How do apertures which seem too large to physically fit work? [duplicate] The Next CEO of Stack OverflowIs the size of the entrance pupil the same as the size of the effective aperture?Why doesn't the picture become darker the more you zoom in?How do zoom lenses restrict their widest aperture at the telephoto end?How is the F stop number derived?Why do lenses have different diameters?How wide does the front element of a lens have to be, given the focal length and the aperture?How do constant aperture zoom lenses work?Does the size of the front glass mean anything?How do different apertures affect photographs?Why aren't lenses designed with extra large apertures for autofocus beyond what's used for imaging?Who tells my camera which apertures my lens hasWhy do landscape photos with large apertures have dark corners?Which filters will fit Voigtlander 15mm?How can I use flash with large apertures?Why are large zoom ratio constant apertures lenses not generally available?Can too-tight lens hoods become accidental apertures?

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How do apertures which seem too large to physically fit work? [duplicate]



The Next CEO of Stack OverflowIs the size of the entrance pupil the same as the size of the effective aperture?Why doesn't the picture become darker the more you zoom in?How do zoom lenses restrict their widest aperture at the telephoto end?How is the F stop number derived?Why do lenses have different diameters?How wide does the front element of a lens have to be, given the focal length and the aperture?How do constant aperture zoom lenses work?Does the size of the front glass mean anything?How do different apertures affect photographs?Why aren't lenses designed with extra large apertures for autofocus beyond what's used for imaging?Who tells my camera which apertures my lens hasWhy do landscape photos with large apertures have dark corners?Which filters will fit Voigtlander 15mm?How can I use flash with large apertures?Why are large zoom ratio constant apertures lenses not generally available?Can too-tight lens hoods become accidental apertures?










12
















This question already has an answer here:



  • Is the size of the entrance pupil the same as the size of the effective aperture?

    2 answers



A 400mm f4.0 lens is supposed to have a maximum aperture diameter of 10cm. Looking at such a lens they don't seem big enough to fit that kind of aperture including all the mechanics for control inside them. Do modern lenses have a way of focusing light into a smaller aperture to behave like a bigger one or are they really always the size that the formula (fstop = focal length / aperture diameter) suggests?










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marked as duplicate by Michael C lens
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Mar 23 at 7:42


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  • 1





    Related: How do zoom lenses restrict their widest aperture at the telephoto end? and How wide does the front element of a lens has to be, given the focal length and the aperture? and How is the F stop number derived? and Why doesn't the picture become darker the more you zoom in? and Why do lenses have different diameters?

    – Michael C
    Mar 23 at 8:25











  • I'm not sure this is the same question as the dupe. Answers to that question — for that matter, the question itself — assume understanding of effective aperture, which is basically the answer here. That question is more of a follow up detail.

    – mattdm
    Mar 23 at 14:54















12
















This question already has an answer here:



  • Is the size of the entrance pupil the same as the size of the effective aperture?

    2 answers



A 400mm f4.0 lens is supposed to have a maximum aperture diameter of 10cm. Looking at such a lens they don't seem big enough to fit that kind of aperture including all the mechanics for control inside them. Do modern lenses have a way of focusing light into a smaller aperture to behave like a bigger one or are they really always the size that the formula (fstop = focal length / aperture diameter) suggests?










share|improve this question









New contributor




LuLeBe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











marked as duplicate by Michael C lens
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  • 1





    Related: How do zoom lenses restrict their widest aperture at the telephoto end? and How wide does the front element of a lens has to be, given the focal length and the aperture? and How is the F stop number derived? and Why doesn't the picture become darker the more you zoom in? and Why do lenses have different diameters?

    – Michael C
    Mar 23 at 8:25











  • I'm not sure this is the same question as the dupe. Answers to that question — for that matter, the question itself — assume understanding of effective aperture, which is basically the answer here. That question is more of a follow up detail.

    – mattdm
    Mar 23 at 14:54













12












12








12


1







This question already has an answer here:



  • Is the size of the entrance pupil the same as the size of the effective aperture?

    2 answers



A 400mm f4.0 lens is supposed to have a maximum aperture diameter of 10cm. Looking at such a lens they don't seem big enough to fit that kind of aperture including all the mechanics for control inside them. Do modern lenses have a way of focusing light into a smaller aperture to behave like a bigger one or are they really always the size that the formula (fstop = focal length / aperture diameter) suggests?










share|improve this question









New contributor




LuLeBe is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.













