### Filters and Snell's law

If the filters have different thicknesses (or different refractive indices), the focal length will change!  This is due to Snell's law which is n1*Sin(theta1) = n2*Sin(theta2) where n1 and n2 are the refractive indices of the two materials that form the interface and theta1 and theta2 are the angle between the incident ray and a normal to the interface surface.

Here is how significant this effect is for two filters I was (inadvertently) experimenting with years ago:

The image on the left was taken through a clear filter and is in focus.  The image on the right resulted from merely switching to a different filter without making any focus adjustments.  Since focusing in the past was usually a major effort, refocussing simply to compensate for filters of different thickness was a major inconvenience.  (Maxim DL now allows a "focus offset" table that will automatically move to the correct offset when a filter is changed.) I did not have a micrometer (and it might have damaged the filters to use one) so my measurements were "eyeball" measurements.  I measured the thicknesses of several filters that I had. Filter #1 appeared to be 1.5 times thicker than filter #2 which in turn appeared to be 1.5 times thicker than the filter #3, which in turn appeared to be 1.5 times thicker than the filter #4.  So one of the filters was 1.5*1.5 or 2.25 times thicker than the least thick filter and resulted in the defocussing effect shown in the images above when the filters were used with a 100" focal length, f/10 scope and an f/3.3 focal reducer.

The upshot of this is that to minimize focussing effort, filters that are the same thickness and the same refractive index are preferred if possible.  There does not appear to be any standard for filter thickness.  SBIG appears to be aware of this and their filters appear to be matched.  Note that this is another reason for them to provide a clear filter along with the red, green and blue filters.  If you were to use red, green, blue, and "empty", the filters would extend the focal plane but the "empty" slot would not so it would have a different focal plane and would require extra focussing effort.  Astrodon seems to have mastered this problem and the filters I have from them are parfocal as near as I can tell. Once the filter offsets (if any) have been determined, Maxim DL allows them to be placed in a table and focus is automatically adjusted by the offset when a filter is selected. This will automatically maintain focus across various filters.