Here's the f/stop formula.
|Focal Length ÷ Lens Opening Number = Diameter of the Lens Opening|
So, a 200 mm lens at f/4 has a lens opening with the diameter of 50 mm.
|200 mm ÷ f/4 = 50 mm|
Here are all of the diameters of a 200 mm lens.
|50 mm||36 mm||25 mm||18 mm||12.5 mm||9 mm|
If you change from one f/stop to the next one, above, the amount of light is halved or doubled.
Yet, the diameters above are not changing by 1/2X or 2X.
That's because the area of the circle needs to change by 1/2X or 2X—not the diameter.
To double the area, increase the diameter by 1.414 (the square root of 2).
If you doubled the diameter instead, the area of the lens opening would quadruple, not double.
Below, you can see how the areas of the lens openings change by 1/2X or 2X.
|50 mm||36 mm||25 mm|
|1962 sq. mm||1017 sq. mm||490 sq. mm|
|18 mm||12.5 mm||9 mm|
|254 sq. mm||123 sq. mm||64 sq. mm|
Focal length affects how much light reaches the sensor.
Let's say you're opening and closing some blinds, and the sunlight is hitting a wall opposite the windows.
You're varying the light entering the room, sort of like changing the lens opening.
If the wall is close to the windows, the sunlight coming through the blinds will be brighter.
If the wall is twenty feet away, the same sunlight will be much dimmer.
The close wall is like a wide-angle focal length—the sensor is optically closet to the lens opening.
The far wall is like a telephoto focal length—the sensor is further away from the lens opening.
Have you noticed that your zoom lens is probably marked with two lens openings?
Your zoom lens probably has a variable focal length.
As you zoom from wide angle to telephoto, the lens opening changes.
There are zoom lenses with fixed a lens opening.
Look at the front of your zoom lens.
If you see numbers similar to the ones below, your zoom lens has variable lens openings.
When your zoom lens is at the widest focal length, the lens opening is the largest, such as f/3.5.
As you zoom, increasing the focal length, the amount of light reaching the sensor decreases.
The "wall" is moving further away.
The lens opening, at the longest focal length, is the smallest lens opening, such as f/4.5.
|Widest Focal Length||Most Telephoto Focal Length|
Why did photographer's starting using f and the term stop?
The f in f/stop is often assumed to stand for focal length.
However, it has also been described as representing factor or function.
The usage may have come from the Italian word for window, finestra.
Stop may have originated from the usage of bands or wheels with lens opening stamped into them.
Photographers pulled the bands back and forth, or turned the wheels, to change the lens opening of their cameras.
The bands or wheels may have had points, stops, at which the chosen lens opening was in the proper position.