Optical limits to eyes

[GeeKay]

I understand that there's a definite relationship between the size of an eye and the wavelengths it can receive. This being so, just how small can an eye be, while still able to receive light in the visual spectrum? NB. Here, I'm referring to what might be described as 'camera' (or animal) eyes, rather than the compound eyes of insects. Many thanks.

[swansont]

It's related to the Rayleigh criterion caused by diffraction. As eyes get smaller it's harder to resolve features.

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/raylei.html

[Enthalpy]

It relates to the eye sensitivity also. Night-active animals have bigger eyes.

[GeeKay]

Re. the Rayleigh criterion. Yes, I begin to understand now. This raises another question, though: if the eye's resolving power is determined by the size of the pupil, does this explain how glasses (or other forms of external lenses) can overcome this problem?

[swansont]

Re. the Rayleigh criterion. Yes, I begin to understand now. This raises another question, though: if the eye's resolving power is determined by the size of the pupil, does this explain how glasses (or other forms of external lenses) can overcome this problem?

 

Glasses work to correct focusing errors of the eye's lens. They don't improve resolving power beyond the Rayleigh criterion, AFAIK.

[Enthalpy]

Our eye's diameter imposes a limit to the angular resolution, but most people (even young...) are not near to this limit.

 

I had seen the report of an attempt to fine-machine a cornea in order to attain this limit. It supposedly failed, because the report stopped before showing the fantastic success. The cornea being of evolving material, it seems logical that an artificial perfect tune doesn't last long.

 

Would contact lenses do the same? As a very first difficulty, one would need to place them at exactly the right position on the cornea. Do contact lenses move accurately with the eyes?

 

Glasses don't have this function and, because they're farther away from the focus and they don't move with the eyes, it would be seriously difficult for them.

[John Cuthber]

Whatever you might do with the cornea, the lens is imperfect and so is the retina. There's also the stuff between them.

The actual resolution of the eye isn't bad

"The maximum angular resolution of the human eye at a distance of 1 km is typically 30 to 60 cm. This gives an angular resolution of between 0.02 to 0.03 degrees, "

from

http://en.wikipedia.org/wiki/Visual_acuity

The theoretical limit is about 0.007 degrees

from

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/raylei.html

 

So it's within a factor of 10 of the best it could possibly be.

[MigL]

Not mine.

 

Myopic since age 5, diagnosed with PDS glaucoma at 37 after losing vision in left eye, filtering surgery at 39 and cataracts removed a few years ago. But I can still work and drive, although its an adventure in bad weather.

[GeeKay]

If glasses do not increase the resolving power of the eye, what's the situation with binoculars, telescopes etc? Or is there a trade-off here between resolution and field-width? I'm sorry if this seems a stupid question.

[studiot]

The eye-ring is a stop placed where the eyepiece forms an image of the objective.

Its diameter is just sufficient to enclose all rays passing through the instrument.

In a telescope the eye-piece comes just outside the eyepiece.

 

The magnification or magnifying powere is the ratio of the objective diameter to the eye-ring diameter.

 

The diameter of the eye-ring should not exceed that of the pupil of the eye.

Edited October 7, 2014 by studiot

[swansont]

If glasses do not increase the resolving power of the eye, what's the situation with binoculars, telescopes etc? Or is there a trade-off here between resolution and field-width? I'm sorry if this seems a stupid question.

 

No, that's a good question. You have a multiple-lens system that gives you magnification of the image, though a magnifying glass would do the same thing. Normal eyeglasses are not designed to do that (it would be kinda weird, IMO); the price of the magnification is a loss of depth-of-field — only things at a certain distance are in focus. (reading glasses are an exception to this — they magnify)

 

With the lens or lenses you are forming an image, and the image will be subject to the Rayleigh criterion of the lens(es). That is, if you use lenses the same size as your pupil, you should run into the same resolving issues. (If I'm remembering all this correctly)

[John Cuthber]

Swansont, given this

"only things at a certain distance are in focus. (reading glasses are an exception to this — they magnify)"

I'm assuming you don't wear reading glasses.

 

Also, there are two reasons why telescopes use big mirrors (or, occasionally lenses).

They gather more light and they improve angular resolution.

The same goes for binoculars.

 

Since most of the time, if you are using binoculars or a telescope the object you are watching is distant, you can pretty much assume it's at infinity and so the depth of field isn't much of a problem.

Edited October 7, 2014 by John Cuthber

[swansont]

Swansont, given this

"only things at a certain distance are in focus. (reading glasses are an exception to this — they magnify)"

I'm assuming you don't wear reading glasses.

 

 

Whether I do or not doesn't change the fact that lenses magnify, and it's a trivial task to find magnifying reading glasses.

[John Cuthber]

The magnification is undefined.

Someone with reading glasses can't focus on a book without them.

So you can't measure the size of the image at the retina wit, and without them in order to find the magnification ( the ratio of those two image sizes).

 

The lenses move the "near point" they don't make the image bigger- because there isn't an image in the first place.

 

They are "magnifying" lenses, in that they are converging.

But they don't magnify.

 

It is, of course, possible to use a positive lens (like these glasses) to produce a diminished image of an object.

if you form an image of the sun with a "magnifying"glass, it's not bigger than the sun.

 

Magnifying glasses don't always magnify.

[GeeKay]

Many thanks: l learnt a great deal about optics from this thread. So the upshot then is that the size of the pupil determines its capability to resolve incoming light within a given spectrum of wavelengths. And this limiting factor applies whether one is viewing an object with or without the aid of magnifying glasses, and so forth. So the only way a human being is able to 'view' infrared radiation, for instance, is to use an infrared scanner of some kind, an external device that detects infrared radiation - i.e heat - and converts this radiation into 'visible' light.

 

Re depth of field: I well recall a childhood memory of my brother and I taking turns to watch incoming traffic through a pair of fairly powerful binoculars while travelling in our father's car. It made for quite a strange visual experience - comic-strip Special Relativity for beginnners almost. Not to be recommended while driving, however.