This question already has an answer here:



  • Is the size of the entrance pupil the same as the size of the effective aperture?

    2 answers



A 400mm f4.0 lens is supposed to have a maximum aperture diameter of 10cm. Looking at such a lens they don't seem big enough to fit that kind of aperture including all the mechanics for control inside them. Do modern lenses have a way of focusing light into a smaller aperture to behave like a bigger one or are they really always the size that the formula (fstop = focal length / aperture diameter) suggests?





This question already has an answer here:



  • Is the size of the entrance pupil the same as the size of the effective aperture?

    2 answers







lens aperture lens-design physics






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share|improve this question









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share|improve this question




share|improve this question








edited Mar 22 at 17:46









mattdm

122k40357653




122k40357653






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asked Mar 22 at 16:13









LuLeBeLuLeBe

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633




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marked as duplicate by Michael C lens
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marked as duplicate by Michael C lens
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This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.









  • 1





    Related: How do zoom lenses restrict their widest aperture at the telephoto end? and How wide does the front element of a lens has to be, given the focal length and the aperture? and How is the F stop number derived? and Why doesn't the picture become darker the more you zoom in? and Why do lenses have different diameters?

    – Michael C
    Mar 23 at 8:25











  • I'm not sure this is the same question as the dupe. Answers to that question — for that matter, the question itself — assume understanding of effective aperture, which is basically the answer here. That question is more of a follow up detail.

    – mattdm
    Mar 23 at 14:54












  • 1





    Related: How do zoom lenses restrict their widest aperture at the telephoto end? and How wide does the front element of a lens has to be, given the focal length and the aperture? and How is the F stop number derived? and Why doesn't the picture become darker the more you zoom in? and Why do lenses have different diameters?

    – Michael C
    Mar 23 at 8:25











  • I'm not sure this is the same question as the dupe. Answers to that question — for that matter, the question itself — assume understanding of effective aperture, which is basically the answer here. That question is more of a follow up detail.

    – mattdm
    Mar 23 at 14:54







1




1





Related: How do zoom lenses restrict their widest aperture at the telephoto end? and How wide does the front element of a lens has to be, given the focal length and the aperture? and How is the F stop number derived? and Why doesn't the picture become darker the more you zoom in? and Why do lenses have different diameters?

– Michael C
Mar 23 at 8:25





Related: How do zoom lenses restrict their widest aperture at the telephoto end? and How wide does the front element of a lens has to be, given the focal length and the aperture? and How is the F stop number derived? and Why doesn't the picture become darker the more you zoom in? and Why do lenses have different diameters?

– Michael C
Mar 23 at 8:25













I'm not sure this is the same question as the dupe. Answers to that question — for that matter, the question itself — assume understanding of effective aperture, which is basically the answer here. That question is more of a follow up detail.

– mattdm
Mar 23 at 14:54





I'm not sure this is the same question as the dupe. Answers to that question — for that matter, the question itself — assume understanding of effective aperture, which is basically the answer here. That question is more of a follow up detail.

– mattdm
Mar 23 at 14:54










2 Answers
2






active

oldest

votes


















17














Your observations of the lens leads you to both a correct, and incorrect, conclusion.



  1. Correct: the aperture (i.e., mechanical iris) of the lens is substantially smaller than the 10 cm it supposedly should be. Only the front element is anywhere near 10 cm diameter. Where the iris mechanism is in the lens barrel, the diameter is substantially smaller than 10 cm.


  2. Incorrect: the stated aperture size is not actually 10 cm in diameter. In reality, it is the the apparent size of the wide-open aperture (the iris), when viewed through the front of the lens, that is 10 cm in diameter.


For any lens, the aperture when viewed through the front of the lens is known as the entrance pupil. It is the entrance pupil that is 10 cm in diameter.



See also:



  • Size of the entrance pupil vs size of the aperture





share|improve this answer




















  • 1





    That made it so clear, even better than the first answer. I think I understood it now, hopefully! Thank you very much!

    – LuLeBe
    Mar 22 at 18:30






  • 3





    Or to flip the description around: the light that gets through the aperture formed a 10 cm disk where it met the objective lens. When you increase the f-stop you start intercepting some of that light.

