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

[Frank Henriquez <frank@ucla.edu>]

While not directly related to the original question,  but when I was 
cutting the curve (on a lathe0 into my 6' Al mirror, I had to determine the 
sagitta at any radius, but I couldn't find the equation anywhere.

I started with the equation for the sagitta of a spherical mirror:

  S = ROC - (ROC^2 - r^2)^0.5

  then derived (through pretty basic geometry) the sagitta at any radius of 
a spherical mirror:

  S = (ROC^2 - y^2)^0.5 - (ROC^2 - r^2)^0.5

  where:
  ROC = radius of curvature
  r = radius of mirror
  y = radius at which sagitta is measured

Frank