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Re: How does the AstraIIIb split mirror work?
From: Trevor Kenchington
Date: 2004 Apr 24, 19:49 +0000

```George,

I could not understand your argument for why the reflections off the two
surfaces of the glass would appear coincident and was going to comment
on what seemed to be your mistake. Clearly, a ray of light reflected off
the two surfaces must leave the glass as two separate rays (plus the
third one that passes right through). However, if I now understand you
correctly, your point is that the two reflected rays will be exactly
parallel to each other. In a sextant observation, those will also be
parallel to (and indistinguishable from) all of the other rays reflected
from the whole area of the mirror. The eye, with or without the aid of a
telescope, will then focus all of those rays (all that reach the pupil)
to a single image.

If that does capture your point, I think your explanation also covers
Jim's observation of dual images of a pencil: The pencil is so close to
the mirror that rays of light from the one to the other are not
parallel. When each is then broken into two by the twin reflecting
surfaces, the eye focuses them into separate images.

Is that the point you are making? If so, it seems correct to me.

Trevor Kenchington

You wrote:

> 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.

--
Trevor J. Kenchington PhD                         Gadus@iStar.ca
Gadus Associates,                                 Office(902) 889-9250
R.R.#1, Musquodoboit Harbour,                     Fax   (902) 889-9251
Nova Scotia  B0J 2L0, CANADA                      Home  (902) 889-3555

Science Serving the Fisheries
http://home.istar.ca/~gadus

```
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