Geometric optics - why pinhole bends rays like lens

[Mårten]

We were discussing in an https://www.physicsforums.com/showthread.php?t=284322" that pinholes work like lenses, in that they form inverted real images. The other day, a friend told me, that pinholes even do bend the light rays like a lens do. I can - as being nearsighted - actually use a pinhole in a cardboard paper instead of my glasses, and then I really get a sharp image of the things I look at through the pinhole! How do you explain this?

 

[mgb_phys]

You are restricting the bundle of rays entering your eye, so you are using a smaller part of your lens. It more closely approximates the correct surface over a smaller area - it is the off axis rays that need to be bent to form an image.
You do the same thing with a camera - a sharper image is formed with a smaller iris aperture.

In this example, your imperfect eye produces a different image for two parts of the scene (orange and green rays), so giving you a blurred view - if you put an aperture (pinhole) in the way to block the orange ray you will only get the single green image.

(from http://support.svi.nl/wiki/index.php?WikiWikiWeb)

 

[Mårten]

Interesting - thank you! Also interesting there with the camera thing.

It's like if I look at an arrow, there is only one ray coming from the top of the arrow, and only one ray coming from the bottom of the arrow. This makes an image on my retina built up by dots that have a 1:1 relation with each dot on the real object. So when I take of my glasses and see a blurred image, it's actually because there are a lot of "redundant" rays that disturbs the image! I haven't thought about that before.

So, actually the pinhole doesn't make any bending!

Also, one thing I noticed is that the image I see through the pinhole, feels a little bit magnified. My theory goes now that depending on the degree of nearsightedness, one get different degrees of magnification? Cause the single rays coming from the different dots on the object, get bended in my eye lens in different degree depending on nearsightedness, and this makes in the same degree smaller or bigger images on my retina. Is that right?

BTW, I found these funny glasses on Wikipedia:
http://en.wikipedia.org/wiki/Pinhole_glasses

 

[turbo]

You don't even need a pinhole if you're in a pinch (need to read a phone-book and have no glasses, for instance). As long as you have sufficient light, you can curl your index finger tightly to make a tiny gap and peer through that.

 

[mgb_phys]

Also, one thing I noticed is that the image I see through the pinhole, feels a little bit magnified.

It might be psychological - with nothing else around it the view through the pinhole fills your field of view and so your brain expands it. It's the same way that the moon looks very large on the horizon (with other buildings in view) but tiny high up when compared to the empty ski.

 

[symbolipoint]

Is this any different from the topic, "Geometric optics - why inverted image from thin lens"? The only meaningful difference is that with a lense of a material other than just a hole, the lense refracts light. Either kind of lense alone will invert the image.

 

[mgb_phys]

No it's a continuation of that thread - see the link in the OP

the importna tpoint is that a pinole doesn't bend light and to a first approximation neither does a lens! The rays through a simple lens really don't deviate that much.

 

[Mårten]

As long as you have sufficient light, you can curl your index finger tightly to make a tiny gap and peer through that.

Actually, what my friend told me the other day, was that he used his thumbs and index fingers from both hands, making a small diamond-like shape between the tips of the fingers. That works pretty well, as well.

It might be psychological - with nothing else around it the view through the pinhole fills your field of view and so your brain expands it. It's the same way that the moon looks very large on the horizon (with other buildings in view) but tiny high up when compared to the empty ski.

Hm, it might be so. But still, doesn't the real image on the retina now get bigger, than the real image produced on the retina with glasses? The sharp image produced on the retina when the rays go through the pinhole, should be as big as the blurred image on the retina in this pic, or?

http://www.lensandframes.com/images/myopias.jpg

the importna tpoint is that a pinole doesn't bend light and to a first approximation neither does a lens! The rays through a simple lens really don't deviate that much.

Now I'm getting confused. Doesn't the rays bend in a simple lens? If a ray comes in parallel at the top of the lens, the ray get bended down to the focal point. Or?

 

[mgb_phys]

The size of the image on your retina depends on the curvature of the lens and it;s distance from the retina. All the pinhole (or curled fingers) does is limit the part of the lens that is being used. If your eyes's lens doesn't focus properly then rays going through different parts end up in different points on the retina = blurred. The pinhole just limits the rays to those that go through a small part of the lens - so only a single image - so sharp.

I realized the lens bending statement was confusing - but draw a picture of a mountain being imaged with a pinhole camera, now expand the pinhole a bit and replace it with a lens. The lens simply allows rays that were a little bit off for the pinhole to be bent slightly to form an image. Their path is still pretty straight - at least for long focal length lenses

 

[Mårten]

Okey, I'll be fine with that. Thank you very much mgb_phys for all the help!

 

[Lambduh]

A little off topic but also fun to do:

Pinch your index finger and thumb as close together as you can without touching and focus on a light source behind your fingers. You can actually see diffraction! Pretty cool.

 

[Mårten]

Pinch your index finger and thumb as close together as you can without touching and focus on a light source behind your fingers. You can actually see diffraction! Pretty cool.

Are you sure this is a diffraction pattern? Isn't it just light passing through different irregularities on my fingers? I tried with two flat metal surfaces, and coudn't see much of this. What you mean is that a small light beam passing in between my fingers, would result in a diffraction pattern on my retina?

 

[rcgldr]

Light will diffract around any relatively sharp edge, but it's not that noticeable with white light unless the edge is very sharp and the distortion layer is thin. However in monochromatic light, moderately sharp edges will cause significant diffraction, including small holes (much larger than pin holes):

diffraction.pdf

I seem to recall that if you use the stick from a soap bubble blower and look at black lighted source, the distortion through the open hole is significant compared to white light.