I can understand the Front focal length of Cemented Doublet lens will be the same with BFL if each parts of lenses were consist with same material(e.g. SF10).(lenses are surrounded with air)
But I think that if each part of doublet lens had different material,(e.g. Lak21 and SF10) then the BFL and FFL will become different.
Then how can I calculate the FFL from BFL, EFL and refractive index? (Without Raytracing)
Dear all, I agree that FFL, BFL and EFL are defined with regard to the principal planes of the optical system. But I recommend you to define the principal planes for each lens element of the doublet lens rather than the principal planes for the doublet lens. Using the two set of principal planes and the lens formula, you can calculate FFL and BFL for the doublet lens. Attached please find Excel sheet for the calcuation. Lens data is taken from an EFL=75mm achromatic lens consisting N-BK7 positive lens element and N-SF5 negative lens element. Notations and formulae are consistent with Kingslake's Lens Design Fundamentals.
The FFL, BFL and EFl are defined vs the principal planes of the optical system. First you have to determine the position of the object (H) and image (H') principal planes of the doublet with respect to the first surface (say distance d1) and the last surface (say distance d2) of the system and then FFL = e+d2+EFL and BFL=EFL-d2 with e the distance between the front surface and the last surface of the doublet.
It is a quick and dirty approximation, you may have to check teh maths however the principle is correct.
N>B : FFL=BFL only for thin lenses.
e = distance between the doublet front surface and doublet back surface.
d1 = distance of the image principal plane H' to the front surface of the doublet
d2 = distance of the image principal plane H' to the back surface of the doublet
Those distances have a positive sign when counted in the same direction as the light propagation in the doublet, negative otherwise.
Dear Luis,
Sorry for bother you again,
I still misunderstand how FFL became e+d2+EFL.
I attached some figure based on you described. (at least I understand)
from the picture, FFL+e+d2 is much longer than even EFL.
Why I was wrong?
Regards,
Dear all, I agree that FFL, BFL and EFL are defined with regard to the principal planes of the optical system. But I recommend you to define the principal planes for each lens element of the doublet lens rather than the principal planes for the doublet lens. Using the two set of principal planes and the lens formula, you can calculate FFL and BFL for the doublet lens. Attached please find Excel sheet for the calcuation. Lens data is taken from an EFL=75mm achromatic lens consisting N-BK7 positive lens element and N-SF5 negative lens element. Notations and formulae are consistent with Kingslake's Lens Design Fundamentals.
Dear Shigeo,
Your sheet helps me a lot. It works almost perfectly.
However, I think I need study a lot.
Thanks!!
Regards,
Dear Kang, It is good to know my sheet works well. Here is its Mathematica version, which will be more understandable about what lens formulae are used. I should add the calculation results for given doublet lens data are checked by lens design software OSLO independently.
Oups, small typo I meant : EFL = BFL for (very) thin lenses.
Anyway, keep in mind that the FFL, BFL and EFL relationships are valid only in paraxial optics. It is enough to have a first order knowledge of your system but not much more.
Dear Kubota,
Thanks again for your scripts. I am currently downloading trial version of Mathematica. :)
Dear Venacio,
Okay, I'll keep in mind. I think I need to study about geometrical optics of thick lens for a little.
Dr. Kang,
I have added single thick lens formulae and calculation of EFL into Excel sheet. They will be helpful for you. After you get accustomed to geometrical optics, you may be interested in the lens design software such as OSLO, of which EDU version can be free downloaded.
Shigeo
Actually I leand a little about ZEMAX , But I didn't have an experience about OSLO.
But it looks simmilar. I will try it.
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