# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: How flat do sextant mirrors need to be?
From: Clive Sutherland
Date: 2009 Jan 27, 13:41 -0000

```Bill;

Bill

Unfortunately the 'Wavelength Deviation' is not a good descriptor for this
type of use. The depth or otherwise of the hills and valleys  forming the
surface is not the point. What is needed is a way of describing the angular
slopes of the undulations in conjunction with their relative areas.
To give a simple explanation, let us suppose that the mirror has two perfect
areas,  disposed at a small (say 1 minute) angle to each other in the
vertical plane.
This mirror would reflect Two images of the Sun (etc) into the telescope,
which (if the two reflecting areas are equal), would be indistinguishable
from each other. Two equally plausible altitudes, 1 minute apart could be
measured.
In reality a mirror could have many such reflections from an undulating
surface and the result would be a blur in all directions around the edge of
the sun, or a scattering of the images in all directions around a star.

The problem is that there is no easy means of measuring the surface of the
mirror in a way that quantifies  this phenomena.
Obviously the two types of measurement are related but it would be quite
difficult to translate the one from the other.
Personally I do not think that your question can be rigorously answered and
only a subjective assessment can be provided.
To give just a ball park figure and using 0.5 micron for the wavelength of
light. Consider a mirror 100 mm long. An error of one wavelength high in the
middle of this glass would produce two otherwise flat surfaces at an angle
of 6 secs to each other. However suppose this same hill were to be several
at about 10 mm apart. Several reflections would be produced as large as 32
secs from each other. This mirror would be unsuitable for high quality work.

Clive.

> -----Original Message-----
> From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf
> Of engineer@clear.net.nz
> Sent: 27 January 2009 06:20
> To: NavList@fer3.com
> Subject: [NavList 7172] How flat do sextant mirrors need to be?
>
>
>
> I recently checked some old sextant mirrors against a tenth wave
> optical flat prior to resilvering them and found that the greatest
> deviation was a half wavelength. 3 mm modern mirror float glass
> compared favourably, suggesting a cheap solution to replacing
> deteriorated mirrors in old instruments.
>
> I have posted some images in my blog on my website www.sextantbooks.com
>
> Can one of our erudite members suggest how flat the mirrors need to be on
> theoretical grounds? I have vague memories that people aimed for a quarter
> wave when making the flats of amateur Newtonian telescopes, but this may
> well be irrelevant.
>
> Bill Morris
>
>
>
>
> >
>
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> 1/26/2009 6:37 PM

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