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What we have been considering is how an image of the Sun is seen in the
UNSILVERED part of a split horizon mirror. So the question of whether the
silvered part is at the front or back of the mirror, which Joel holds to be
important, is really of little relevance.

I think it's accepted (isn't it?) that from the clear, unsilvered part of
the horizon mirror some fraction of the sunlight incident on it from the
index mirror will be reflected by the glass surface into the telescope. And
in roughly equal amounts from the front surface and the back. The argument
put forward, which I wish to dispel, is that this would create two separate
light beams, displaced vertically by some amount that depends on the
thickness of the horizon glass, [and therefore to two separate images of
the Sun as seen through the telescope]. The only part of the argument that
I argue with is the final phrase, that I have put within square brackets.


Today we had a bright sunny morning, and the low Sun was shining brightly
on to my living-room windows, more-or-less broadside on. First, I shifted
the secondary glazing out of the way. Then, by swinging the window about
its vertical axis, I could change the angle of incidence of the sunlight,
to roughly match the angle at which light from the index mirror strikes the
horizon mirror (say 30deg from "normal" incidence).

Then, from outside the house, close to the glass, I observed the view of
the Sun as observed by reflection in that window from its two glass
surfaces combined. Even though it's only a small fraction of the sunlight
that is reflected in that way (most of the light passing straight through),
it's still bright enough to dazzle, and maybe damage, eyes. To look at the
Sun that way, you need VERY dark glasses. I used a shade from an old
sextant.

Question: what would you expect? Should I see two images of the Sun, of
roughly equal brightness, displaced by some fraction of the thickness of
the glass, or only one?

Answer: I saw a single image of the Sun. Even though about half the light
came from the back surface, and half from the front, the two images of the
Sun coalesced, and were quite undistinguishable.

But it depends somewhat on the quality of your window glass. If there is
any significant ripple, or non-uniformity, in your window glass, then you
will see two separate images of the Sun, that will dance about with respect
to each other, as you shift your viewpoint to force the reflection to occur
at different spots in the pane.

The house I live in, with its glazing, is over 40 years old now, but even
then, in Britain, the float-glass process, which was invented here, was
being used for domestic glazing. At earlier dates and perhaps in other
countries, window panes may be expected to show significant ripple.

But just try it and see if you agree with me.

Go back to the question of the sextant, now. I will restate what we are
arguing about. If others differ about the terms of the discussion, I hope
they will speak up.

"I think it's accepted (isn't it?) that from the clear, unsilvered part of
the horizon mirror some fraction of the sunlight incident on it from the
index mirror will be reflected by the glass surface into the telescope. And
in roughly equal amounts from the front surface and the back. The argument
put forward, which I wish to dispel, is that this would create two separate
light beams, displaced vertically by some amount that depends on the
thickness of the horizon glass, [and therefore to two separate images of
the Sun as seen through the telescope]. The only part of the argument that
I dispute is the final phrase, that I have put within square brackets."

I fully accept Bill Arden's $0.02 analysis of the amount of the parallel
displacement between the two reflections of a beam of light from a slab of
glass. What I will argue is that this makes no difference at all to the
observed image.

Here's the point. Parallel rays of light, incident on the objective glass
of a telescope, are brought to a focus at a single point, no matter which
part of the objective they enter. And when seen through the eyepiece, they
all appear to be coming from the same direction, from a particular point in
the sky. You can block off part of the objective, the top or the bottom,
with a bit of black tape, and it will make no difference (except to the
brightness, and perhaps a bit to the resolution). Ken Muldrew himself
argues that when he blocks off part of the lens with his finger, it affects
only the brightness of the image, nothing else.

Even if you collimate the light falling on the telescope to a narrow pencil
with a pinhole, the image will be the same, but dimmer. And then, moving
that light-pencil about on the objective by shifting the pinhole, it will
make no difference. What IS important is that the ANGLE of the parallel
light beam remains unaltered. And so, it's clear that any vertical
displacement between light-rays leaving the front surface and the back
surface of the clear part of the horizon mirror won't have the slightest
effect on the image seen through the eyepiece. The two will combine
imperceptibly. The important proviso is that there's no ANGULAR
displacement, so it's vital that the horizon glass should be
plane-parallel, front and back: a rule that sextant-makers know well.

The same argument applies just as well to direct viewing by the eye, with
the telescope removed. The eye, after all, acts just like an imaging
telescope. Parallel light passing through any part of the lens pupil forms
an image at a common point on the retina (after allowing for some of the
eye's optical deficiencies), and appears to come from the one direction.
However, because of its small aperture compared with a telescope, lateral
displacement of a narrow beam may cause light to miss the pupil completely.
The analogy with the telescope isn't perfect, then, but it's pretty good.

George.



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contact George Huxtable by email at george@huxtable.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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