    – dmckee
    Mar 22 at 19:14











  • @dmckee Absolutely, great way of stating it from the iris's viewpoint! =)

    – scottbb
    Mar 22 at 19:30











  • So, this is why we almost always see f-numbers used instead of absolute sizes in centimeters! Because f-numbers don't change when zooming while sizes of entrance pupil do.

    – Ruslan
    Mar 22 at 22:15












  • @bogl Actually, the opposite is true. Almost all of the light passing through a telephoto lens is nearly perpendicular to the imaging plane, thus the front element needs to be as wide as the ep. With a WA lens the front element can be smaller than the ep, but this leads to darker edges of the frame. Wider angle lenses (particularly retrofocus designs) require a much larger front element than ep in order to allow the ep (or at least most of it) to be seen from the lens' full angle of view. Please see this answer for more.

    – Michael C
    Mar 23 at 8:31



















2














Lens designers have a few tricks up their sleeves. As an example, zoom lenses change focal lengths but the aperture diameter does not physically change with the zoom. This is an oddity because as the focal length changes, so does image brightness. In fact, if the focal length is doubled, image brightness falls off 4X. Conversely, if the focal length halves, image brightness will increases 4X. How do you think the optician compensated and maintained the exposure? The front group of lens elements acts as a magnifier. In other words, the diameter of the iris as seen by the outside world appears expand and contract with the zoom when in fact it is fixed as to diameter. It is the apparent diameter of the iris and not the actual diameter that determines the light gathering power of the lens. Note: most inexpensive zooms give up the ghost as the user zooms towards max magnification. A more costly zoom will likely maintain a constant exposure throughout the zoom.






share|improve this answer


















  • 1





    Right yes I know about constant aperture zoom lenses. I originally thought they'd have a larger aperture and just close it down when zoomed out. But that makes much more sense the way you explained it, thanks!

    – LuLeBe
    Mar 22 at 17:26

















2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









17














Your observations of the lens leads you to both a correct, and incorrect, conclusion.



  1. Correct: the aperture (i.e., mechanical iris) of the lens is substantially smaller than the 10 cm it supposedly should be. Only the front element is anywhere near 10 cm diameter. Where the iris mechanism is in the lens barrel, the diameter is substantially smaller than 10 cm.


  2. Incorrect: the stated aperture size is not actually 10 cm in diameter. In reality, it is the the apparent size of the wide-open aperture (the iris), when viewed through the front of the lens, that is 10 cm in diameter.


For any lens, the aperture when viewed through the front of the lens is known as the entrance pupil. It is the entrance pupil that is 10 cm in diameter.



See also:



  • Size of the entrance pupil vs size of the aperture





share|improve this answer




















  • 1





    That made it so clear, even better than the first answer. I think I understood it now, hopefully! Thank you very much!

    – LuLeBe
    Mar 22 at 18:30






  • 3





    Or to flip the description around: the light that gets through the aperture formed a 10 cm disk where it met the objective lens. When you increase the f-stop you start intercepting some of that light.

    – dmckee
    Mar 22 at 19:14











  • @dmckee Absolutely, great way of stating it from the iris's viewpoint! =)

    – scottbb
    Mar 22 at 19:30











  • So, this is why we almost always see f-numbers used instead of absolute sizes in centimeters! Because f-numbers don't change when zooming while sizes of entrance pupil do.

    – Ruslan
    Mar 22 at 22:15












  • @bogl Actually, the opposite is true. Almost all of the light passing through a telephoto lens is nearly perpendicular to the imaging plane, thus the front element needs to be as wide as the ep. With a WA lens the front element can be smaller than the ep, but this leads to darker edges of the frame. Wider angle lenses (particularly retrofocus designs) require a much larger front element than ep in order to allow the ep (or at least most of it) to be seen from the lens' full angle of view. Please see this answer for more.

    – Michael C
    Mar 23 at 8:31
















17














Your observations of the lens leads you to both a correct, and incorrect, conclusion.



  1. Correct: the aperture (i.e., mechanical iris) of the lens is substantially smaller than the 10 cm it supposedly should be. Only the front element is anywhere near 10 cm diameter. Where the iris mechanism is in the lens barrel, the diameter is substantially smaller than 10 cm.


