MATH behind F STOP numbers (aperture sizes) - how to memorize aperture numbers

Summary

In this video, the creator explains the math and science behind the sequence of f-stop numbers in photography. Beginning with an easy-to-memorize sequence starting from F1 and F1.4, the video delves into the reasoning behind these numbers, showing how doubling the aperture size affects light exposure. The script also explores the geometric nature of f-stop numbers and the relationship between aperture size, focal length, and light intensity. With a clear breakdown of the formulas and logic, viewers gain a deeper understanding of why these specific numbers appear in the sequence and how they can use this knowledge in their photography.

Takeaways

• 😀 The sequence of F-stop numbers in photography may seem odd, but it follows a logical progression based on the area of the aperture opening and the amount of light it lets in.
• 😀 To memorize the F-stop sequence, start with F1 and F1.4, then double the previous number to get the next one, continuing the pattern (e.g., F2, F2.8, F4, etc.).
• 😀 The F-stop numbers correspond to changes in the aperture size, which directly affect the amount of light entering the camera, impacting exposure.
• 😀 Stepping down the aperture (e.g., from F2.8 to F4) halves the amount of light, while stepping up (e.g., from F1.4 to F2) doubles the amount of light.
• 😀 The size of the aperture is represented by a circle, and doubling the area of this circle lets in double the amount of light.
• 😀 The formula for F-stop is F = L / D, where L is the focal length of the lens and D is the aperture diameter. The diameter is twice the radius.
• 😀 The area of a circle is calculated using the formula A = π * R², where R is the radius, which relates directly to the F-stop numbers.
• 😀 By substituting the diameter into the F-stop formula, we can express the F-stop as a function of area, which is crucial for understanding how aperture size affects light.
• 😀 The relationship between F-stop numbers follows a geometrical sequence, where each number is related to the previous one by a factor of √2 (about 1.4).
• 😀 The F-stop sequence can be derived by continuously doubling the previous aperture size, leading to the well-known sequence: F1, F1.4, F2, F2.8, F4, F5.6, F8, F11, and so on.
• 😀 F1 is chosen as the starting point because it is a simple and intuitive value in a geometrical sequence, providing a logical foundation for calculating all subsequent F-stops.

Q & A

What is an f-stop in photography?

An f-stop is a numerical value that represents the size of the aperture (the opening in the lens) in a camera. It determines how much light enters the camera, which directly affects exposure.

How can you easily memorize the f-stop sequence?

To memorize the f-stop sequence, start with F/1 and F/1.4. Then, double the previous number to get the next f-stop. For example, F/1 to F/1.4, F/1.4 to F/2, F/2 to F/2.8, and so on.

Why does the f-stop sequence involve doubling the previous number?

The f-stop sequence is based on a geometrical relationship where doubling the aperture area (which lets in double the amount of light) results in the next f-stop number. This ensures that each step in the sequence either halves or doubles the light entering the camera.

What does the equation F = L / D represent?

The equation F = L / D defines the f-stop number, where 'L' is the focal length of the lens, and 'D' is the diameter of the aperture. This relationship helps determine the f-stop numbers.

How does the area of the aperture affect the light entering the camera?

The area of the aperture directly influences how much light enters the camera. A larger aperture (bigger area) lets in more light, while a smaller aperture (smaller area) lets in less light.

Why is the f-stop number expressed as a square root of 2?

The square root of 2 (approximately 1.4142) represents the relationship between aperture areas. When you step down by one f-stop, the area of the aperture is halved, and the light entering the camera is also halved. This is why each f-stop number is roughly 1.4 times the previous one.

What is the role of the constant 'C' in the f-stop formula?

The constant 'C' represents a simplified value that combines the lens' focal length and a fixed mathematical factor (square root of pi divided by 2). This allows for a more manageable formula when calculating f-stop numbers.

Why is F/1 chosen as the starting point in the f-stop sequence?

F/1 is chosen as the starting point because it is the simplest and most intuitive number in a geometrical sequence. Starting with 0 would be impractical, so F/1 provides a meaningful and manageable starting point for the sequence.

What happens if you step up the aperture by one stop?

When you step up by one stop, you double the amount of light entering the camera, which increases the exposure. For example, going from F/2.8 to F/2 doubles the light coming in.

What is the significance of the number 1.4 in the f-stop sequence?

The number 1.4 is significant because it is roughly the square root of 2, which is used to calculate the progression between f-stop numbers. Each f-stop is about 1.4 times larger than the previous one, meaning it lets in approximately double or half the amount of light.