My spectacles defy the laws of physics

[Steve4Physics]

TL;DR Summary

Why do my spectacles apparently violate the Helmholtz reciprocity principle?

For curiosity (obviously not having anything better to do with my time) I turned my spectacles the ’wrong way round’ - so that they were upside down, with the arms pointing outwards - and looked though them. (This gives the correct lens for each eye of course.)

The image is noticeably worse than with the spectacles the right way round.

I tried different lens-eye distances but this doesn’t affect the image enough change to account for the difference. I tried looking through different parts of the lens but this made virtually no difference.

I can’t explain this. I thought the 'Helmholtz reciprocity principle ('principle of reversibility') would ensure that a lens did the same whichever way round it is. But maybe I’m missing something.

Any explanations welcomed!

(The lenses are for distance and corrected for some astigmatism. )

 

[Ibix]

The axis of the astigmatism is flipped - if it looks like \ it becomes / under the reversal. Mine improve to near perfection if, after flipping them, I rotate them in the plane of the lenses until (I presume) the astigmatic axis is correct. I'm not a snail, so I can only do that one eye at a time, obviously...

 

[Steve4Physics]

The axis of the astigmatism is flipped - if it looks like \ it becomes / under the reversal. Mine improve to near perfection if, after flipping them, I rotate them in the plane of the lenses until (I presume) the astigmatic axis is correct. I'm not a snail, so I can only do that one eye at a time, obviously...

Aha - it's obvious now you've said it! Thankyou - I will now be able to sleep at night!

 

[Redbelly98]

I would imagine that spherical aberration is much worse with the glasses pointing the wrong way. There's a reason why both the inner and outer lens surfaces both generally have the concave side toward your face.

 

[Steve4Physics]

I would imagine that spherical aberration is much worse with the glasses pointing the wrong way. There's a reason why both the inner and outer lens surfaces both generally have the concave side toward your face.

That sounded interesting so I tried an experiment.

With the glasses 'the wrong way' I rotated them to get the astigmatism axis correct (for one eye at a time of course). Vision in each eye was then (at least subjectively) the same as when wearing the glasses normally.

I also tried it with some (non-prescription) reading glasses. Having the glasses the wrong way made no perceptible difference.

I presume any spherical aberration/concavity effect is small enough to be neglected.

 

[Ibix]

I rather suspect your eye itself is the major contributor to the aberration in your optical system, even with your glasses correcting the worst of it. You might be able to see a difference in the appearance of a point source in a very dark room with your glasses either way around, but my guess is that the differences are too tiny to be visible.

 

[hutchphd]

TL;DR Summary: Why do my spectacles apparently violate the Helmholtz reciprocity principle?

I can’t explain this. I thought the 'Helmholtz reciprocity principle ('principle of reversibility') would ensure that a lens did the same whichever way round it is. But maybe I’m missing something.

If memory serves the reciprocity is a statement about simple focal length only. So I do not understand your surprise that the rest of the eyeball system would change. Your eyeballs are not paraxial nor do they have flat image surfaces.
Can you provide a reference for the statement of the principle? (If i'm wrong I would like to know !)

 

[topsquark]

When you are tested for your lens specifications, one of the things they measure is where the center of the sphere should be. The horizontal diameter of the lens is not typically on a line through the center of the eye, so when you flip the glasses you will not get the correct prescription.

(I recently tutored someone for their exam at an Optician's office. It was fascinating.)

-Dan

 

[Steve4Physics]

If memory serves the reciprocity is a statement about simple focal length only. So I do not understand your surprise that the rest of the eyeball system would change. Your eyeballs are not paraxial nor do they have flat image surfaces.
Can you provide a reference for the statement of the principle? (If i'm wrong I would like to know !)

The principle essentially says that the path of a light ray is independent of the direction: if a light ray travels A→B→C, then a ray travelling C→B will pass through A.

This applies to reflection as well as refraction so isn’t limited to lenses and focal lengths.

I don’t have any optics texts, but I think the above is consistent with the description in the Wikipedia article: https://en.wikipedia.org/wiki/Helmholtz_reciprocity

In the OP, I badly misapplied the principle - wrongly expecting that turning a lens around would have have no effect.

