Finally, in Concept 6, we show the image as determined by the convergence point of the virtual rays. The image formed is upright, smaller than
the original object, and virtual. Note that this is the only possible result for a convex mirror.
This ray-tracing diagram can be used to explain why security and automobile passenger-side mirrors are often convex. The mirror forms
viewable images when the corresponding objects extend quite far above (or below) the principal axis, providing a very wide field of view. As
you know, mirrors like this, typically used on the passenger side of vehicles, are often labeled with safety warnings that state, “Objects in mirror
are closer than they appear.”
However, if you look at concept 6, you will note that the object is actually fartherfrom the mirror than the virtual image is, and this is always true
for images formed by a convex mirror. So are the warnings wrong? No, the convex mirror’s virtual image is always smaller than the image that
would be produced by a planar mirror. Since the human brain relates size to distance, the image appears distant: We do interpret the object as
being farther away than it really is.
Image
Upright, smaller, virtual
31.14 - Interactive problem: image in a convex mirror
Here you use an interactive simulation to view the image produced by a convex
mirror. You drag the object farther from and closer to the mirror and observe its
image. You can turn on ray tracing with the SHOW RAYS button, and see how the
rays can be used to determine the location of the image.
Some questions to consider include: Is the image ever inverted? Is it ever larger
than the object? Is it ever real? Is it ever farther from the mirror than the object is?
The object can be moved to positions that allow you to answer all these questions.
31.15 - Mirror equations
In this section, we discuss several equations used to determine the nature of images produced by mirrors. Before doing so, we will review and
explain the mathematical sign conventions used in these equations.
Some of the notation we have already introduced: d is used for distance, f for focal length, and h for height. More specifically, do represents
the distance of the object from the mirror and di the distance of the image from the mirror. Also, ho is the height of the object and hi is the
height of the image.
With a single mirror, the object distance is always positive, although it can be negative in the more complex optical systems discussed below.
The image distance is positive when the image is real, on the same side of the mirror as the object from which the image is created. The image
distance is negative when the image is virtual, on the opposite side of the mirror. Remember that the focal length is positive for concave mirrors
and negative for convex mirrors. The image height is positive for upright images and negative for inverted ones.
The magnification, represented by m, equals the image height divided by the object height. When the magnification is positive, the image is
upright; when it is negative, the image is inverted relative to the object. Sometimes, the magnification as defined here is called lateral
magnification to make it clear that it represents the change in height. When m is greater than one, then the image is larger than the object:
Variables in the mirror equations
Interpretation of signs