# Light converging inside the eye

• ViolentCorpse

#### ViolentCorpse

Does all the light entering our eyes converge to a single point on the retina (assuming minimal aberration)? If this is true then that means that only a tiny point is exposed to light inside the eye so it will hit and activate a single cell (unless the cells are much smaller than the point of light). I just want to know if that's correct. I doubt that because light is processed by millions of cells working together to produce vision. Perhaps light hits a single or a very small number of cells which in turn activate others by some chemical reaction?

I'm not interested in the biological details, only the optical ones (whether it focuses to a single point)

Thank you!

Does all the light entering our eyes converge to a single point on the retina (assuming minimal aberration)?
Not in general.

Does all the light entering our eyes converge to a single point on the retina (assuming minimal aberration)?

No. If this were true, then all the light entering a camera lens would converge to a single pixel on the camera's sensor, or to a single point on the film in an antique pre-digital camera.

Ideally, all the light entering the eye from a single point on the object converges to a single point on the retina. But points at different locations on the object produce point-images at different locations on the retina.

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Ideally, all the light entering the eye from a single point on the object converges to a single point on the retina. But points at different locations on the object produce point-images at different locations on the retina.
I see. Does this also hold for convex glass lenses? A common diagram in any textbook discussing geometric optics depicts several rays of light from different points converging to a single point.

I see. Does this also hold for convex glass lenses? A common diagram in any textbook discussing geometric optics depicts several rays of light from different points converging to a single point.

Such diagrams normally show several rays of light from the same point on an object striking the lens at different points and then converging onto the same point on the real image.

Rays from other points on the object converge at other points on the real image.

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A common diagram in any textbook discussing geometric optics depicts several rays of light from different points converging to a single point.

Can you find an example online, or maybe you have one of the books that I have at hand?

• Halliday, Resnick & Walker, Fundamentals of Physics, 6th ed.
• Knight, Jones & Field, College Physics, 2nd ed.
• Hecht, Optics, 4th ed.
• Pedrotti, Pedrotti & Pedrotti, Introduction to Optics, 3rd ed.

I see. Does this also hold for convex glass lenses? A common diagram in any textbook discussing geometric optics depicts several rays of light from different points converging to a single point.

Such diagrams normally show several rays of light from the same point on an object striking the lens at different points and then converging onto the same point on the real image.

Rays from other points on the object converge at other points on the real image.

Yes, and sometimes the rays are depicted as being perfectly parallel before they enter the lens, which may lead to some confusion as in reality these rays are *nearly* parallel, not perfectly parallel, and were emitted by a single point on the object.

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I see. Does this also hold for convex glass lenses? A common diagram in any textbook discussing geometric optics depicts several rays of light from different points converging to a single point.
You mean parallel light rays converging to a single point? For very distant light sources, like a distant star, the rays that enter your eye are almost parallel. So despite orignating from different points on the star, they converge into a single point.

You mean parallel light rays converging to a single point? For very distant light sources, like a distant star, the rays that enter your eye are almost parallel. So despite orignating from different points on the star, they converge into a single point.

Those rays don't originate from different points on the star, they originate from a single point but the distance to the star makes them very nearly parallel.

Can you find an example online, or maybe you have one of the books that I have at hand?

• Halliday, Resnick & Walker, Fundamentals of Physics, 6th ed.
• Knight, Jones & Field, College Physics, 2nd ed.
• Hecht, Optics, 4th ed.
• Pedrotti, Pedrotti & Pedrotti, Introduction to Optics, 3rd ed.

Like this for instance: http://www.sciencelearn.org.nz/var/sciencelearn/storage/images/contexts/light-and-sight/sci-media/images/converging-lens/685327-1-eng-NZ/Converging-lens.jpg

But Drakkith has made it clear. These rays look parallel, but are actually coming from the same point. Thank you Drakkith.

So I've learned that rays originating from different points converge at different points. Surely all these points of coincidence are the same distance away from the lens i.e the focal length (assuming the source of light to be infinitely far away)? Also I wonder if, hypothetically, the rays from different points of an object were actually all parallel, would they then all converge on a single focus?

Thank you everyone. You've been a great help!

Those rays don't originate from different points on the star,
They do.

they originate from a single point but the distance to the star makes them very nearly parallel.
The distance also makes rays from different points on the star nearly parallel, so they all converge in a single point

The distance also makes rays from different points on the star nearly parallel, so they all converge in a single point

I would rather say that "they all converge nearly on a single point", or "they converge on points that are very very very close together."