  2. Incorrect: the stated aperture size is not actually 10 cm in diameter. In reality, it is the the apparent size of the wide-open aperture (the iris), when viewed through the front of the lens, that is 10 cm in diameter.


For any lens, the aperture when viewed through the front of the lens is known as the entrance pupil. It is the entrance pupil that is 10 cm in diameter.



See also:



  • Size of the entrance pupil vs size of the aperture





share|improve this answer




















  • 1





    That made it so clear, even better than the first answer. I think I understood it now, hopefully! Thank you very much!

    – LuLeBe
    Mar 22 at 18:30






  • 3





    Or to flip the description around: the light that gets through the aperture formed a 10 cm disk where it met the objective lens. When you increase the f-stop you start intercepting some of that light.

    – dmckee
    Mar 22 at 19:14











  • @dmckee Absolutely, great way of stating it from the iris's viewpoint! =)

    – scottbb
    Mar 22 at 19:30











  • So, this is why we almost always see f-numbers used instead of absolute sizes in centimeters! Because f-numbers don't change when zooming while sizes of entrance pupil do.

    – Ruslan
    Mar 22 at 22:15












  • @bogl Actually, the opposite is true. Almost all of the light passing through a telephoto lens is nearly perpendicular to the imaging plane, thus the front element needs to be as wide as the ep. With a WA lens the front element can be smaller than the ep, but this leads to darker edges of the frame. Wider angle lenses (particularly retrofocus designs) require a much larger front element than ep in order to allow the ep (or at least most of it) to be seen from the lens' full angle of view. Please see this answer for more.

    – Michael C
    Mar 23 at 8:31














17












17








17







Your observations of the lens leads you to both a correct, and incorrect, conclusion.



  1. Correct: the aperture (i.e., mechanical iris) of the lens is substantially smaller than the 10 cm it supposedly should be. Only the front element is anywhere near 10 cm diameter. Where the iris mechanism is in the lens barrel, the diameter is substantially smaller than 10 cm.


  2. Incorrect: the stated aperture size is not actually 10 cm in diameter. In reality, it is the the apparent size of the wide-open aperture (the iris), when viewed through the front of the lens, that is 10 cm in diameter.


For any lens, the aperture when viewed through the front of the lens is known as the entrance pupil. It is the entrance pupil that is 10 cm in diameter.



See also:



  • Size of the entrance pupil vs size of the aperture





share|improve this answer















Your observations of the lens leads you to both a correct, and incorrect, conclusion.



  1. Correct: the aperture (i.e., mechanical iris) of the lens is substantially smaller than the 10 cm it supposedly should be. Only the front element is anywhere near 10 cm diameter. Where the iris mechanism is in the lens barrel, the diameter is substantially smaller than 10 cm.


  2. Incorrect: the stated aperture size is not actually 10 cm in diameter. In reality, it is the the apparent size of the wide-open aperture (the iris), when viewed through the front of the lens, that is 10 cm in diameter.


For any lens, the aperture when viewed through the front of the lens is known as the entrance pupil. It is the entrance pupil that is 10 cm in diameter.



See also:



  • Size of the entrance pupil vs size of the aperture






share|improve this answer














share|improve this answer



share|improve this answer








edited Mar 22 at 18:32

























answered Mar 22 at 18:28









scottbbscottbb

20.7k75895




20.7k75895







  • 1





    That made it so clear, even better than the first answer. I think I understood it now, hopefully! Thank you very much!

    – LuLeBe
    Mar 22 at 18:30






  • 3





    Or to flip the description around: the light that gets through the aperture formed a 10 cm disk where it met the objective lens. When you increase the f-stop you start intercepting some of that light.

    – dmckee
    Mar 22 at 19:14











  • @dmckee Absolutely, great way of stating it from the iris's viewpoint! =)

    – scottbb
    Mar 22 at 19:30











  • So, this is why we almost always see f-numbers used instead of absolute sizes in centimeters! Because f-numbers don't change when zooming while sizes of entrance pupil do.

