Biomedical Engineering Reference
In-Depth Information
Appendix A: Entrance
and Exit Pupils of Telescopes
In Chapter 12, we learned that an optical system's
entrance pupil
limits the
amount of light
entering
the system. The entrance pupil can be a real aperture or
an image of one. For a Galilean telescope, there are two possibilities: the objective
lens or the image of the eyepiece as seen when looking through the objective. Let's
do some calculations to determine which it is.
The first step is to locate the image of the eyepiece as seen through the objective
and to determine its size. Figure A-1A shows a Galilean telescope viewed from the
objective lens side of the telescope. We'll assume that both the objective and eye-
piece have a diameter of 1.5 cm. Since the objective has a power of
+
10.00 D and
eyepiece a power of
25.00 D, when focused for infinity the tube length is 6.0 cm.
We can use the vergence relationship to locate the image of the eyepiece as seen
through the objective as follows:
L
′
=
−
L
+
F
100
⎛
⎝
⎞
⎠
′
=
L
+
10.00 D
= −
6.67 D
−
6.00 cm
n
L
′
l
=
′
100
′
=
l
= −
15.00 cm
−
6.67 D
The objective forms a virtual image of the eyepiece that is located 15.00 cm to
the left of the objective. What is the size of this image? We calculate magnification
as follows:
l
−
l
M
=
15.00 cm
−
M
=
=
2.50
×
6.00 cm
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