I would rather say that "they all converge nearly on a single point", or "they converge on points that are very very very close together."
Yes, sure. Nearly parallel -> nearly a point. For all practical purposes: We see the star as a point, but the light rays come from all over the huge star.

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Yes, sure. Nearly parallel -> nearly a point. For all practical purposes: We see the star as a point, but the light rays come from all over the huge star.

This makes sense though it raises another confusion for me. If we look through a telescope, the star is no longer a single point, but a big collection of them. Does a telescope not converge the nearly parallel rays to an approximately single point?

If we look through a telescope, the star is no longer a single point, but a big collection of them.

Diffraction.

Diffraction.

Explained nicely:

They do.

The distance also makes rays from different points on the star nearly parallel, so they all converge in a single point

To simplify things you can consider all the light from the entire star as being parallel, no matter where it originates from on the star. In reality it is not.

I'd prefer to keep the effects of diffraction a separate discussion from the oncoming rays, as different optical systems will behave differently when viewing an object. For example, my home telescope cannot make out any stars as anything more than point sources. However, the HST has sufficient resolution to directly image Betelgeuse. In both cases the light is very nearly parallel when it arrives at the aperture. It is only once you start converging the light that the situation changes and you have to account for diffraction.

On ground based telescopes stellar disc imaging can be achieved using masking interferometry - re: http://arxiv.org/abs/1302.2722. The first image of a stellar disc other than sol was Betelgeuse, achieved by the Hubble in the UV spectrum [shorter wavelengths increase resolving power]. UV images can only be achieved by space based telescopes due to Earth's atmosphere. Using the aforementioned interferometry method, R Doradus, one of the largest known stars, was found to have an angular diameter of about 60 milliarcseconds, re: http://arxiv.org/abs/astro-ph/9701021, making it slightly larger than the apparent angular diameter of Betelgeuse. A milliarcsecond is about the size of a billiard ball at a distance of 5000 kilometers.

One thing that may be interesting to note is that all images are presented to the brain upside-down. Not only that, but each eye sends half the image to each side of the brain, through the optic chiasm. And, No, "Does all the light entering our eyes converge to a single point on the retina." Ideally the light spreads itself out to cover the foveal region of the retina. People that need glasses use these to optimize the focus on this foveal region.

So, this was really a lesson for me in my early studies of neurobiology. Your senses are not presented to you like you think a video camera might present them. It actually arrives mostly in a confused and disorganized manner through your dorsal root ganglia and cranial nerves. It is the job of the brain to "construct" from this an image of the world. I try to impress this fact on physicists at my university all the time, try to incorporate not only the data your sensors are giving you, but also try to account for the manner in which your brain recognizes and interprets the data. That sentiment typically falls on deaf ears, though.

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And, No, "Does all the light entering our eyes converge to a single point on the retina." Ideally the light spreads itself out to cover the foveal region of the retina. People that need glasses use these to optimize the focus on this foveal region.

That's not really an accurate description of what happens. Also, this is more of an optics question than a biology question, so the details of how the brain reconstructs the image is probably best left to another thread.

I think the key point is that plane waves traveling in different directions will focus on different points in the focal plane of a lens (or the retina of an eye).

This is the fundamental Fourier-transforming characteristic of lenses and the basis of Fourier optics.

Claude.

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Thank you, Claude! I just realized that all the material that I've studied geometric optics from is very basic introductory stuff and all the discussions proceeded from the assumption of a point-source of light, hence my confusion. I understand it now, but now I'm troubled by another question and I've scoured google without a single relevant result.

Q: If the eye is placed next to a convex lens (a far-sighted person wearing convex lens spectacles, for instance) so that the light rays that enter the spectacle lens are bent towards each other which are then further bent by the eye's lenses to form an image on the retina, how is the eye (or rather the brain) able to trace these converging rays back to a common point of convergence? I mean, we need two points of convergences on both ends to be able to see right? Like when a point on a light-source first radiates light, which is then converged back together to a point by the eye to form an image. But if the rays of the light that is entering the eye are already a little bent toward one another, and since we see things in straight lines, so if we trace those bent rays straight backwards, they will never converge! So how could the brain judge where the origin of these seemingly stray light rays is? I'm at my wits' end.

Thank you so much for your help so far, dear fellows! You illuminate my world.