By the way, the thread is a few month old now.

 

[hutchphd]

The principle essentially says that the path of a light ray is independent of the direction: if a light ray travels A→B→C, then a ray travelling C→B will pass through A.

This applies to reflection as well as refraction so isn’t limited to lenses and focal lengths.

I don’t have any optics texts, but I think the above is consistent with the description in the Wikipedia article: https://en.wikipedia.org/wiki/Helmholtz_reciprocity

In the OP, I badly misapplied the principle - wrongly expecting that turning a lens around would have have no effect.

By the way, the thread is a few month old now.

Thanks for the answer. That comports with my understanding of the principle. I did see the OP was old but thought that either nobody had given it the appropriately strong answer or perhaps I was confused. Now it is tidied up.

 

[sophiecentaur]

TL;DR Summary: Why do my spectacles apparently violate the Helmholtz reciprocity principle?

I thought the 'Helmholtz reciprocity principle ('principle of reversibility') would ensure that a lens did the same whichever way round it is.

Afair, the Helmholtz reciprocity theorem doesn't go as far as that. In the context of Radio Wave Propagation, I believe that it just means that, if you swap a transmitter and reciever in a radio link ( from the same point - to-point and using the existing antenna systems) then the output at the transmitter end will be the same as when the systems were not reversed.

In terms of optics, it means for instance that, if the image is replaced with an identical object then an image will be formed where the original object was which will be the same as that object.

If astigmatism is introduced into the system then you'd need to mimic, precisely, the phases of the original image to form an identical image where the original object was. i.e. a distorted image to use as an object. Does that make sense, I wonder. Did I put it the right way?

 

[Steve4Physics]

Afair, the Helmholtz reciprocity theorem doesn't go as far as that.

Yes. I misapplied the theorem. If there were sufficient symmetry, reversing the lens wouldn't have any effect. But with astigmatism, symmetry is lost. I didn't think the problem through properly.

In the context of Radio Wave Propagation, I believe that it just means that, if you swap a transmitter and reciever in a radio link ( from the same point - to-point and using the existing antenna systems) then the output at the transmitter end will be the same as when the systems were not reversed.

That's sounds correct to me. However, I note that Wikipedia (https://en.wikipedia.org/wiki/Helmholtz_reciprocity) says the theorem "does not apply to moving, non-linear, or magnetic media". If, say, ionospheric effects were involved in the propagation, the theorem might not apply. But I don't know enough about radio propagation to have a view on that.

In terms of optics, it means for instance that, if the image is replaced with an identical object then an image will be formed where the original object was which will be the same as that object.

Yes, that sounds like a valid way of expressing the theorem.

If astigmatism is introduced into the system then you'd need to mimic, precisely, the phases of the original image to form an identical image where the original object was. i.e. a distorted image to use as an object. Does that make sense, I wonder. Did I put it the right way?

Yes, I get what you are saying. Of course, in practical terms, it would be extremely difficult to do - but might be possible (at least in principle) by using holograms!

 

[hutchphd]

I think for any extended sources (or images) the argument falls apart. It would be physically impossible to create a real object that mimics many aberrations images

 

[sophiecentaur]

Yes. I misapplied the theorem. If there were sufficient symmetry, reversing the lens wouldn't have any effect. But with astigmatism, symmetry is lost. I didn't think the problem through properly.That's sounds correct to me. However, I note that Wikipedia (https://en.wikipedia.org/wiki/Helmholtz_reciprocity) says the theorem "does not apply to moving, non-linear, or magnetic media". If, say, ionospheric effects were involved in the propagation, the theorem might not apply. But I don't know enough about radio propagation to have a view on that.Yes, that sounds like a valid way of expressing the theorem.Yes, I get what you are saying. Of course, in practical terms, it would be extremely difficult to do - but might be possible (at least in principle) by using holograms!

The original (?) RF theorem wouldn’t have that problem because the antenna feed points are point sources.

Paths in the ionosphere don’t tend to be reciprocal.