Diagrams for Convave Mirrors - Case A
Located Beyond the Center of Curvature
Ray diagrams are useful diagrams for determining the location of an image
as produced by a concave mirror. To determine the location of an image using a
ray diagram, at least two sets of incident and reflected rays must be
constructed for strategic positions on the object. The image of an object is
the location where light rays from that object intersect upon reflecting from a
mirror. By constructing at least two sets of incident and reflected rays, this
image location can easily be found.
If the object is represented by an arrow, then it is common practice to
pick the two extreme positions (the top and the bottom of the arrow) as
starting points for the incident and reflected rays. Ray construction will
result in the determination of the image locations for these two extreme
positions on the object. The complete image is merely an arrow connecting these
two image locations. This task is further simplified if the object is
positioned as an arrow standing upon the principal axis of the mirror.
If this is the case, then the image will be standing upon the principal
axis of the mirror (and either inverted or upright).
Of all the rays which emanate from the top of the object arrow and are
incident to the mirror, there are two rays whose behavior at the mirror surface
can be easily predicted. These are the two incident rays which are used in the
ray construction. One of the rays moves parallel to the principal axis and
reflects through the focal point. The second ray passes through the focal point
on the way to the mirror and reflects parallel to the principal axis. All
concave and convex mirror ray diagrams can be constructed from knowledge of the
behaavior of these two rays.
In the animation above, a right-side-up object is located above the
principal axis at a position beyond the center of curvature (C). The ray
diagram shows that the image of this object is located as an upside-down image
positioned between the center of curvature (C) and the focal point (F). In
fact, it can be generalized that anytime the object is located beyond the
center of curvature, the image will be located somewhere between the center of
curvature and the focal point. In such cases, the image will be inverted and
reduced in size (i.e., smaller than the object). Such images are characterized
as a real images because they are formed by the actual convergence of
reflected light rays at the image location. Real images are always formed on
the same side of the mirror as the object.