Gauss Lens Formula

[CycloWizard]

This may be a really dumb question, but I have to ask. Is the standard Gauss lens formula (1/f=1/d_object+1/d_image) true only in air or in any medium? I am trying to compute the object distance for a lens submerged in water where I know the image distance. I found a similar situation in an ophthalmology textbook, but I don't trust real doctors to calculate anything correctly. They suggested that the formula for this situation should be n/d_object=1/f+ n/d_image, where n is the refractive index of the medium surrounding the lens.

I think that the Gauss formula holds in any medium and that the focal length accounts for the effects of non-unity refractive index, but when I saw the ophthalmologists' formula, it gave me pause and I wanted to be sure I'm doing this properly before I get myself into trouble.

 

[Born2bwire]

There must be some sort of correction done to the Gauss lens formula because if a lens is submerged in a dielectric, then the refractive index is going to change since the interface is now glass to water (for example) as opposed to glass to air.

 

[CycloWizard]

Originally posted by: Born2bwire
There must be some sort of correction done to the Gauss lens formula because if a lens is submerged in a dielectric, then the refractive index is going to change since the interface is now glass to water (for example) as opposed to glass to air.

I believe that this correction comes in the focal length calculation, which uses the refractive index of the surrounding medium.

 

[Born2bwire]

Originally posted by: CycloWizard

Originally posted by: Born2bwire
There must be some sort of correction done to the Gauss lens formula because if a lens is submerged in a dielectric, then the refractive index is going to change since the interface is now glass to water (for example) as opposed to glass to air.

I believe that this correction comes in the focal length calculation, which uses the refractive index of the surrounding medium.

Well then I guess it would be easy to check the modified equation that you found. If the focal length is modified by 1/n then it's equivalent.

 

[Ticky]

Your equation n'/D'=n/D+1/f is infact correct. This is becuase d/n is the reduced, or air-equivelent, distance, and thus, we can model this system as if it were in air. Keep in mind that this equation does assume a thin lens. May I ask what you are using this for?

 

[CycloWizard]

I found an actual derivation of the Gauss equation and it's fairly straightforward. Link here for anyone interested. I'm not Gauss, so I wouldn't have figured this out on my own, but once you have the basics of the derivation (pp. 21-22 in the linked file), it's easy to generalize it to any simple lens system like the one I'm working with. I'm not going to bother typing out the analytical equation, since I need to avoid the thin lens approximation, but it's really very simple.

My application is actually working on computing the focal distance of the ocular lens. This has been done by lots of people (most notably Gullstrand, who got the Nobel Prize for his schematic eye back in 1909 or so), but I have no optics background and need to solve it many, many times to test how the shape of the lens affects the results. I'm replacing the lens cells with a polymer, so the shape of the lens depends on the refill volume in a complex way that I determined experimentally. With this schematic eye, I can now maximize the amount of accommodation that the lens gives by controlling the polymer volume. In theory, anyway.

 

[Ticky]

You probably want a different method than Gaussian optics, if your doing aspheric surfaces... Have you considered raytracing? OSLO-EDU is free if your are a student, or are willing to pretend to be one. Also, keep in mind the eye is quite complicated, much more so than most people assume. Are you using some sort of eye-model?

 

[CycloWizard]

Originally posted by: Ticky
You probably want a different method than Gaussian optics, if your doing aspheric surfaces... Have you considered raytracing? OSLO-EDU is free if your are a student, or are willing to pretend to be one. Also, keep in mind the eye is quite complicated, much more so than most people assume. Are you using some sort of eye-model?

I actually wrote my own ray tracing software, but was told to keep it simpler since no one has even done this for paraxial optics yet. The lens has a refractive index gradient as well as being aspherical, though the shape of the lens is a source of some debate with about four different formulations proposed in the literature over the last five years. The ray tracing analysis can be the second paper in the series. There are a variety of eye models available, but I'm modifying a 1988 schematic eye for pigs (since I used pig eyes) by adding more recent biometric data and results from my own experiments.

 

[Ticky]

Cool, sounds fancy. Good luck.