Why is aperture backwards??

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CarterJamison012

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So, I get that larger f numbers like f/22 actually mean that it's a smaller opening and that smaller f number like f/2 is a big opening. I learned that thanks to a really helpful beginner video I just watched - https://www.youtube.com/watch?v=fpdxMUWF0k0. But my question is this...WHY is the size of the aperture backwards from the numbers. Shouldn't f/22 be a big aperture since it's a big number and f/2 should be a small aperture since it's a small number???
 
The aperture is a size measurement.

The "ƒ" is the focal length and the number under the / is the number by which it is divisible. So...a 50mm lens at ƒ/2 would be 50/2 or 50 divided by 2. That would be 25mm.

But if it's 50mm divided by 4 (i.e. ƒ/4), it would be 12.5mm--a smaller size.

And at ƒ/22 it is 50 divided by 22=2.272727. So that "22" is a smaller size than the "2".
 
It is the proportion of the smaller opening to the max opening
eg 1:2.8, 1:4, 1:5.6 as you can see the numbers have to go up when the opening gets smaller.
 
Why is aperture backwards??

And most lenses go to 11 just like some amplifiers. 😊

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santino said:
It is the proportion of the smaller opening to the max opening
eg 1:2.8, 1:4, 1:5.6 as you can see the numbers have to go up when the opening gets smaller.
Click to expand...

That's not quite right. It isn't derived from the maximum aperture of an individual lens. If it were, any given aperture number, e.g. f/5.6, on a lens of different maximum aperture, would pass a different amount of light, putting the makers of exposure meters out of business!

The explanation offered above, that the aperture number is a quotient of the focal length divided by the diameter (of the iris) is the answer. When we divide by a larger number, the quotient gets smaller. That's all there is to it!
 
The little sign "/" in the middle of (say) f/2 means "divided by" or it did when I went to school. Like 3/4 is three quarters etc...

So the bigger the number the smaller the hole.

Edit: the letter f should be in italics and is - or perhaps was - the standard symbol for the focal length.


Regards, David


PS The other question everyone asks is why such and odd sequence and the answer is that the numbers are the square root of the series 1,2,4,8,16 and so on.
 
Bill Clark said:
OK, here goes:

Camera lens F Stops use an apparently odd set of numbers. The problem is that the amount of light entering the lens is governed by the area of the aperture; a squared function, not a linear one. If the F Stops increased in a 2 fold linear form (1,2,4,8...) then the exposure would not increase two fold but as a square of this, which is 4 fold. Opening the aperture by one F Stop would therefore quadruple the exposure as 2² = 4. So a set of numbers is needed, that when squared comes to 2, to give the double exposure required. In other words, numbers need to increase by √2, as √2² = 2, to give twice the area.
•  1  x √2 = 1.4
• 1.4 x √2 = 2
• 2  x √2 = 2.8
• 2.8 x √2 = 4
•  4  x √2 = 5.6
• 5.6 x √2 = 8 etc.
Hence the familiar sequence of 1, 1.4, 2, 2.8, etc, used on camera lenses. This now means that one F Stop increase doubles the light exposure, and likewise one F Stop decrease halves it.

Example:

As will be shown below, if we start by f/1.0 as the smallest possible f/stop, the next full stop is 1.0xSqrt(2) = 1.414. This is the first f/stop that corresponds to the bottom row. Now
1.414x2 = 2.828
2.828x2 = 5.686
5.686x2 = 11.312
11.312x2 = 22.624
22.624x2 = 45.248

At any rate, I believe this is correct.
Clear as mud!
Click to expand...

This is correct, and as mentioned above, at f/1.0 the apertures' diameter is equal to the focal length of the lens. There are some rare lenses with the largest opening larger than the focal length, in which case the f-stop becomes a number smaller than 1. The Canon 50mm f0.95 comes to mind, but there are others.

Incidentally, this number sequence is also used to differentiate A paper sizes. The ratio between the short and the long side is 1.4. When you go from an A4 to an A3 paper size, you are doubling the area. In fact a landscape A3 will fit two standing A4 sheets side by side. Going from A3 to A2 it again doubles the area, fitting two standing A3 sheets on a landscape A2. An A2 will be 4 times the area of an A4, so you can fit 4 landscape A4 sheets on a landscape A2 sheet. That would be a 200% increase on a copy machine.
 
On a far more basic level, it's convenient for one new to photography to remember that higher shutter speed numbers (as in 30, 60, 125, etc) and higher f-numbers both correspond to less light. :)

- Murray
 
I remember when year ago teaching my wife to use a film camera in manual mode and seeing her a little confused by the number I told her to forget what I had previously said and just think high level of light, much light she had to use high number like 11 0r 16 or even more. Very low light she had to use small number, 2 2,8 or 3.5. Medium light ? just stay in the middle...

Not a scientific explanation but it worked !
 
robert blu said:
I remember when year ago teaching my wife to use a film camera in manual mode and seeing her a little confused by the number I told her to forget what I had previously said and just think high level of light, much light she had to use high number like 11 0r 16 or even more. Very low light she had to use small number, 2 2,8 or 3.5. Medium light ? just stay in the middle...

Not a scientific explanation but it worked !
Click to expand...

I like that, Robert! An explanation of that kind could be really helpful for someone who is new to photography, and still finding his/her feet, with regard to some of the basic concepts.
 
I'm so glad back in Jr. High no one was trying to explain the math of lens openings to me. I just looked at the aperture and the effect turning the ring had on it. Kind of obvious, right?
 
robert blu said:
I remember when year ago teaching my wife to use a film camera in manual mode and seeing her a little confused by the number I told her to forget what I had previously said and just think high level of light, much light she had to use high number like 11 0r 16 or even more. Very low light she had to use small number, 2 2,8 or 3.5. Medium light ? just stay in the middle...

Not a scientific explanation but it worked !
Click to expand...


My method of learning was just to line up the needles in the viewfinder. After a few months I learned what it meant.:D
 
raydm6 said:
And most lenses go to 11 just like some amplifiers. ��

giphy.gif
Click to expand...

That amplifier that goes to 11 is not actually any louder than one that goes to 10.

Even though it’s one more.

I can refer you to a good documentary: Spinal Tap.

Richard (not exploding any time soon)
 
davidnewtonguitars said:
I'm so glad back in Jr. High no one was trying to explain the math of lens openings to me. I just looked at the aperture and the effect turning the ring had on it.
Click to expand...

Whatever works or learning, right?

Strangely learning the math of it actually helped and appealed to me.

At least recently - I doubt in high school that would have been the case.
 
The f values are the diameter, expressed as the ratio of the diameter to the focal length, of a circle of area equal to the area of the aperture. What’s hard about that? As pointed out above, light transmission is an area thing, and a change in diameter of 1:√2 doubles or halves area. In most cases, apertures are as near as makes no difference circular, so the f stop is focal length/aperture diameter, but there are situations (mirror lenses for example) where the aperture has a blank spot in the middle, and the lens is wider, and depth of field shallower, than might otherwise be expected.
 
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