A real image is produced on a screen
(or some other detector) when all of the rays from a single point on an object
strike a single point on the screen. The intensity distribution on the screen
is a reproduction of the intensity distribution emitted by the object. The
image may be smaller or larger; it may be erect or inverted – it is the
one-to-one relationship between the image and the object that is important.
A virtual image is produced when rays
of light reach our eyes that appear to come from a real object, but there is in
fact no object at the apparent source of the light. The most common example is
when light from an object strikes a simple plane mirror. The reflected rays
appear to come from an identical object that is located behind the mirror. The
spatial distribution of rays is completely consistent with what we would see if
there really was an object behind the mirror. Note that we cannot actually
place a screen at the point where the image appears to be.
The law of reflection – that the angle
of incidence is equal to the angle of reflection, can be used to construct the
image from any object placed in front of a mirror. This construction is
relatively simple when the mirror is a single flat surface. A ray from object
point O that strikes the mirror results in a reflected ray that appears to be
coming from image point I. This construction is the same for every ray from O
that hits the mirror anywhere, so that there is a one-to-way relationship
between the points O and I. However, point I is behind the mirror, and is
therefore a virtual image. However, the
rays reflected by the mirror are completely consistent with those that would be
produced if there were a physical object at point I.
This construction can be completed for
any point on the object side of the mirror, so that the image space is an exact
reproduction of the points on the object side of the mirror. The reflected rays
preserve the size and shape of the object, so that the magnification (the ratio
of the size of the image to the size of the object) is always 1. The image
point I always appears to be the same distance behind the mirror as the object
point O is in front of it. The mirror has therefore reversed the coordinate axis
perpendicular to the plane of the mirror – object points that are further to
the left of the mirror in the figure below have image points that appear to be
further to the right in the virtual image.
If
the geometrical construction above is repeated for a point just above point O,
the resulting image point will be just above point I. Thus the mirror preserves
the vertical relationship between objects.
Also
note from the figure that it is possible to see the image of an object O even
if the mirror does not extend that far, since the reflected ray only uses a
higher point on the mirror. For example, if the object O is your shoe, then you
can see the reflection of your shoes with a mirror that is only one-half of
your height. (This point is discussed
in more detail in Topic
19. Field of View.)
Finally,
these constructions are exact – the image is a perfect replica of the object
(within the limits imposed by geometrical optics). This is the last time in our
study of mirrors and lenses that we will be able to say that.
In
addition to the single-mirror geometry shown above, there are a number of
useful configurations of two (or more) mirrors. Two of these configurations are
shown in the following diagrams:
1. Two parallel mirrors (or any two parallel
surfaces) produce an output beam that is offset in space but parallel to the
input:
2.
Two mirrors at 90 degrees (a “corner cube”) reflect a light beam back along its
direction of incidence, no matter what the direction was.
These
constructions are special cases of two mirrors that are tilted with respect to
each other. The output beam is offset by 360 degrees minus twice the tilt
angle.
In general, if a mirror is tipped by some angle, then both the angle of incidence and the angle of reflection change by this tip angle. The angle between the incident and reflected beams therefore changes by twice the tilt angle.