F stop scale3/22/2023 ![]() For example, you've probably heard of the Mach number "M". The advantage of using a dimensionless quantity is that any results drawn form an experiment on a specific device (lens in this case) will equally apply to any other device with the same dimensionless number. In our case, since the focal length and the diameter both describe a length (m, cm, mm.), their ratio is dimensionless because the units can be simplified (just like simplification of numbers). In science & engineering, S is referred to as a dimensionless number, meaning that it does not have any units associated with it. The action of closing or opening the diaphragm is called stopping down the lens (whether full or half). The surface area of this opening can be adjusted by the use of a diaphragm. In photography, the lens aperture is that opening in the lens (or on the camera body) that determines the amount of light that is to be admitted to the light sensitive medium (film or CCD. Nowįor those of you who are mathematically inclined, the analysis that follows provides the rationale behind the construction of the stop number. ![]() This is the first f/stop that corresponds to the bottom row. The actual f/stop used by the lens is 11.312).Īs 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. So why do we choose 11? To the best of my knowledge, it is just a convention to keep the numbers easy to remember. Looking at the odd set (bottom row), you can notice that 5.6x2 = 11.2, not 11.(As will be explained below, to go one full stop at a time, you'd have to multiply by Sqrt(2)~1.4, e.g. Being multiplied by two should emphasize that fact - for f/1.4, the lens diameter is twice as much as that for f/2.8. f/1.4 lets in four times more light than f/2.8. Note that each set presents jumps in two stops, not one stop.Then construct the entire f-stop range just by multiplying by 2. Separate them into two sets: the even set (first row) and the odd set (bottom row). These are given by the following set of numbersĪs you can see, you only need to remember the first two f-numbers, i.e. I will start with the most common f-stop numbers. I will then present the mathematical formalism for the way f-stop numbers are constructed. I will first quickly present the method so that you don't have to read this entire article. All that is needed is to remember the first two numbers. In this article, I will explain the method I use to remember the f-stop sequence. You will have to memorize them or just rely on your camera - unless you know the mathematics behind these numbers. Often times, you will have to rely on your calculations to determine how many stops there are between two stop numbers. No matter where you stand as a photographer, you will be faced with these numbers. One of the most widely used sequences is the f-number or f-stop (f/stop) series of numbers in photography. Sequences often show up in pure mathematics, number theory, and computer science. Some sequences are very obvious to decipher, while others require more mathematical manipulation, such as the Fibonacci sequence. How? Start with any integer (positive or negative). The most obvious of these is the set of natural numbers (integers). A sequence is a set of numbers that can be constructed using a formula known as a recurrence relation.
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