Re: ATM 21" F/6: response about sagitta equations

[astro.electronic@t-online.de (Michael Koch)]

Hi Dominic-Luc,

> Richard Schwarz claimed that:
>
> S = r^2 / 2*R    eq (2)

Some years ago I derived this formula and I'm sure that it is correct for the 
parabola, but now I didn't find the derivation.

The formula for the parabola is: y = x^2 / (2 * R) 

For  x = r  and  S = y  you get eq(2).

If you try to derive it yourself I think this idea will help: The optical path 
length must be equal for all parallel rays coming from the light source (at 
infinite distance) and the focal point.

Do not try to derive it using the angles between the light and the mirror 
surface. This will be difficult.

Michael

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 ASTRO ELECTRONIC  Dipl.-Ing. Michael Koch
         www.astro-electronic.de
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