For such
optical system there is an equation: 1/d_{1} + 1/d_{2} = 1/f_{R}
(2.1)
d_{1} . d_{2} = f_{R}.d_{1}  f_{R}.d_{2}
(2.2)
For extendending factor of focal reducer
lentgh there is:
F_{E}
= d_{2} / d_{1}
(2.3)
So from (2.2) and (2.3) there is:
F_{E} = 1  d_{2} / f_{R} (2.4)
F_{E} = f_{R} / (f_{R} + d_{1}) (2.5)
The result focal length
of telescope with objective with f_{O}
is:
f = f_{O} . F_{E} = f_{O} . (1  d_{2} / f_{R}) (2.6)
If reducing factor of
focal reducer is N (thus F_{E}
= N), then
d_{2} = (1  N) . f_{R} (2.7)
d_{1} = (1/N  1) . f_{R} (2.8)
For given lens with f_{R} (and d2 calculated according to
2.7) the next equation can be useful:
d_{1} = f_{R}.d_{2} / (f_{R}  d_{2}) (2.9)

Distance between CCD position in
prime focus and CCD position in focus with focal
reducer is Dd:
Dd = d_{1}  d_{2}
= d_{2} / N  d_{2} = d_{2} . (1/N  1)
As d_{2}
= l_{R}
(l_{R}
is distance between focal reducer lens and CCD),
then
Dd = l_{R} . (1/N  1) (2.10)
Using (2.9) we get:
Dd = l_{R}^{2} / (f_{R}  l_{R}) (2.11)
