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My impression is that the aperture value of a lens determines its light gathering ability, but I'm not sure I understand how it works...

When considering light gathering in telescopes, it is dependant on the diameter of the objective lens (or mirror). This makes perfect sense to me, since light is radiated in all directions, so a larger area means you gather more light. It seems to me it should be the same in camera lenses also - a larger lens would pick up more of the cone of light from the subject, and focus it onto the sensor.

What got me thinking about it was I've seen an F/0.95 lens, but it doesn't look hugely larger than F/2.8 lenses, so I don't understand the physics of how that would work.

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Related: How does the lens diameter influence photo quality? –  mattdm Jan 13 '12 at 14:30
    
Just had a good look through that and I'm still left a bit confused! Does the aperture relate in some way to the diameter of the lens? –  asc99c Jan 13 '12 at 15:08
    
Not particularly, no, but you ask about the diameter of the objective lens. –  mattdm Jan 13 '12 at 15:20
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4 Answers

up vote 7 down vote accepted

Essentially yes, light gathering ability of a lens is determined by its maximum aperture. Transmission rates of the materials used also has an effect but it is very small.

You intuition is correct in that you would expect a large aperture lens to have a large barrel, however the aperture is specified as a ratio of the apparent* size of lens opening divided by the focal length. So a 200mm f/2.0 lens must have a front element large enough to see a 200/2.0 = 100mm aperture, so the barrel must be at least 10cm. However a 20mm f/2.0 only appears to have a 10mm aperture, which is small is comparison to most lens sizes.

To complicate matters wide angle lenses need larger front elements than dictated by their aperture to prevent vignetting across the frame. For focal lengths shorter than about 50mm lens sizes increase as focal length decreases despite apertures, and thus light gathering ability, also decreasing.

Here's nice example, this Nikon lens is only f/2.8:

but is absolutely huge, due to its extreme wide angle nature.

* note that 100mm f/2.0 doesn't mean the physical opening in the middle of the lens is actually 50mm diameter, only that the image of said opening when viewed through the front of the lens appears to be 50mm in diameter. The actually opening is often smaller, but the lens front element has to be large enough to accommodate its theoretical size.

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Love your last paragraph there! It seems obvious now - but I always did wonder why, when I knew what I explained in my answer, my 24mm f/1.4 lens was so much bigger than my 50mm f/1.4! –  Mike Jan 13 '12 at 17:19
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I think I've got it. Essentially for a F/0.95 50mm lens, the effective diameter has to be 52.6mm. That isn't particularly enormous, but to be that size, the lens would have to be able to focus light hitting the very edge of the lens back to the correct point of the sensor. Generally cheap lenses will not be able to achieve this, so even though the cheap lens may be 52.6mm or bigger, only light hitting fairly close to the centre can actually be used for a focused image - if you dismantled it to remove the aperture blades, you would get more light in, but not focused to an image. –  asc99c Jan 13 '12 at 18:13
    
Just for reference, the f/# usually refers to the "entrance pupil", which is the official term for the aperture size as viewed through the front of the lens. Conversely, the "exit pupil" would be the aperture size as viewed through the back of the lens. –  jrista Jan 13 '12 at 18:29
    
@Matt Grum: Just out of curiosity, what Nikon lens is that? Is that actually how big it is, and what it looks like? Probably the oddest SLR lens I've ever seen... –  jrista Jan 13 '12 at 18:30
    
@jrista That's the 220-degree Nikon 6mm f/2.8 circular fisheye. Yes, 220 degrees -- you can stand behind the camera, and if you're too close, peeking over the top of the camera, you can actually appear in the picture. –  user2719 Jan 14 '12 at 2:39
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Think about stopping down your telescope. Many scopes come with lens caps that have a circular hole cut in the center with a secondary cap on that.

If you operate your scope with the lens cap ON but the secondary cap OFF you have now stopped down your scope. Your f8 scope could now be, say, an f20 scope without any changes to the objective lens diameter. This really freaked me out since I started in telescopes before cameras and I had the exact same confusion you have.

