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Why does a larger apeture gather more light?

Beginner Optics
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#1 nhanimator

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Posted 21 September 2021 - 09:16 AM

I'm hoping someone can explain this to me like I've five. I'll make some assumptions and a conclusion here. Please tell me where I am wrong.

 

I think of the light coming from Jupiter as a non-stop stream of photons. Sort of like a hose pointed directly at my eyes. And that stream is essentially round - like the planet's facing surface. This stream is actually pointing out in all directions, but only the particles that are pointed directly towards my eye are the ones I see. The person standing next to me is getting their own stream and the two do not mix (i.e. we don't see the same particles).

 

Let's say that Jupiter is 40 arcseconds across. This defines the width of said stream and is essentially identical for me, the person next to me, my 4.5" scope and my 10" scope. So the diameter of mirror being directly struck seems like it would be the same. Yet the 10" scope is capturing more photons.

 

My initial guess was that the larger mirror had a higher 'resolution' (better construction) and was better able to resolve the stream. But further thinking leads me to believe that it has to do more with the curvature of the mirror. If I look directly down the tube, then the flow of photons would appear to be hitting the mirror in a circular fashion. Yet the concavity of a mirror means that the area being struck by photos is not circular, but oval-shaped, and that that shape itself is 'elongated' across the surface. The elongated oval is wider on the 10" (as the concavity is perhaps less pronounced) and thus has more area. This results in more photons captured.

 

Am I close?


Edited by nhanimator, 22 September 2021 - 05:57 AM.


#2 lphilpot

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Posted 21 September 2021 - 09:35 AM

Photons coming off Jupiter (or effectively any other object) don't consist of narrow finite sets of parallel streams. They're divergent and radiate in all directions (X, Y & Z) so the larger the objective, the more photons it captures and focuses. The diameter of Jupiter is apparent size of the source, but it's not the size of the 'stream' once it reaches us, FWIW.

 

IOW, not like a hose, but rather like a 360 degree / 3D shower head of infinitely small individual streams.


Edited by lphilpot, 21 September 2021 - 09:38 AM.

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#3 Barlowbill

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Posted 21 September 2021 - 09:35 AM

Seems like your eye has to fit into the equation somewhere.  If your eye was twice as large as it is, would you garner more photons?  Does the size of the object emitting the photons define the "steam"?  Hopefully, some rocket scientist optics guys and gals will clear this up for us.



#4 blazek

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Posted 21 September 2021 - 09:36 AM

The light from a point like sources spreads in all directions, so your "light beam " on your drawings is not parallel , it is divergent 
(iit is a cone, not a cylinder). So if you take it with bigger aperture, you collect more. Imagine, small object makes small shadow, the large one makes large shadow, in other words, they block/collect less or more light respectively.  If it wold be perfectly collimated (parallel) then indeed you would gain nothing with aperture larger than a beam . 

The curvature of mirrors and lenses is there to focus all collected light to desired point/surface.


Edited by blazek, 21 September 2021 - 09:38 AM.


#5 RalphMeisterTigerMan

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Posted 21 September 2021 - 09:36 AM

I believe the way it works is the more surface area that you have, in the case of any reflecting type telescope, or the larger the main lenses the more light you will collect to be able to bend and bring to a focus, in the case of refractors.

 

The theory is, the more light you collect the brighter the image.

 

Clear skies and keep looking up!

RalphMeisterTigerMan



#6 Couder

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Posted 21 September 2021 - 09:37 AM

Think of adding what your friend's eyes see to yours - and a larger yet aperture - add a few more friends. Or the reverse - would you rather watch a show on the smallest smart phone screen, or on a big screen?


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#7 nebulasaurus

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Posted 21 September 2021 - 09:38 AM

For the same reason a bigger bucket catches more rain.

 

It's all about the area of the objective end.


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#8 spacemunkee

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Posted 21 September 2021 - 09:43 AM

Guess one way you could think of it is you have a small bucket and a big bucket sitting out in the rain. Come back in an hour and you're going to have more water caught in the larger one than the smaller(assuming hypothetical even rainfall of course.)
Then said rainfall amount from each is concentrated down to the same diameter into your eye, assuming scope, eyepiece, etc. brings the light path to within roughly the same.
More water, wetter eyes! smile.gif

 

Edit: Got beat to the bucket idea as I typed. wink.gif


Edited by spacemunkee, 21 September 2021 - 09:45 AM.

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#9 nhanimator

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Posted 21 September 2021 - 09:47 AM

Photons coming off Jupiter (or effectively any other object) don't consist of narrow finite sets of parallel streams. They're divergent and radiate in all directions (X, Y & Z) so the larger the objective, the more photons it captures and focuses. The diameter of Jupiter is apparent size of the source, but it's not the size of the 'stream' once it reaches us, FWIW.

 

IOW, not like a hose, but rather like a 360 degree / 3D shower head of infinitely small individual streams.

Yeah. I get this. And I think I over-simplified my diagram. I understand that photons sourced from the right "edge" of Jupiter are not all traveling in a direct straight line to my eye. Some of them are moving off to the left slightly. Some are traveling off in unobservable directions. And some are crossing photons originating from the left side, etc.

