The
ray tracing rules that we have described in previous topics specify the size
and position of an image in any position relative to a lens or mirror. However,
these rules do not tell the whole story when the image formed by one lens is an
object for a second lens. This situation arises in telescopes, compound
microscopes, etc.
To
illustrate the problem, consider the lens configuration of a compound
microscope (see Topic
39. The Compound Microscope). The
objective lens forms a real and inverted image of the object as shown in the
following figure.
All of the rays from any point on the object are focused at the
same point on the image. If there were
a screen or some other target at the position of the image then all of these
rays really would strike the target at that position, and the intensity of
light striking any point would be given by the sum of the intensities of all of
these rays.
However, if there is no physical target at the image plane, then
while the rays still converge to a single point in the image plane, there is
nothing there for them to hit and they continue traveling in straight lines.
In
the figure above, the red rays, which come from the top of the first object, converge
to a point in the image plane as shown. However, if this is the image formed by
the objective lens of a microscope or telescope, then there is no screen there.
Instead, that image is the object for the second eye-piece lens. However, after
converging to the point as shown, the red rays continue to travel in straight
lines and never strike the second eye-piece lens. In other words, even though
the objective lens formed an image of the tip of the original object, that point
is not visible through the second lens since no rays from that point can ever
strike it. Points on the original
object closer to the axis can be seen through the second lens, as shown by the
purple rays. This point on the original object can be seen through the eye-piece,
since rays from the original object reach the eye-piece.
There
are obviously intermediate points on the original object between the source of
the purple rays, which has all of
its rays striking the eye-piece lens, and the source of the red rays, which has
none of the rays striking the eye-piece lens. For these intermediate
points, some of the rays strike the eye-piece lens and so these points
are visible but are not very bright. The bottom line is that the brightness of
the image seen through the final eye-piece lens gradually gets dimmer for object
points further and further from the axis, and there are points on the object
which cannot be seen at all through the eye-piece lens.
The
solution to this problem is to use a field lens, which is another positive lens
located between the objective and the eye-piece as shown in the following
figure.
There
are a number of different designs for the strength and position of the field
lens, but the general idea is always the same. The field lens bends rays that would
miss the eye-piece lens (or the next lens in a multiple lens system) back towards
the axis, so that they pass through the next lens instead of continuing off
into space. As an example, the effect of the field lens on the red rays is shown
in the figure.
On
page 176, the text shows the field lens located exactly where the intermediate image
would be formed if it were not present, but this is not always true. (If you
are interested in this, look at the Hugyens and Ramsden designs for field lenses
in a microscope).
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