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Q: If the eye is placed next to a convex lens (a far-sighted person wearing convex lens spectacles, for instance) so that the light rays that enter the spectacle lens are bent towards each other which are then further bent by the eye's lenses to form an image on the retina, how is the eye (or rather the brain) able to trace these converging rays back to a common point of convergence?

There is no tracing of rays involved here. The rays converge on the retina to form an image. This image is then transmitted to the brain. That's it. The brain does not trace rays back to their source.

Note that you rarely have parallel rays entering your eye. Since most of what you see everyday is fairly close to you, the rays are always diverging when they enter your eye.

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There is no tracing of rays involved here. The rays converge on the retina to form an image. This image is then transmitted to the brain. That's it. The brain does not trace rays back to their source.
Oh. I'm a little surprised by that, but I'll have to wrap my head around that, hehe.

Though when there's a virtual image involved (as in plane mirrors) a real image is still being formed on the retina, right? And I presume we can observe the image formed by a convex lens in space at a point outside our eye? In these cases, the rays from the actual position of the images travel to the eye and form another real image on the back of it. Like, an image of the image.
In other words, these images aren't directly being formed on the retina.

And this "tracing back in straight lines" tendency of the brain is evident when we see an object in the glass of water in a position where it actually isn't. I guess that's what fooled me.

Am I wrong about these cases as well?

Thank you so much Drakkith!

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Though when there's a virtual image involved (as in plane mirrors) a real image is still being formed on the retina, right?

Yes. The rays bounce off of the mirror and then enter the eye.

And I presume we can observe the image formed by a convex lens in space at a point outside our eye? In these cases, the rays from the actual position of the images travel to the eye and form another real image on the back of it. Like, an image of the image.
In other words, these images aren't directly being formed on the retina.

If you can focus the rays down onto your retina, then sure. Whether you can or not depends on the properties of the lens, the distance between the object and the lens, the distance between the lens and your eye, and a few other things.

And this "tracing back in straight lines" tendency of the brain is evident when we see an object in the glass of water in a position where it actually isn't. I guess that's what fooled me.

Okay, I see what you mean. In this case the brain is being fooled because the rays are refracted to different angles when they come out of the water, so a straight line traced to the image would not intercept the object. Note that you have a cone of rays of differing angles entering your eye from every point source, so in reality your brain isn't tracing light rays back to their source, but extrapolating the position of objects based on the image formed on your retina. Hence the reason it can be fooled by refracted rays.

Okay, I see what you mean. In this case the brain is being fooled because the rays are refracted to different angles when they come out of the water, so a straight line traced to the image would not intercept the object. Note that you have a cone of rays of differing angles entering your eye from every point source, so in reality your brain isn't tracing light rays back to their source, but extrapolating the position of objects based on the image formed on your retina. Hence the reason it can be fooled by refracted rays.

Certainly. That makes sense.
I have good eyes, so I don't wear spectacles, but I presume that the refraction of rays caused by glasses would change the angles of rays slightly and the brain would err slightly in extrapolating the exact location of the source, just like you've mentioned above?

Drakkith, I'm sincerely very grateful to you for persisting with such a dunce, ignorant fellow. Thank you so much!

I have good eyes, so I don't wear spectacles, but I presume that the refraction of rays caused by glasses would change the angles of rays slightly and the brain would err slightly in extrapolating the exact location of the source, just like you've mentioned above?

Not really. Glasses are designed to correct your vision, not to alter it. The combined effect of the lenses and your eye add up to normal vision.

Also, consider the following. When you place an object underwater, the light coming from it passes through the boundary and changes its angle before making its way to your eye. Now imagine looking through a fish tank at an object on the other side. The light passes through the far side, refracts, passes through the tank and refracts again. The two refractions (well, four really since there is an air-glass boundary and a glass-water boundary on both sides) cancel each other out in angle. (The same thing happens when looking through a normal window)

Also, consider the following. When you place an object underwater, the light coming from it passes through the boundary and changes its angle before making its way to your eye. Now imagine looking through a fish tank at an object on the other side. The light passes through the far side, refracts, passes through the tank and refracts again. The two refractions (well, four really since there is an air-glass boundary and a glass-water boundary on both sides) cancel each other out in angle. (The same thing happens when looking through a normal window)
I understand. But surely that doesn't hold with spectacles since the front and back surfaces aren't parallel and it would defeat the whole purpose of using spectacles anyway.

Thank you once again. No more questions. =D