Quote:
Originally Posted by JA
Hi R,
As an exercise of the grey matter I decided to flesh out what I thought was the basis for the 1/3rd thickness of the filter rule of thumb....
It looks like it's quite a valid supposition if you take the refractive indices involved as ~1 for air (1.0003) and ~1.5 for the glass (this could be anywhere from 1.4 to 1.7 depending on glass used). Anyway if you're interested in the derivation of the difference in focal length of an optic WITH and WITHOUT an intermediary optical layer (glass) just completed, then see the attached.
Long story short .... SEE THE RED BOX. If you substitute typical values for refractive indices of air and glass of 1 and 1.5 respectively you will note that the focal point shifts backwards from POINT A in the diagram to POINT B in the diagram by a distance of 1/3rd the filter thickness, when the filter is included in the optical path. Given by the derived expression ...
b = x [1 -(n1/n2)]
where
b = distance focal point moves with and without filter (see diagram)
x = glass / filter thickness
n1 = refractive index of medium before filter (i.e: that of the air)
n2 = refractive index of the filter medium (i.e: that of the glass)
Best
JA
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Many thanks JA. Are we missing an attachment?