But if we were to look at the area of my retina being illuminated by photos, it will only be a small 'circle' if you will. That is why our brain perceives Jupiter as round. And so this area is not only measureable, but should be similar to the area of the primary mirror being illuminated. The exception being the surface characteristics of the receiving device.



#10 nhanimator

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Posted 21 September 2021 - 09:51 AM

Okay, wait. I think I get this now. The bucket analog got me thinking correctly. Essentially, every single square millimeter of the mirror is receiving photons originating from Jupiter.

 

Duh. And thanks!


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#11 Jon Isaacs

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Posted 21 September 2021 - 09:51 AM

For the same reason a bigger bucket catches more rain.

 

It's all about the area of the objective end.

 

Personally, I think you're all wet.  :)

 

Sorry but I just couldn't resist another stupid joke. 

 

Jon


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#12 lphilpot

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Posted 21 September 2021 - 09:53 AM

But if we were to look at the area of my retina being illuminated by photos, it will only be a small 'circle' if you will. That is why our brain perceives Jupiter as round. And so this area is not only measureable, but should be similar to the area of the primary mirror being illuminated. The exception being the surface characteristics of the receiving device.

I'm no optician but Jupiter looks round because it is round, not because our irises are round. If that were true, everything we see would look round. That's only true as you age and gain weight...  smile.gif  The image of Jupiter is formed from gazillions of photons forming overlapping Airy disks that when focused resemble the source of the image.


Edited by lphilpot, 21 September 2021 - 09:54 AM.

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#13 csrlice12

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Posted 21 September 2021 - 10:02 AM

I think of it as garden hose vs fire hose....



#14 blazek

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Posted 21 September 2021 - 10:03 AM


But if we were to look at the area of my retina being illuminated by photos, it will only be a small 'circle' if you will. That is why our brain perceives Jupiter as round. And so this area is not only measureable, but should be similar to the area of the primary mirror being illuminated. The exception being the surface characteristics of the receiving device.

Tere is a lens between your retina and anything you look to. 

Btw, think about why we all try to close our eyes when looking to Sun.  ( limiting the aperture?)



#15 nhanimator

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Posted 21 September 2021 - 10:06 AM

I'm no optician but Jupiter looks round because it is round, not because our irises are round. If that were true, everything we see would look round. That's only true as you age and gain weight...  smile.gif  The image of Jupiter is formed from gazillions of photons forming overlapping Airy disks that when focused resemble the source of the image.

I wasn't implying our retinas were round. It's the retina's job to receive light, convert it to signals and send them to the brain which then interprets those signals. It's receiving photons that are making up a round shape.

Whether Jupiter actually IS round is a whole other discussion because we can't ever actually SEE Jupiter itself.


Edited by nhanimator, 21 September 2021 - 10:07 AM.


#16 MikeTahtib

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Posted 21 September 2021 - 10:06 AM

It took me  along time to figure this out.  But Jupiter is not forming an image on the mirror that then gets projected into your eye.  Rather, every spot on the mirror is receiving light from every spot in front of it.  It then focuses that light to a particular spot at the focal plane.  The spot on the focal plane is determined by how far off axis the spot on Jupiter is.  So the very center of Jupiter will shine light all around a hemispherical dome throughout the universe.  You mirror will grab a 10" circle of that light and project it to a point on the focal plane.  The next spot over on Jupiter will also project a similar dome, your entire mirror will grab a 10" circle of that light and focus it right next to the first spot, because the light is coming from off-axis.  This happens for every spot on Jupiter.


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#17 nhanimator

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Posted 21 September 2021 - 10:09 AM

It took me  along time to figure this out.  But Jupiter is not forming an image on the mirror that then gets projected into your eye.  Rather, every spot on the mirror is receiving light from every spot in front of it.  It then focuses that light to a particular spot at the focal plane.  The spot on the focal plane is determined by how far off axis the spot on Jupiter is.  So the very center of Jupiter will shine light all around a hemispherical dome throughout the universe.  You mirror will grab a 10" circle of that light and project it to a point on the focal plane.  The next spot over on Jupiter will also project a similar dome, your entire mirror will grab a 10" circle of that light and focus it right next to the first spot, because the light is coming from off-axis.  This happens for every spot on Jupiter.

Yes! This is how I see it now. Excellent explanation. Thanks!


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#18 Asbytec

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Posted 21 September 2021 - 10:13 AM

Okay, wait. I think I get this now. The bucket analog got me thinking correctly. Essentially, every single square millimeter of the mirror is receiving photons originating from Jupiter.

Duh. And thanks!

Remember Jupiter is huge. Larger than the Earth. So it's "raining" photons over a very large spherical area, larger than the thin beam captured by your iris or your "light bucket". Someone halfway around the world is catching light from Jupiter, too.

Think of a cookie cutter cutting a sheet of dough into small cookies. The light arriving from Jupiter is pretty much flat like the dough and your mirror is cutting "cookies" from it. So is the telescope halfway around the world.

Jupiter is at optical infinity. So, by the time the spherical waves from every point on Jove hit earth they are, for all intents and purposes, flat. Your mirror cuts "cookies" from that flat wavefront. As does every scope observing Jove.

