Using Ray Diagrams
to Locate Images
version of this page]
Images of Objects Far From the Mirror
Suppose we place some object in front of a concave mirror. Light
will bounce off the object in all directions if it is a diffuse
reflector or be produced by it in all directions if it is a candle or
a light bulb. Some of this light will strike the concave mirror and
reflect from it according to the Law of Reflection. In order to
locate any image produced by the mirror, you do not have to trace the
paths of an arbitrary number of rays - the
three rays discussed on the preceding page will do!
Suppose we place an object in front of a concave mirror, with the
bottom of the object resting on the axis of the mirror, at a distance
greater than the radius of curvature from the mirror. In order to
locate the image:
- Draw a ray that leaves the tip of the object, travels parallel
to the axis, strikes the mirror, and is reflected through the
focus of the mirror. Notice that if you were looking back along
this ray toward the mirror, you would see the image (reflection)
of the tip of the object in the mirror.
- Draw a ray that leaves the tip of the object, travels through
the focus of the mirror, strikes the mirror, and is reflected
parallel to the axis. Again, if you would look back along this ray
toward the mirror, you would see the image of the tip of the
object in the mirror.
- Draw a ray that passes through the center of curvature of the
mirror and the tip of the object. It is reflected straight back
along its original path.
So where is the image of the tip of the object? A little (well,
maybe a lot of ...) thought should convince you that the only place
that the image can be is at the point of intersection of the three
rays! Notice that this image is IN FRONT OF THE MIRROR! The
image is inverted (upside down), and, in this case, smaller than the
object. It is called a real image.
Where is the rest of the image? If you trace a ray that leaves the
bottom of the object (on the axis), travels down the axis, strikes
the mirror, and is reflected back along the axis, you will see that
the bottom of the image must also be located on the axis of the
mirror as shown in the diagram above. You can also draw the three
rays for other points on the object.
Locating an image in this way is called drawing a ray
diagram or ray tracing. It is a very common procedure in
elementary optics. Notice that the ray diagram not only tells us the
location of the image, but also its size and orientation (right-side
up or upside down). This makes a ray diagram a very convenient and
An Object Between the Focus and the Mirror
If the object is closer than one focal length from the mirror,
something surprising happens. As shown in the diagram, the object
produces an upright, enlarged, virtual image behind the mirror!
Converging mirrors can produce both real and virtual images!
version of this page]
last update October 21, 1998 by JL