Image Characteristics for Concave Mirrors
Previously in Lesson 3, ray diagrams were constructed in
order to determine the general location, size, orientation, and type of image
formed by concave mirrors. Perhaps you noticed that there is a definite
relationship between the image characteristics and the location where an object
placed in front of a concave mirror. The purpose of this portion of the lesson
is to summarize these object-image relationships - to practice the L•O•S•T art of
image description. We wish to describe the characteristics of the image for any
given object location. The L of L•O•S•T represents
the relative location. The O of L•O•S•T represents
the orientation (either upright or inverted). The S of L•O•S•T represents
the relative size (either magnified, reduced or the same size as the object).
And the T of L•O•S•T represents the type of image (either real or
virtual). The 
best means of summarizing this relationship between object location and
image characteristics is to divide the possible object locations into five
general areas or points:
· Case 1:
the object is located beyond the center of
curvature (C)
· Case 2:
the object is located at the center of
curvature (C)
· Case 3:
the object is located between the center of
curvature (C) and the focal point (F)
· Case 4:
the object is located at the focal point (F)
· Case 5:
the object is located in front
of the focal point (F)
Case 1: The object is located beyond C
When the object is located at a location beyond the center of curvature, the image will always be located
somewhere in between the center of
curvature and the focal point. Regardless of exactly where the object is
located, the image will be located in the specified region. In this case, the
image will be an inverted image. That is
to say, if the object is right side up, then the image is upside down. In this
case, the image is reduced in size; in other
words, the image dimensions are smaller than the object dimensions. If the
object is a six-foot tall person, then the image is less than six feet tall.
Earlier in Lesson 2, the term magnification was
introduced; the magnification is the ratio of the height of the image to the
height of the object. In this case, the absolute value of the magnification is
less than 1. Finally, the image is a real image. Light rays actually converge
at the image location. If a sheet of paper were placed at the image location,
the actual replica of the object would appear projected upon the sheet of paper.
Case 2: The object is located at C
When the object is located at the center of
curvature, the image will also be located at the center of
curvature. In this case, the image will be inverted (i.e., a right side up
object results in an upside-down image). The image dimensions are equal to the
object dimensions. A six-foot tall person would have an image that is six feet
tall; the absolute value of the magnification is equal to 1. Finally, the image is a real image. Light rays actually
converge at the image location. As such, the image of the object could be
projected upon a sheet of paper.
Case 3: The object is located between C and F
When the object is located in front of the center of curvature, the image will be located beyond the center of curvature. Regardless of
exactly where the object is located between C and F, the image will be located
somewhere beyond the center of
curvature. In this case, the image will be inverted (i.e., a right side up object
results in an upside-down image). The image dimensions are larger than the
object dimensions. A six-foot tall person would have an image that is larger
than six feet tall; the absolute value of the magnification is
greater than 1. Finally, the image is a
real image. Light rays actually converge at the image location. As such, the
image of the object could be projected upon a sheet of paper.
Case 4: The object is located at F
When the object is located at the focal point, no image is formed. As
discussed earlier in Lesson 3, light rays from the same
point on the object will reflect off the mirror and neither converge nor
diverge. After reflecting, the light rays are traveling parallel to each other
and do not result in the formation of an image.
Case 5: The object is located in front of F
When the object is located at a location beyond the focal point, the
image will always be located somewhere on the opposite side of the mirror.
Regardless of exactly where in front of F the object is located, the image will
always be located behind the mirror. In this case, the image will be an upright image. That is to say, if the object is right side up, then the image will
also be right side up. In this case, the image is magnified; in other words, the image dimensions are greater than the object
dimensions. A six-foot tall person would have an image that is larger than six feet
tall; the magnification is greater than 1.Finally, the
image is a virtual image. Light rays from the same point on the object reflect
off the mirror and diverge upon reflection. For this reason, the image location
can only be found by extending the reflected rays backwards beyond the mirror.
The point of their intersection is the virtual image location. It would appear
to any observer as though light from the object were diverging from this
location. Any attempt to project such an image upon a sheet of paper would fail
since light does not actually pass through the image location.
It might be noted from the above descriptions
that there is a relationship between the object distance and object size and
the image distance and image size. Starting from a large value, as the object
distance decreases (i.e., the object is moved closer to the mirror), the image
distance increases; meanwhile, the image height increases. At the center of curvature, the object distance equals the
image distance and the object height equals the image height. As the object
distance approaches one focal length, the image distance and image height
approaches infinity. Finally, when the object distance is equal to exactly one
focal length, there is no image. Then altering the object distance to values
less than one focal length produces images that are upright, virtual and
located on the opposite side of the mirror. Finally, if the object distance
approaches 0, the image distance approaches 0 and the image height ultimately
becomes equal to the object height. These patterns are depicted in the diagram
below. Nine different object locations are drawn and labeled with
a number; the corresponding image locations are drawn in blue and labeled with the identical number.
Check Your Understanding
1. Compare and contrast the images formed by concave and
plane mirrors.
Plane mirrors always produce virtual images which are upright
and located behind the mirror; they are always the same size as the object
Concave mirrors
can produce both real and virtual images; they can be upright (if virtual) or
inverted (if real); they can be behind the mirror (if virtual) or in front of
the mirror (if real); they can also be enlarged, reduced, or the same size as
object.
2. Identify the means by which you can use a concave and/or a
plane mirror to form a real image.
Only a concave mirror can be used to produce a real image; and
this only occurs if the object is located at a position of more than one focal
length from the concave mirror.
Plane mirrors
never produce real images.
3. Identify the means by which you can use a concave and/or a
plane mirror to form a virtual image.
A
plane mirror will always produce a virtual image. A concave mirror will only
produce a virtual image if the object is located in front of the focal point.
4. Identify the means by which you can use a concave and/or a
plane mirror to produce an upright image.
A plane mirror
will always produce an upright image. A concave mirror will only produce an
upright image if the object is located in front of the focal point.
close
5. Identify the means by which you can use a concave and/or a
plane mirror to produce an inverted image.
Only a concave mirror can be used to produce an inverted image;
and this only occurs if the object is located at a position of more than one
focal length from the concave mirror.
Plane mirrors
never produce inverted images.
6. Are all real images larger than the object?
No. Real images
can be larger than the object, smaller than the object, or the same size as the
object.
7. The famous Chinese magician, Foo Ling Yu, conducts a
classic magic trick utilizing a concave mirror with a focal length of 1.6 m.
Foo Ling Yu is able to use the mirror in such a manner as to produce an image
of a light bulb at the same location and of the same size as the actual light
bulb itself. Use complete sentences to explain how Foo is able to accomplish
this magic trick. Be specific about the light bulb location.
Foo Ling Yu has
probably placed the object at the center of
curvature - a distance of 3.2 meters from the mirror. When Foo does this, a
real image is formed at the same location and of the same size.