What is an F-Stop

I’ve always had trouble understanding what an F-stop on a camera lens is all about.  I guess I’m more of a visual person as I can easily understand length, angles, and mechanical physics.

But more obscure terms and things like electrical watts or amps are hard for me to explain or visualize in my brain. Sure, I can memorize formulas, or understand the thresholds that may be dangerous or such, but to see a representative image or perceive the concept is often beyond my capacity.

Hopefully, the exercise of writing this article will help me better understand what is meant when someone says F-stop. So I can better explain what an F-stop is other than how F-stops shape and manipulate our images.

Narrowing Down What is an F-stop

F-stop has everything to do with the aperture of the camera lens. Aperture is a term I can visualize and understand.

The lens aperture is the opening of the camera lens blades that are mechanically or electrically pulled open from the outside edges of the camera lens body.

I also understand that the values of F-stop or F-number as it is sometimes referred to, dictate the size of the aperture or opening that allows light into the lens and onto the camera sensor.

How Are F-numbers Related to Camera Lens?

The conceptual problem I have is what the numbers mean (I doubt they are arbitrary), how are they chosen, and why don’t they change from lens to lens.

F-stop definition

By definition, the F-stop is the ratio of the focal length divided by the diameter of the aperture.

That means when we see the marks of f/2.8 or f/11 on the lens it is the ratio of the focal length set on our camera.

Time for some Basic Algebra

The placeholder f is set to the number 1 in the ratio when we set up the proportion to calculate the diameter of the aperture of a 50mm lens at an F-number of 11.

For example, f/11 of a 50mm lens is this ratio 1/11 to x/50 or 11x = 50 or 4.55 mm aperture or opening. The aperture opening of a lens set to a focal length of 80mm at f/11 is 1/11 = x/80 or 11x = 80 or 7.27mm. 

Let’s take this a step further, look at a single focal length, and see what the aperture diameter is for a series of common F-stops. I chose a zoom lens set to a focal length of 100mm.

f/2.8 = 25.7mm diameter aperture

f/4 =  25mm diameter aperture

f/5.6 = 7.9mm diameter aperture

f/8 = 12.5mm diameter aperture

f/11 = 9.1mm diameter aperture

f/16 = 6.25mm diameter aperture

f/22 = 4.5mm diameter aperture

Note* this isn’t the actual diameter because of the magnifying effect of the lens element in front of the aperture. The numbers shown above are called aperture stop diameters, however, because of the glass magnification the actual diameter is called the entrance pupil diameter. The magnification of the front glass varies from manufacturer to manufacturer and lens model to lens model. So the actual aperture diameter times the magnifying effect equals what the true ratio expression would be.

All of this F-stop Stuff Messes with My Head 

Maybe because it’s backward. The larger the f-number the smaller the aperture opening. Even the term (explained later in the article) “faster F-stop” is backward, as a lens with a minimum F-stop setting of f/2.8 is called a faster lens than one with a minimum F-stop of f/4.

So as you probably already know, the aperture of a lens at an f/2.8 F-stop has a larger aperture opening than the same lens set to an F-stop of f/22. Therefore, a lens set at f/2.8 allows more light to reach the camera sensor than the same lens set at f/22.

Because there is more light reaching the sensor at f/2.8 than at f/22 you need to reduce the shutter speed (how long the aperture is open) to let in the same volume of light (photons).

Reducing the shutter speed means the opening is closed faster (quicker) at f/2.8 than at f/22. This is why a lens with a minimum F-stop of 2.8 lens is called a faster lens than a lens with a minimum F-stop of 4. 

F-stops with a smaller number make a bigger relative opening and are faster than a larger F-stop making it all the more confusing. 

A lens with a minimum of F-stop of f/2.8 is faster than one with a minimum F-stop of f/4 lens because you need to set the shutter speed to a quicker duration to allow the same amount of light to reach the camera sensor.

Again, it can be confusing because the smaller number is faster than the larger number. It’s contradictory to how we usually think about things.

Another Reason F-stop Settings Confuse Me

Every book, article, or video I have seen never explains why all lenses have the same F-stops (depending on the minimum or maximum capacity of the lens) marked on the lens, such as f/2.8, f/4, f/5.6, f/8, etc. 

I always wondered why.

Plus the same books or videos say that each of these numbers is called a “Stop”. And that each stop lets in half as much light as the previous when you go from say f/2.8 to a /f4 to f/5.6.

However, if you work out the area of the aperture opening there isn’t twice as much area in a f/2.8 aperture when compared to a f/4 aperture.

I assumed that to let in half as much light the area of the aperture should be half as large. 

What is Never Mentioned

Here is why each F-stop lets in twice as much or half as much light.

What the camera sensor measures isn’t the number of light photons hitting it.

It senses the brightness or illuminance of the projected image relative to the brightness or luminance of the actual scene in the lens field of view.

The illuminance value of the projected image decreases from the luminance of the field of view by the square of the f-number. 

What Does This Mean?

Well, it isn’t a simple arithmetic problem anymore.

Because of the ratio difference between the brightness of the field of view and the projection of the image on the sensor, the difference is a factor of 1 divided by the square root of 2, or about 0.7071, and hence a halving of the area of the pupil when compared to the aperture opening.

Why Do All Lenses Have the Same F-stops? 

Lenses use a standard f-stop scale, which corresponds to the sequence of the powers of the square root of 2: f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22, etc.

Each element (stop) in the sequence is one stop lower than the element to its left, and one stop higher than the element to its right.

Stops to the left let in twice as much “projected” light and those to the right let in half as much.

This makes it easier (once explained) to think about and more consistent from one lens to another. 

Of course, we can adjust the stops fractionally by using the exposure compensation. I believe the EC can be manually changed to ⅓ or ½ stops. 

Sometimes I drive myself crazy with all of my curiosity or having to know why something is the way it is.

The Important Takeaway From All of This

I know the important takeaway is that the F-stop brightens the projected image by ½ as much or twice as much depending on which way you are going on the exposure scale. 

But if you are like me, knowing how something works, how it is derived, or what it is made of gives me a better understanding of what I can do or how to manipulate or modify a process to get what I want from the process.

Also, when I’m watching a video and they say they raised the exposure of the image in Lightroom by 2 Stops, I now know that they brightened it by a luminance value of 4 times!

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