Square-Root Aperture

You may not be a person of science, someone who uses physics to help you make better photographs but it’s impossible to make photos without being a mathematician. At least, a good amateur mathematician. 

Having the ability to visualize the math of f-stops will help make you a better photographer. Your exposures will be more accurate and you will use aperture to help you make better compositions. 

The Essence of Aperture 

Aperture is essentially an opening in a camera lens through which light passes to enter the camera body. It's like the iris of an eye, controlling the amount of light that reaches the retina — or in this case, the sensor The role of the aperture in photography is pivotal, especially in setting the depth of field. 

Getting Confused 

At the heart of depth of field lies circles of confusion. This refers to the optical blur that occurs when a point light source is not perfectly focused or blurred. Smaller circles of confusion are perceived as sharp, while larger ones appear blurry. The aperture size directly influences these circles, affecting an image's overall sharpness and focus. 

Use The Formula, Luke 

The term "f-stop" refers to the ratio of the lens's focal length to the diameter of the aperture opening. Mathematically, it is a simple formula: F-Stop(N) = Focal Length of the Lens (F)/Diameter of the Aperture.

If a 100mm lens has an aperture diameter of 25mm, the f-stop is f/4. A 50mm lens with an opening of 25mm has an f-stop of F/2.  

This relationship is inverse; a larger aperture (smaller f-stop number) means more light and a shallower depth of field, while a smaller aperture (larger f-stop number) means less light and a deeper depth of field. 

Remember, larger is smaller, smaller is larger circles of confusion. Larger f-stop is smaller circles of confusion or less blur. Smaller f-stop is larger circles of confusion or more blur.

Study the Sequence 

The f-stop values follow a geometric sequence (1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, etc.), where each number is approximately the square root of 2 times the previous number. This sequence ensures that each f-stop change either halves or doubles the amount of light entering the lens. That’s important math for a photographer. 

F/1.4 has twice the light as F/2. F/2 has twice the light of f/4. And on ... 

Now that we’ve gotten the math figured out, let's see how we can use that to our advantage. 

Aperture allows photographers to manipulate the depth of field. This is crucial for either isolating the subject with a blurred background or capturing a scene with everything in focus.

A narrow depth of field puts subject focus on a very select section of the photo. The primary subject is emphasized by blurring other elements removing distracting detail and perhaps creating an artistic bokeh for the background. 

Along with shutter speed and ISO, aperture is a key component in the exposure triangle, crucial for achieving the right exposure in various lighting conditions.  

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