Project Cyclops, A Design... - Department of Earth and Planetary ...

APPENDIX
I
CASSEGRAINIAN
GEOMETRY
Consider the paraboloidal primary mirror with its
vertex at V and its focus at F as shown in Figure I-1. The
equation of its surface is
2/ f
r - - (I1)
1 + cos 0 ) cos 2(01/2)
where f is the focal length FV. The diameter of the
paraboloid included by the cone of rays of half-angle 0
is d = 2r sin 01, so
d sin01 01
--- - tan- (I2)
4f 1 + cos01 2
If an isotropic radiator radiating I W/sr is placed at F,
the flux reflected off the parabola will be:
V ....
\\
\ \
\ \
J
_J..1___--lez_ __ _.
! I v'L i vl'
/
/
/
/
/
/
/
/
/
rl
-\
\
\
\
r2 f2 f2 c°s2 2 (13)
Now assume that a hyperbolic secondary mirror is
introduced with its vertex at V1. Received energy will
now be broughl to focus at F'. If we let 1he distance
OV = OV' = a, then OF = OF' = ea where e is the
eccentricity of the hyperboloid. Thus the focal distancc
FI:_ = f) = (e - l)a and the focal distance
F'V_ = J'2 = (e + 1)a. The magnification is
f2 e+l
m - - 04)
f_ e- 1
or, conversely,
Figure I-1. A Cassegrainian telescope.
m- I
(15')
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