Edited by Asbytec, 21 September 2021 - 10:25 AM.


#19 OldManSky

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Posted 21 September 2021 - 11:12 AM

Seems like your eye has to fit into the equation somewhere.  If your eye was twice as large as it is, would you garner more photons?  Does the size of the object emitting the photons define the "steam"?  Hopefully, some rocket scientist optics guys and gals will clear this up for us.

Your eye has an iris that opens and closes.  Fully open (like it does at night), it gathers more photons.  Because its area is larger.  Fully stopped down (which isn't "fully closed"), like it does during the daytime when the sun is bright, it lets in less photons -- because its area is smaller.  :)



#20 swsantos

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Posted 21 September 2021 - 11:32 AM

I'm hoping someone can explain this to me like I've five. I'll make some assumptions and a conclusion here. Please tell me where I am wrong.

 

I think of the light coming from Jupiter as a non-stop stream of photons. Sort of like a hose pointed directly at my eyes. And that stream is essentially round - like the planet's facing surface. This stream is actually pointing out in all directions, but only the particles that are pointed directly towards my eye are the ones I see. The person standing next to me is getting their own stream and the two do not mix (i.e. we don't see the same particles).

 

Let's say that Jupiter is 40 arcseconds across. This defines the width of said stream and is essentially identical for me, the person next to me, my 4.5" scope and my 10" scope. So the diameter of mirror being directly struck seems like it would be the same. Yet the 10" scope is capturing more photons.

 

My initial guess was that the larger mirror had a higher 'resolution' (better construction) and was better able to resolve the stream. But further thinking leads me to believe that it has to do more with the curvature of the mirror. If I look directly down the tube, then the flow of photons would appear to be hitting the mirror in a circular fashion. Yet the concavity of a mirror means that the area being struck by photos is not circular, but oval-shaped, and that that shape itself is 'elongated' across the surface. The elongated oval is wider on the 10" (as the concavity is perhaps less pronounced) and thus has more area. This results in more photons captured.

 

Am I close?

A telescope is like a bucket in a rainstorm the bigger the bucket the more rain it gathers.

 

Given that Jupiter’s photons are not converging on the Earth, the width of the parallel light rays coming from Jupiter is the diameter of the planet so about 89000 miles in diameter, the small pictogram of Jupiter being smaller than the objective of the telescope is not an accurate analogy.


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#21 nhanimator

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Posted 21 September 2021 - 11:57 AM

A telescope is like a bucket in a rainstorm the bigger the bucket the more rain it gathers.

 

Given that Jupiter’s photons are not converging on the Earth, the width of the parallel light rays coming from Jupiter is the diameter of the planet so about 89000 miles in diameter, the small pictogram of Jupiter being smaller than the objective of the telescope is not an accurate analogy.

Wait. Are you saying that Jupiter is LARGER than my telescope?!?shocked.gif


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#22 t-ara-fan

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Posted 21 September 2021 - 01:10 PM

Remember there are no stupid questions, only ...   lol.gif



#23 johnnyt

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Posted 21 September 2021 - 02:45 PM

Think about it like this.  If you are gathering rain water during a storm, a vessel with a larger surface area is going to collect more water than one with a smaller surface area for a given time period.



#24 teashea

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Posted 21 September 2021 - 07:32 PM

I'm hoping someone can explain this to me like I've five. I'll make some assumptions and a conclusion here. Please tell me where I am wrong.

 

I think of the light coming from Jupiter as a non-stop stream of photons. Sort of like a hose pointed directly at my eyes. And that stream is essentially round - like the planet's facing surface. This stream is actually pointing out in all directions, but only the particles that are pointed directly towards my eye are the ones I see. The person standing next to me is getting their own stream and the two do not mix (i.e. we don't see the same particles).

 

Let's say that Jupiter is 40 arcseconds across. This defines the width of said stream and is essentially identical for me, the person next to me, my 4.5" scope and my 10" scope. So the diameter of mirror being directly struck seems like it would be the same. Yet the 10" scope is capturing more photons.

 

My initial guess was that the larger mirror had a higher 'resolution' (better construction) and was better able to resolve the stream. But further thinking leads me to believe that it has to do more with the curvature of the mirror. If I look directly down the tube, then the flow of photons would appear to be hitting the mirror in a circular fashion. Yet the concavity of a mirror means that the area being struck by photos is not circular, but oval-shaped, and that that shape itself is 'elongated' across the surface. The elongated oval is wider on the 10" (as the concavity is perhaps less pronounced) and thus has more area. This results in more photons captured.

 

Am I close?

No, not close.  The diagram is incorrect.  It does now show the light be focused.

 

More collecting area equals more photons collected.  



#25 nhanimator

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Posted 22 September 2021 - 05:59 AM

I removed the diagram from my original post. I was asking a question about something I didn't understand and had illustrated my original thoughts on the subject. Despite completely understanding the concept now (with thanks to the many who helped explain it), I don't wish to propagate confusion for any new readers. So it's gone.


Edited by nhanimator, 22 September 2021 - 06:00 AM.

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