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# Why is aperture backwards??

#### CarterJamison578

##### New member
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???

#### Shashin

##### Well-known member
Because it is the focal length (f) divided by 22 (f/22), for example. It is basically a ratio where the number is the denominator. Just like 1/4 is bigger than 1/8. But the numerator is always the focal length, hence the term f-number. It is simply saying that an aperture of 1/22 of the focal length will always give the same intensity of illumination at the focal plane. and this will be true for any focal length when the aperture diameter is 1/22 of that length.

#### Godfrey

##### Well-known member
As Shashin said, the aperture numbering system is the way it because it is a mathematical expression of division: the ratio of the diameter of the lens opening normalized to the focal length by division. This means that f/2, f/3.5, f/16, etc all mean the same thing with respect to the amount of light per Unit Area falling on the recording medium regardless of the focal length of the lens; that is, f/8 means the same thing with respect to light transmission for a 35mm lens as it does for an 800mm lens.

The convention of articulating aperture values retaining the f/number designation reinforces and reminds us of how the calculation is made. Given an f/number and a lens's focal length, you can calculate the size of the lens opening in mm in a second, should you need to. For example, f/8 on a 35mm lens says the diameter of the lens opening is 35mm divided by 8 or 4.375mm, and f/8 on an 800mm lens is 800 divided by 8 or 100mm. And vice-versa: if you have an unmarked barrel lens and have determined through measurement that the focal length is, for example, 165mm and the diameter of the optics measures out to 56mm, you can get the f/number of f/2.9 (just a wee bit faster than f/2.8) and plug that into your standard exposure calculating system to determine exposure.

Other systems of numerically representing aperture size existed before the f/number system was adopted and became convention, and they proved a lot harder to work with in determining exposure settings. Probably more information than you really want to know is available on Wikipedia: https://en.wikipedia.org/wiki/F-number

G

#### Shashin

##### Well-known member
What Godfrey said, and...

It is a really useful number as the angle of light cone from a lens is always proportional to the f-number, meaning you can calculate both depth of field (the area in front of the camera that appears sharp) and depth of focus (the area on each side of the image plane the sensor needs to be to make a sharp image (think focus tolerance)). You can also calculate the relative f-number for a system, for example when you are using a lot of extension for macro photography, to determine exposure.

The f-number is also proportional to diffraction, when your image becomes softer with the smaller aperture. The smaller the format or pixels, the more important and useful it becomes.

One thing the f-number has not become is a strange photography swear word, although...

But now we are just heading off topic, but that is a fine art around here.

#### lensbian

##### New member
The aperture opening is measured in f-stops, which are, in fact, a fraction.

f/22 = 1/22 and f/4 = 1/4
which is larger?
which is smaller?

Last edited:

#### Jack

Staff member
Everyone is wrong. Apertures work that way just so the “Sunny 16” rule will work!

(KIDDING!!!)

#### JoelM

##### Active member
Light, like many forms of energy, fall off according to the inverse square law. So, from f1.4 to F2, you lose a stop of light. F-stops are based on the square root of two (1.414...).

Edit: I found this article that might shed some light on the subject :

Joel

#### CarterJamison578

##### New member
Because it is the focal length (f) divided by 22 (f/22), for example. It is basically a ratio where the number is the denominator. Just like 1/4 is bigger than 1/8. But the numerator is always the focal length, hence the term f-number. It is simply saying that an aperture of 1/22 of the focal length will always give the same intensity of illumination at the focal plane. and this will be true for any focal length when the aperture diameter is 1/22 of that length.
thanks

#### CarterJamison578

##### New member
Light, like many forms of energy, fall off according to the inverse square law. So, from f1.4 to F2, you lose a stop of light. F-stops are based on the square root of two (1.414...).

Edit: I found this article that might shed some light on the subject :

Joel
ok

#### CarterJamison578

##### New member
What Godfrey said, and...

It is a really useful number as the angle of light cone from a lens is always proportional to the f-number, meaning you can calculate both depth of field (the area in front of the camera that appears sharp) and depth of focus (the area on each side of the image plane the sensor needs to be to make a sharp image (think focus tolerance)). You can also calculate the relative f-number for a system, for example when you are using a lot of extension for macro photography, to determine exposure.

The f-number is also proportional to diffraction, when your image becomes softer with the smaller aperture. The smaller the format or pixels, the more important and useful it becomes.

One thing the f-number has not become is a strange photography swear word, although...

But now we are just heading off topic, but that is a fine art around here.
ok thanks

#### JoelM

##### Active member
I think we're done here.

#### doug

##### Active member
Light, like many forms of energy, fall off according to the inverse square law. So, from f1.4 to F2, you lose a stop of light. F-stops are based on the square root of two (1.414...).

Edit: I found this article that might shed some light on the subject :

Joel
Yes there's a stop of light difference between f/1.4 and f/2 but it's not because of the inverse square law. It's because the area of the aperture - the opening the light passes through - at f/2 is half of the area at f/1.4

#### JoelM

##### Active member
The apertures work similar by replicating distance by limiting the light into the camera. It's still by the square root of 2, but not exactly as the inverse square law.
Joel

#### doug

##### Active member
The apertures work similar by replicating distance by limiting the light into the camera. It's still by the square root of 2, but not exactly as the inverse square law.
Joel
The effect of the inverse square law is normalized by dividing by the focal length. f/2 is f/2 no matter how far the aperture is from the image plane and no matter what the aperture's physical diameter is.