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Our choice and reasons for the
optics we used in our replicas
and discussion on how this
impacts other dimensions of the
telescope:
Conflict in the modern
measurements of the exiting
lenses at IMSS:
One of the many departures often
made in building replicas of
Galileo telescope is to
compromise in the focal lengths
and the shapes of the lenses.
The objective lens in Galileo's
# IMSS 2428 telescope have been
reported in the literature to be
98.0 cm in one case by Greco et
al in 1992 and 95.6 cm as
measured by Ronchi in 1923,
(please see our references).
Using either of these focal
lengths requires nonstandard
focal lengths which cost
hundreds of dollars more as
compared with the much cheaper
standard of one diopter or 100
cm. Use of the less expensive
lens leads to a domino affect of
compromises.
a)
It changes the over all length
of the telescope by almost an
inch.
b)
This in turn alters the location
and size of the gilt decorations
on the body of the telescope.
c)
It also changes the optical
power!
Where does it stop? If these
telescopes are to be used to
tell the powerful story of the
Galileo telescopes and teach
people how science works, then
to be trustworthy, we must
follow the first basic rule of
science: accurate repeatable
testable measurements. This
must also apply to our
replication of the dimensions
and characteristics in building
this symbolic telescope!
Our final choice for the
objective lens:
We used a plano convex lens as
in the original and chose the
1992 Greco et al 980mm
focal length rather than the
1923 value of 956 mm by Ronchi
et al. There are three reasons
for this decision.
1st. The overall
length of the body of the
telescope is too long to focus
the telescope at infinity using
a 956 mm objective with an
eyepiece of 5 cm focal length.
To accommodate this objective,
the eyepiece would have to have
a considerably shorter focal
length resulting in powers
greater than 20.(see below on in
this web site for how to
determine the over all length)
2nd. If one takes
the refractive index of Ronchi's
calculation and his measured
radius of curvature
one calculates the focal length
to be 980mm rather than
956mm suggesting an
inconsistency within the data of
the reference.
3rd. Greco, et al
measured 980 mm. Since He etal had the benefit of Ronchi’s
measurements because he
references Ronchi and his
was different we feel that
it can be safely assumed he
would have checked his data to
be sure his measurements were
correct to
reconcile any differences for
the earlier measurement.
Based on these reasons we chose
a 980 mm focal length for the
plano convex lens for the
objective of our replica.
The Eyepiece.
The current lens in the leather
covered telescope IMSS 2428
located in Florence, Italy, is
not the Galileo original. It is
estimated that the original
eyepiece was lost some time
during the eighteenth century.
We used the same focal length
as is reported for the original
today, based on our arguments of
telescope length and our own
measurements as described
below. However for the shape we
made an independent decision to
use a plano concave
eyepiece instead of the
biconcave lens as is presently
used in the current telescope.
We offer three rational for
this decision.
1st. The original
objective of the telescope is
plano and the second, longer
paper covered Galileo telescope,
IMSS 2427, uses a plano convex
lens for the eyepiece.
2nd. There is a fair
consensus that Galileo made a
number of his own lenses, and it
would have been easier and
faster for Galileo to make the
simpler plano-concave lens.
He’d have only had to grind and
finish one rather two surfaces.
Grinding is faster than
polishing and he would have had
only one surface to polish.
3rd There are significantly
fewer problems going the plano
concave route - problems like
getting the two radii lined up
etc. which, in our opinion,
Galileo would have certainly
known about from his
experiments.
Of course if our choice is
incorrect, it is simple to
change the eyepiece lens to a
concave-concave configuration.
The overall length of the
telescope is determined by the
optics:
There is an inconsistency in the
length of the IMSS #2428
telescope as we measured it and
as reported in the literature.
It is reported that the length
of the telescope is the same as
the focal length of the
objective, namely 98cm. This
does not leave room for the
eyepiece when focused on distant
objects.
Total length of a telescope
focused for infinity = Focal
length objective + Focal length
eyepiece + lens holder over
hangs.
NOTE the overall length will
vary, of course, depending on
how far the lenses have been
extended for focusing. It
appears that both the
objective lens holder and the
eyepiece lens holder can be used
to extend the optical length for
terrestrial focusing (see figure
9). This “draw” distance may be
about 10 cm each or 20 cm for
both lens tubes combined.
The present telescope at IMSS
has an objective that is plano
convex with a focal length of
980 mm and a diameter of 37mm.
The eyepiece is biconcave with a
focal length of -47.5mm and a
diameter of 22mm.
Therefore the optical length of
the telescope for an object at
infinity would be the sum of the
focal lengths, namely:
(980 -47.5) =
932.5
mm. Add 12 mm for the lens
holder over hangs = 944.5 mm
overall
This is the calculated value for
the overall length of the IMSS
telescope when both lens tubes
are fully inserted for viewing
at infinity. We have measured
the scope at IMSS (with the
apparatus described earlier and
a video showing its operation)
to be 945 + or - 5mm. It
appeared that both tubes were
fully inserted when we made our
measurement.Our best guess at
present is that it can open 20
cm more giving a maximum length
of 1145 mm for focusing on
nearby objects.
The catalog of early telescopes
by Albert Van Helden, page 30
lists the telescope's overall
length as 980 mm which is off by
about 35 mm or nearly 1 3/8 of
an inch different according to
our measurements. |
