Convex Mirrors
Lesson 3 focused on the reflection of light by concave
mirrors and on the formation of images by this reflected light. In that lesson,
it was shown that concave mirrors can produce both real and virtual
images, depending upon the object location. In Lesson
4, we will follow a similar pattern of inquiry for convex mirrors:
investigating how convex mirrors reflect light and produce images. We will also
investigate how ray diagrams can be used to estimate image location, size,
orientation, and type for objects placed in front of convex mirrors. Finally,
we will use the mirror equation to calculate numerical information about image
distance and size if given an object distance, object size and focal length.
The diagram at the right depicts a convex mirror. In Lesson 3, a convex mirror was described as a portion of a sphere that had been
sliced away. If the outside of the sphere is silvered such that it can reflect
light, then the mirror is said to be convex. The center of that original sphere is known as the center of curvature (C) and the line that passes from
the mirror's surface through the sphere's center is
known as the principal axis. The mirror has a focal point (F) that is located
along the principal axis, midway between the mirror's surface and the center of curvature. Note that the center of curvature and the focal point are located on
the side of the mirror opposite the object - behind the
mirror. Since the focal point is located behind the
convex mirror, such a mirror is said to have a negative focal length value.
A convex mirror is sometimes referred to as a diverging mirror due to
the fact that incident light originating from the same point and will reflect
off the mirror surface and diverge. The diagram at the right shows four
incident rays originating from a point and incident towards a convex mirror.
These four rays will each reflect according to the law of reflection. After
reflection, the light rays diverge; subsequently they will never intersect on
the object side of the mirror. For this reason, convex mirrors produce virtual
images that are located somewhere behind the mirror.
Throughout this unit on Reflection
and the Ray Model of Light, the definition of an image
has been given. An image is the location in space where it appears that
light diverges from. Any observer from any position who is sighting along a
line at the image location will view the object as a result of reflected light.
Each observer sees the image in the same location regardless of the observer's
location. As the observer sights along a line, a ray of light is reflecting off
the mirror to the observer's eye. Thus, the task of determining the image
location of an object is to determine the location where reflected light
intersects. The diagram below shows an object placed in front of a convex
mirror. Light rays originating at the object location are shown approaching and
subsequently reflecting from the mirror surface. Each observer must sight along
the line of a reflected ray to view the image of the object. Each ray is
extended backwards to a point of intersection - this point of intersection of
all extended reflected rays is the image location of the object.
The image in the diagram above is a virtual image. Light does not actually pass through the image
location. It only appears to observers as though all the reflected light from
each part of the object is diverging from this virtual image location. The fact
that all the reflected light from the object appears to diverge from this
location in space means that any observer would view a replica or reproduction
when sighting along a line at this location.
Of course to determine the image location, only a pair of
incident and reflected rays need to be drawn. It is customary to select a pair
of rays that is easy to draw. Of the five pairs of incident and reflected rays
in the diagram above, two correspond to the rays that are customarily drawn. In
fact, they may closely resemble the two rays that were used in concave mirror
ray diagrams. Recall from Lesson 3 that there were two rules of
reflection for concave mirrors. They are:
· Any
incident ray traveling parallel to the principal axis on the way to a concave
mirror will pass through the focal point upon reflection.
· Any
incident ray passing through the focal point on the way to a concave mirror
will travel parallel to the principal axis upon reflection.
The revised rules can be stated as follows:
· Any
incident ray traveling parallel to the
principal axis on the way
to a convex mirror will reflect in such a manner that its extension will pass
through the focal point.
· Any
incident ray traveling towards a convex mirror such that its extension passes
through the focal point will reflect and travel
parallel to the
principal axis.
In the diagram above, the second and
third (from the top) blue incident rays exemplify these two rules of reflection
for convex mirrors. Using this pair of incident and reflected rays will greatly
simplify the task of drawing ray diagrams and determining the location of images.
In the next section of this Lesson, such ray
diagrams will be shown.