Ray
Diagrams for Convave Mirrors - Case A
Object Located Beyond the
Center of Curvature
A GIF Animation
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.
For more information on the ray nature of light, visit
The
Physics Classroom. Specific information is available there on the
following topics:
This page was created by
Tom
Henderson of
Glenbrook South
High School.
Comments and suggestions can be sent by e-mail to
Tom
Henderson.
A hearty thanks is due to lab assistant Bryce Mautner for her
assistance with the graphics and GIF animation.
This page last updated on 8/11/98.