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

["Nils Olof Carlin" <nilsolof.carlin@telia.com>]

Dominic-Luc,


>Richard Schwarz claimed that:
>
>S = r^2 / 2*R    eq (2)
>
>is exact, but for a parabola. ......
>........I would say 
>that my original claim is correct and that eq(2) 
>cannot be for a parabola, or, Neale Howard 
>may be in error. Perhaps I missed something? 
>I tried deriving eq(2) myself and could 
>not. Richard, if you are certain this is exact, 
>and for a parabola, could I (politely) request 
>the derivation?

Well, eq (2) *is* the equation for the parabola in question, with r as the independent 
and S the dependent variable. What other derivation could you want?

>As for the 21" F/6, Ken Lowther used an equation 
>at a web site that yielded S = 0.21875". This 
>is exactly what I get if I use eq(2). Eq(1) yielded 
>S = 0.21885". These values both yield 0.219" to 
>the nearest thousandth of an inch, so to this level 
>of precision, both equations work in this particular 
>case.

For mirrors of reasonable focal ratio, the difference isn't more than can be removed in 
short time with cerium oxide and pitch ;-)

Nils Olof

This weekend is Star Party time in Mariestad. Do I see you there?