Why is aperture backwards??

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 - this video. 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???

 

Because it is a ratio. f stands for focal length.
so if you have a 100mm lens, f/2 would mean an aperture diameter of 50mm. f/22 would mean 4,55mm.

 

First of all, you need to understand that f/2 Or f/22 is not a "measurement of size" but rather a "ratio" where (f/stop = focal length of the lens ÷ the actual diameter of the effective aperture of the lens). Here's a chart you might find useful.


Note under full stops if you stop down from f5.6 to f/8 you have reduced the light available by 1/2, likewise if you open up from f/8 to f/5.6 you double the amount of light avaible. Interesting to note on the chart every other f/stop is doubled ( 1, 2, 4, 8, 16, etc.) but the light passing between these is quadrupled. Below is a chart showing the calculations in the area of the opening. See the starting aperture area = 3.14", when you go up one stop the area doubles, but when double the aperture, the area quadruples.


(Chart courtesy of Understanding Exposure, Part 2: Aperture | B&H Explora)

 

It's a very convenient happenstance that the ratio of the aperture's size to the lens's focal length is a constant measurement of how much light gets in. An aperture iris opened to a circle of 1/4 of the lens's focal length ALWAYS lets in the same amount of light, no matter what the focal length. Expressing the aperture size as that ratio is way the &#*! easier than expressing it as a physical dimension, which differs with focal length. "I'm using a 50mm lens, so I need to set the aperture to 12.5mm. No I'm using a 300mm lens, so I need to set the aperture size to 75mm."

No, no, no!!! I'll just set the aperture to f:4 in each situation, which is 1/4 the focal length.

Since the f-number is the bottom of the fraction, a bigger number produces a smaller aperture, less exposure.

As stated just above, a "stop" change either doubles or halves the amount of light getting into the camera. With shutter speed and ISO, stops are linear: half the speed or half the ISO is half the exposure. Since aperture is a measure of area, that "squared" factors in, so a stop isn't double or twice the number, but "halfway" there, a factor of the square root of 2. That's why a stop of aperture looks fractional. A stop less exposure from f:2 is f:2.8, which is 2 time the square root of 2. Not trying to introduce a bunch of math, which you don't really need to be aware of, just explaining why the scale is what it is. 1.4 - 2 - 2.8 - 4 - 5.6 - 8 -11 - 16, etc.
Every other f-stop is double or half the ratio.

 

Now if someone could also explain why wire gauge is the same. Smaller the number the bigger the wire, bigger the gauge number the smaller the wire.

 

I took that as a joke, but if it wasn't...

Pretty much the same reason: wire gauge is a cross-sectional area rule. Steps between gauge numbers is a constant factor of the area of the wire's cross-section, which you could think of as an electrical aperture.

 

So is paper.

 

Paper is how many sheets make a certain weight. Bigger number is thinner paper.

I've been told that my IQ is supposed to be the denominator of a fraction, not the numerator, in order to be accurate...

 

Yes and no on paper, years ago I worked as a press operator in college and later owned a commercial printing shop. The "Basis Weight" on bond paper is the weight of 500 sheets of the uncut paper in its basic unit, which in the case of bond paper is 17"x22". As the number of sheets remains constant, then the heavier the weight of the stack, the thicker the sheet. Even when the basic unit is cut to a smaller size the bond weight of the paper uncut is still used.

 

Wire gauge - Wikipedia

Its the number of draws (at least originally then a division factor. )

 

Now BTW, I know Ill get raked over the coals for this.

But "F stop" does NOT mean focal distance.

its a symbol used for mathematical functions.

Function (mathematics) - Wikipedia


simply put, its a system where multiple variables are put into an equation and a single answer comes out.
(Think ISO speed and aperture) to get shutter speed, etc.

 

I kinda meant paper size as in A3 is bigger that A4 ets etc.