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Re: How does the AstraIIIb split mirror work?
From: Trevor Kenchington
Date: 2004 Apr 25, 14:20 +0000

```Ken Muldrew wrote:

> George Huxtable 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.
>
> This would be true if the reflected rays from the front surface and back
> surface were parallel. They're not. The reflection from the front surface is
> at an angle that is determined by the incident angle. The light that
> passes into the glass is refracted. The light that continues on and passes
> through the back surface is refracted once again (cancelling the initial
> refraction) and it continues on parallel to the incident light. That's why we
> see a single image when looking through a piece of glass where the
> image extends beyond the edge of the glass. But the light that is
> reflected off the back surface has a different angle of incidence than the
> original ray. So the angles of reflection from the front surface and the
> back surface are different. When this light that is reflected from the back
> surface passes back through the front surface, it is is refracted once
> again by passing into the air. But unlike the case for light passing all the
> way through the glass, this refraction does not cancel the initial refraction
> and the light emerges out of parallel with the front surface reflection.

Ken,

I suggest you check the geometry again:

Let the angle of incidence of a ray of light onto the front of a piece
of parallel-sided glass be A. The reflected ray will then leave the
glass also with angle A but on the opposite side of a line drawn normal
to the plane of the glass.

The refracted ray will pass into the glass with an angle from the normal
of B, such that sineA/sineB is equal to the refractive index of the
glass. That ray will then be (in part) reflected from the back side of
the glass with angles of incidence of B (the glass being parallel-sided).

On returning to the front side of the glass, the light will still have
an angle of incidence of B and will be refracted again such that
sineA/sineB is equal to the refractive index. Thus, it will leave the
glass at an angle A from the normal, just as the ray reflected off the
front of the glass was.

> That is why there is a difference between front-surface mirrors and back-
> surfaced mirrors (in general, not specifically relating to sextants). [snip]

But that is the whole point: If a mirror is not in a sextant, it may be
used to reflect rays coming from nearby objects, such that the incident
rays are not parallel. In that case, the reflections off the two
surfaces of the glass most certainly create separate images ("virtual
images", if I have not forgotten all of my high-school physics of 30
years ago). In critical applications, reflecting non-parallel rays of
light, a front-surfaced mirror certainly has advantages.

Trevor Kenchington

--
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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