Lesson 4: Convex
Mirrors
Reflection and Image Formation for
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 demonstrated
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;
investigating how ray diagrams can be used to estimate image
location, size, orientation, and type for objects placed in
front of convex mirrors; and using 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 which 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 which passes
from the mirror's surface through the sphere's center is
known as the principal axis. The mirror has a focal point
(F) which 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 its ability to take light from a point and diverge
it. The diagram at the right shows four incident rays
emanating 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 which 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. Several rays of light emanating
from the object are shown approaching the mirror and
subsequently reflecting. Each observer must sight along the
line of the 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
indicates 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
the pair of rays which are easiest to draw. Of the five
pairs of incident and reflected rays in the diagram above,
two correspond to the rays which are customarily drawn. In
fact, they may closely resemble the two rays which 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 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 ray 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.
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