s location.