    – Ruslan
    Mar 22 at 22:15












  • @bogl Actually, the opposite is true. Almost all of the light passing through a telephoto lens is nearly perpendicular to the imaging plane, thus the front element needs to be as wide as the ep. With a WA lens the front element can be smaller than the ep, but this leads to darker edges of the frame. Wider angle lenses (particularly retrofocus designs) require a much larger front element than ep in order to allow the ep (or at least most of it) to be seen from the lens' full angle of view. Please see this answer for more.

    – Michael C
    Mar 23 at 8:31













  • 1





    That made it so clear, even better than the first answer. I think I understood it now, hopefully! Thank you very much!

    – LuLeBe
    Mar 22 at 18:30






  • 3





    Or to flip the description around: the light that gets through the aperture formed a 10 cm disk where it met the objective lens. When you increase the f-stop you start intercepting some of that light.

    – dmckee
    Mar 22 at 19:14











  • @dmckee Absolutely, great way of stating it from the iris's viewpoint! =)

    – scottbb
    Mar 22 at 19:30











  • So, this is why we almost always see f-numbers used instead of absolute sizes in centimeters! Because f-numbers don't change when zooming while sizes of entrance pupil do.

    – Ruslan
    Mar 22 at 22:15












  • @bogl Actually, the opposite is true. Almost all of the light passing through a telephoto lens is nearly perpendicular to the imaging plane, thus the front element needs to be as wide as the ep. With a WA lens the front element can be smaller than the ep, but this leads to darker edges of the frame. Wider angle lenses (particularly retrofocus designs) require a much larger front element than ep in order to allow the ep (or at least most of it) to be seen from the lens' full angle of view. Please see this answer for more.

    – Michael C
    Mar 23 at 8:31








1




1





That made it so clear, even better than the first answer. I think I understood it now, hopefully! Thank you very much!

– LuLeBe
Mar 22 at 18:30





That made it so clear, even better than the first answer. I think I understood it now, hopefully! Thank you very much!

– LuLeBe
Mar 22 at 18:30




3




3





Or to flip the description around: the light that gets through the aperture formed a 10 cm disk where it met the objective lens. When you increase the f-stop you start intercepting some of that light.

– dmckee
Mar 22 at 19:14





Or to flip the description around: the light that gets through the aperture formed a 10 cm disk where it met the objective lens. When you increase the f-stop you start intercepting some of that light.

– dmckee
Mar 22 at 19:14













@dmckee Absolutely, great way of stating it from the iris's viewpoint! =)

– scottbb
Mar 22 at 19:30





@dmckee Absolutely, great way of stating it from the iris's viewpoint! =)

– scottbb
Mar 22 at 19:30













So, this is why we almost always see f-numbers used instead of absolute sizes in centimeters! Because f-numbers don't change when zooming while sizes of entrance pupil do.

– Ruslan
Mar 22 at 22:15






So, this is why we almost always see f-numbers used instead of absolute sizes in centimeters! Because f-numbers don't change when zooming while sizes of entrance pupil do.

– Ruslan
Mar 22 at 22:15














@bogl Actually, the opposite is true. Almost all of the light passing through a telephoto lens is nearly perpendicular to the imaging plane, thus the front element needs to be as wide as the ep. With a WA lens the front element can be smaller than the ep, but this leads to darker edges of the frame. Wider angle lenses (particularly retrofocus designs) require a much larger front element than ep in order to allow the ep (or at least most of it) to be seen from the lens' full angle of view. Please see this answer for more.

– Michael C
Mar 23 at 8:31






@bogl Actually, the opposite is true. Almost all of the light passing through a telephoto lens is nearly perpendicular to the imaging plane, thus the front element needs to be as wide as the ep. With a WA lens the front element can be smaller than the ep, but this leads to darker edges of the frame. Wider angle lenses (particularly retrofocus designs) require a much larger front element than ep in order to allow the ep (or at least most of it) to be seen from the lens' full angle of view. Please see this answer for more.

