Concave Mirrors
Student Extras
Visit The Physics Classroom's Flickr Galleries and enjoy a photo overview of the topic of reflection and mirrors.
Teacher's Guide
Looking for a lab that coordinates with this page? Try the Exploring Curved Mirrors Lab from The Laboratory.
Curriculum CornerLearning requires action. Give your students this sense-making activity from The Curriculum Corner.
Curriculum CornerPractice makes perfect with this diagramming activity from The Curriculum Corner.
Treasures from TPFNeed ideas? Need help? Explore The Physics Front's treasure box of catalogued resources on ray optics, including the topic of curved mirrors.
Spherical Mirror Model
Use this EJS simulation from Open Source Physics (OSP) to demonstrate principles of image formation by concave mirrors.
Spherical Mirror Model
Use this downloadable applet from Open Source Physics (OSP) to explore the concave mirrors.
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.
Watch It!
Check
Your Understanding
1. Compare and contrast the images formed by concave and plane mirrors.
2. Identify the means by which you can use a concave and/or a plane mirror to form a real image.
3. Identify the means by which you can use a concave and/or a plane mirror to form a virtual image.
4. Identify the means by which you can use a concave and/or a plane mirror to produce an upright image.
5. Identify the means by which you can use a concave and/or a plane mirror to produce an inverted image.
6. Are all real images larger than 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.