From: "Richard F.L.R. Snashall" 
To: ATM List 
Reply-To: "Richard F.L.R. Snashall" 




Bob May wrote:
> Well, we're back to getting something again!  Now you need to figure out why
> the conversion to the Nd, etc. is still wrong.  I used SF10 numbers that I
> got from the Schott catalog program and the results are still off a fair
> bit.  I'll note that these numbers you are using aren't the same as the
> numbers that are in such catalogs as the Chance catalog that you have on
> your site.

I think it best if I reinsert the answer to this onto the list.

The equation I use for dispersion is:

                         1           dn
     dispersion =    -------- * -------------
                     0.515956   d(1/lambda^2)

and from that:

     v   =   ( n - 1 ) / dispersion

where all of these values are taken at a single wavelength. It is this new
definition of dispersion and Abbe number that enable the user to slide the
minimum focus wavelength.

The choice of the constant 0.515956 is totally arbitrary. This empirical
value is the mean between that for BK7 and that for F2 to make the values
calculated close to the dispersion and Abbe numbers for e light.  For the
longest while, I simply used 0.5, and, in the instance you recount, 0.5616
(which, incidently, had a typo and should have been 0.51616 (BK7)).  But
all that doesn't matter, as, for a doublet, the result will be the same. 
My labeling of the GUI fields, was at fault; I should have never called
them nd, nF-nC and vd.  I have corrected that.  I ran SF10 with the new
constant; it comes out quite reasonably close to the values for nF'-nC and
ve.  The calculation for the index is the actual value calculated for the
central wavelength.

However, I have also totally revamped the interface toward what I think is
a much more meaningful direction.  The top table is now dedicated to
identifying the glass, while the bottom table is dedicated to identifying
the doublet made from that glass.

Also, I have added in the code to allow the use of the Cauchy index of
refraction calculation.  The values are consistent, but the older Cauchy
equation did have a tendency to have a little bit of ripple in the first
derivative.  The calculator should now be able to be used with glasses for
which you have the Sellmeier coefficients, the Cauchy coefficients, or
simply the dispersion and Abbe numbers (The index of refraction is
calculated for the central wavelength, which can be different from the
wavelength of the minimal focus).

        Rick S.

--- BBBS/NT v4.00 MP