Do you have an old 35mm film camera sitting around? Open up the back and look through the lens, essentially, your eye is now the film. Press the shutter. You'll see a brief flash of light through the mostly circular aperture. (Even better, set the shutter speed slow so the brief flash is less brief.) Now play with the aperture setting, compare, say f2.8 with f16. Notice how the size of the circular hole changes?

If you don't have an old film camera, try this with your DSLR, but looking in the front, look for something to change inside the lens, direct center, as you play with aperture.

Cameras gets stopped down a lot. You need to do this to both change the length of the exposure as well as control depth of field.

Telescopes are rarely stopped down. You probably only want to do it for solar or lunar observing. Why? You don't need the extra light but unless you have an APO refractor, stopping it down will decrease the chromatic aberration considerably. I had a chance to see Galileo telescope in Philadelphia. It was perhaps 1 to 1.5 inches in diameter but it was stopped down to something tiny, like 0.5" or so! This was done to reduce the aberrations in his primitive lenses.

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I understand the physical idea of stopping down a lens. Just because you've got a large lens doesn't mean you have to use it wide open. The bit I'm confused about is that the large aperture lenses don't seem to need to be as much bigger compared to the smaller aperture ones as I would expect. –  asc99c Jan 13 '12 at 17:50
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You are nearly correct that the physical diameter of the lens has a direct effect on the light gathering properties of the lens.

However you also need to take into account the focal length of the lens.

The maths is quite straight forward:

Maximum Aperture (F-Stop) = Focal Length / Diameter of lens

As an example, lets choose f/4 as it's a nice easy round number...

  • To achieve f/4 for example at 400mm, the diameter of the lens will be 100mm.
  • To achieve f/4 at 100mm, the diameter of the lens would have to be 25mm.
  • To achieve f/4 at 50mm, the diameter of the lens will be 12.5mm.

So on say, a 50mm lens, to achieve f/0.95 as you stated in your question, and as this is less than f/1, the diameter of the lens will actually need to be slightly larger than the focal length of the lens at 52.63mm.

Note it may be easier to switch the equation to:

Diameter of lens = Focal Length / Maximum Aperture (F-Stop)

So as to your original question about an f/0.95 lens not being much larger than a f/2.8 lens, you would need to ensure that both lenses were of the same focal length. Then you would see that the 0.95 was indeed larger than the 2.8, and using the equation above, you can work out exactly what the diameters of the physical lenses should be in each ;-)

I hope that makes sense???

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That does make sense but I still have some doubts. E.g. 50mm F2.8 here amazon.co.uk/exec/obidos/ASIN/B000GT11FI/watersphotogr-21/… versus 50mm F0.95 here noktor.com/products.php - by this formula, the numbers should be 52.6mm and 17.9mm, and the lenses don't look that far different. –  asc99c Jan 13 '12 at 17:42
    
The pic of the Sony 50mm you link to does't show the glass itself - check the photo on this site swiatobrazu.pl/test_sony_50mm_f28_macro.html and you can see the glass is much much smaller in diameter... :) –  Mike Jan 13 '12 at 18:25
    
Oh yeah! Think things are making sense now. –  asc99c Jan 13 '12 at 18:36
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Others have already explained the difference between entrance pupil and front lens. I would like to add a word for why light gathering power is given by F-numbers.

The difference between a telescope and a photographic lens is that you usually use a telescope to image small objects (small in angular size). Then your subject will almost always fit in the field of view, irrespective of the focal length of the scope. In contrast, you most often use a camera to capture a whole scene that completely fills the frame. Then, shorter focal lengths let you capture more of the scene... and therefore more light!

This makes a big difference in the way “light gathering power” is appreciated. For an astronomer, light gathering power is the ability of a scope to gather luminous flux from a small source providing a given illuminance on earth. It is therefore equivalent to the surface area of the entrance pupil. For a photographer, light gathering power is the ability of a lens (or camera) to gather luminous flux from an extended scene of given average luminance. It then depends on both the entrance pupil and the field of view. That's why we use f-numbers instead of raw aperture diameters.

See also this answer to a related question.

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