What are the physical limitations?

[mateoc15]

1. What are the physical and optical limitations that prevent manufacturers from making every lens f/1.4 all the way to f/32?
2. I seem to get different answers on this one, but what do the aperture numbers mean? Does it vary based on the number of blades in the diaphragm?
3. Why do many zoom lenses have a different maximum aperture at minimum and maximum focal lengths?

Thanks!

[jdgonzalez]

I can't answer definitely number 1 and 3 but number 2 is a ratio. It's the ratio is between the diameter of the aperture in the lens and the focal length of the lens.

I'm curious as to what the answer is for #1. Great questions!

[OsmosisStudios]

The aperture of a lens is expressed as f/#. The f, in this case, is the focal length. The number is a surface area ratio of the opening. What this means is that you can figure out the physical diameter of the aperture by dividing your focal length by the aperture number

100mm at f/2 means a 50mm aperture diameter (the size of the opening in the blades)
100mm at f/4 means a 25mm aperture diameter.
And so on.

The reason you cant have a 300mm f/1.4 is that 300/1.4 = roughly 215mm. Can you imagine a lens with an almost 9inch APERTURE diameter (so at least a foot across at the front)? It's physically possible (Sigma *do* make a 500mm f/2.8), but it's HUGE and expensive. Not to mention the fact that the DoF at 300mm/1.4 would be infinitesimal.

The aperture just depends on the physical size of the lens and the focal length. The number of blades impacts bokeh, but not the aperture.

Those should answer #1 and #2. As for #3...

If you have a zoom, you have multiple focal lengths. For sake of argument, let's assume a 50-100mm f/2-4 lens (round numbers are excellent). Since most of these zooms are fairly small (think the 18-55 kit lenses, for instance), the max aperture of f/2 at 50mm means a maximum 25mm aperture diameter. THis is usually close to the maximum size the aperture can have. So, if you increase the focal length (to 100mm, for instance), your aperture cant get any bigger, so you end up having to have an f/4 aperture (still 25mm).

Why, you might ask, cant we then make a 50-100 f/1.4-2 lens? Well, I'm no lens designer but that would be BIG and expensive, but I know there are other reasons (Where's Inkista when you need her...)

There's a reason a 24-70 f/2.8 lens 2-3 times the size of a 18-55 f/3.5-5.6 lens.

[mateoc15]

Wow Oz. That's the most thorough and informative answer I've ever received on these forums. The "/" in f/4 can actually be thought of as a division sign. Makes sense!

So, the only true physical limitation is the actual physical size and weight of the lens. Anything too big would be impractical (and crazy expensive) which is why they don't exist. But it's physically possible to make a 1000mm f/1.4 if the diameter of the aperture opening were 714mm wide. AWESOME! To the garage for some glass blowing and lathe turning!

I feel enlightened. Thanks!

[BCampbell]

Originally Posted by OsmosisStudios

100mm at f/2 means a 50mm aperture diameter (the size of the opening in the blades)
100mm at f/4 means a 25mm aperture diameter.
And so on.

The reason you cant have a 300mm f/1.4 is that 300/1.4 = roughly 215mm. Can you imagine a lens with an almost 9inch APERTURE diameter (so at least a foot across at the front)? It's physically possible (Sigma *do* make a 500mm f/2.8), but it's HUGE and expensive. Not to mention the fact that the DoF at 300mm/1.4 would be infinitesimal.

That's a really good, succinct breakdown.

To follow up, remember that our lenses focus light. The main issue is that, as you can see, at longer focal lengths you need a larger and larger physical aperture to retain the same f-number. That also means that to get the light through that aperture, you need larger and larger lens elements. You can easily see this just by looking at product photos, for example, the Canon 200mm f/2. That front element is huge, and heavy, and at some point it becomes economically very very difficult to produce these lens elements. In terms of engineering, it just becomes a ridiculous exercise. That lens already weighs five and a half pounds; it's little brother, the 200mm f/2.8 weighs under two. Size and weight increase exponentially.

Good question, though.

[inkista]

Originally Posted by OsmosisStudios

The number is a surface area ratio of the opening. ...

Oh, so close, my young Padawan, but not quite exact. Examples are fine, though.

The f-number is the ratio of the focal length to the aperture opening diameter.

so f_number = focal_length/aperture_diameter.

Which is why, if you know your algebra, you also get:

aperture diameter = focal length/f_number. (which is how the 100mm at f/2 = 50mm works).

That's why aperture is often written as f/#, the f stands for focal length. Expressing aperture as an f:f-number ratio takes the focal length out of the equation and is going to be the same for any lens, regardless of the focal length. (That's also why you'll see it written as 1:# on some lenses).

The reason, though, that the f-number scale isn't linear (where f/1, f/2, and f/3 would be equal steps) is because the proportional amount of light that's let in via the aperture relates to the area of the opening, not the diameter.

πr² is the area (assuming a circular opening). And, obviously, the radius is half of the diameter.

So, compared to the f-number, it's the square of the diameter we're talking about being proportional to the amount of light coming in (we can factor out the half and pi since they're constants and we're talking proportions and ratios). And stops are about doubling/halving the light. So the f-number stop scale is a square-root-of-two scale. Which is why the numbers always look so funky. While iso numbers and shutter speed numbers simply halve/double between the stops (i.e., iso 100-> iso 200 or 1/100s -> 1/50s), f-numbers don't double between stops. Their squares double between stops.

1.4 ~= sqrt (2)
2 = sqrt (4)
2.8 ~= sqrt (8)
4 = sqrt (16)
5.6 ~= sqrt (32)
8 = sqrt (64)
11 ~= sqrt (128)
16 = sqrt (256)
22 ~= sqrt (512)
32 = sqrt (1024)

As for the physical limitations on the minimum aperture side of things, well, mechnically, you can only promise so much precision on how much you can close down the blades. With some focal lengths, the distinction between f/32 and f/45 might be less than a 10th of a millimeter of movement on each blade. That kind of precision also costs, just as shaping larger lens elements with that kind of precision does.

There's reasons why a lens like a 200mm f/2 now costs $5000, while a 200mm f/2.8 only costs about $750. Also, why Canon went from making the 200mm f/1.8L to making the 200mm f/2L.

[mateoc15]

Really helps explain the huge price difference in the Nikon 50mm f/1.4 and the 50mm f/1.8! 30% bigger area with the 1.4, but I can't justify spending that much more. The only real reason I can see for that is if you want extremely shallow DOF, but I get that with my 1.8 just fine.

[mateoc15]

Thanks to everyone! Inkista I figured it had to be more proportional to area of the opening rather than diameter of the opening, but the idea is the same.

Wow... really feel educated.

Back to the glass blowing and lathe...

[RichardTaylor]

@ mateoc15

Also it allows you top shoot at double the shutter speed which when hand holding in low light can make the difference in getting a shot and not getting a shot.

Example with a 135 F2 lens


Camera Canon EOS 40D
Exposure 0.005 sec (1/200)
Aperture f/2.0
Focal Length 135 mm
ISO Speed 3200
Exposure Bias 0 EV
Flash Off, Did not fire

I can't reliably get sharp enough pics when shooting hand held at 1/100
but at 1/200 I get a lot of keepers.

[OsmosisStudios]

Originally Posted by inkista

WHOA

You fascinate me.