– Michael C
Mar 23 at 8:31














2














Lens designers have a few tricks up their sleeves. As an example, zoom lenses change focal lengths but the aperture diameter does not physically change with the zoom. This is an oddity because as the focal length changes, so does image brightness. In fact, if the focal length is doubled, image brightness falls off 4X. Conversely, if the focal length halves, image brightness will increases 4X. How do you think the optician compensated and maintained the exposure? The front group of lens elements acts as a magnifier. In other words, the diameter of the iris as seen by the outside world appears expand and contract with the zoom when in fact it is fixed as to diameter. It is the apparent diameter of the iris and not the actual diameter that determines the light gathering power of the lens. Note: most inexpensive zooms give up the ghost as the user zooms towards max magnification. A more costly zoom will likely maintain a constant exposure throughout the zoom.






share|improve this answer


















  • 1





    Right yes I know about constant aperture zoom lenses. I originally thought they'd have a larger aperture and just close it down when zoomed out. But that makes much more sense the way you explained it, thanks!

    – LuLeBe
    Mar 22 at 17:26















2














Lens designers have a few tricks up their sleeves. As an example, zoom lenses change focal lengths but the aperture diameter does not physically change with the zoom. This is an oddity because as the focal length changes, so does image brightness. In fact, if the focal length is doubled, image brightness falls off 4X. Conversely, if the focal length halves, image brightness will increases 4X. How do you think the optician compensated and maintained the exposure? The front group of lens elements acts as a magnifier. In other words, the diameter of the iris as seen by the outside world appears expand and contract with the zoom when in fact it is fixed as to diameter. It is the apparent diameter of the iris and not the actual diameter that determines the light gathering power of the lens. Note: most inexpensive zooms give up the ghost as the user zooms towards max magnification. A more costly zoom will likely maintain a constant exposure throughout the zoom.






share|improve this answer


















  • 1





    Right yes I know about constant aperture zoom lenses. I originally thought they'd have a larger aperture and just close it down when zoomed out. But that makes much more sense the way you explained it, thanks!

    – LuLeBe
    Mar 22 at 17:26













2












2








2







Lens designers have a few tricks up their sleeves. As an example, zoom lenses change focal lengths but the aperture diameter does not physically change with the zoom. This is an oddity because as the focal length changes, so does image brightness. In fact, if the focal length is doubled, image brightness falls off 4X. Conversely, if the focal length halves, image brightness will increases 4X. How do you think the optician compensated and maintained the exposure? The front group of lens elements acts as a magnifier. In other words, the diameter of the iris as seen by the outside world appears expand and contract with the zoom when in fact it is fixed as to diameter. It is the apparent diameter of the iris and not the actual diameter that determines the light gathering power of the lens. Note: most inexpensive zooms give up the ghost as the user zooms towards max magnification. A more costly zoom will likely maintain a constant exposure throughout the zoom.






share|improve this answer













Lens designers have a few tricks up their sleeves. As an example, zoom lenses change focal lengths but the aperture diameter does not physically change with the zoom. This is an oddity because as the focal length changes, so does image brightness. In fact, if the focal length is doubled, image brightness falls off 4X. Conversely, if the focal length halves, image brightness will increases 4X. How do you think the optician compensated and maintained the exposure? The front group of lens elements acts as a magnifier. In other words, the diameter of the iris as seen by the outside world appears expand and contract with the zoom when in fact it is fixed as to diameter. It is the apparent diameter of the iris and not the actual diameter that determines the light gathering power of the lens. Note: most inexpensive zooms give up the ghost as the user zooms towards max magnification. A more costly zoom will likely maintain a constant exposure throughout the zoom.







share|improve this answer












share|improve this answer



share|improve this answer










answered Mar 22 at 16:53









Alan MarcusAlan Marcus

25.9k23060




25.9k23060







  • 1





    Right yes I know about constant aperture zoom lenses. I originally thought they'd have a larger aperture and just close it down when zoomed out. But that makes much more sense the way you explained it, thanks!

    – LuLeBe
    Mar 22 at 17:26












  • 1





    Right yes I know about constant aperture zoom lenses. I originally thought they'd have a larger aperture and just close it down when zoomed out. But that makes much more sense the way you explained it, thanks!

    – LuLeBe
    Mar 22 at 17:26







1




1





Right yes I know about constant aperture zoom lenses. I originally thought they'd have a larger aperture and just close it down when zoomed out. But that makes much more sense the way you explained it, thanks!

– LuLeBe
Mar 22 at 17:26





Right yes I know about constant aperture zoom lenses. I originally thought they'd have a larger aperture and just close it down when zoomed out. But that makes much more sense the way you explained it, thanks!

– LuLeBe
Mar 22 at 17:26



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