Earlier this month, I took a little time to stop by our local public middle school to share with their students how I use mathematics in my career as Photographer. I signed up immediately because I knew photography has some pretty cool concepts. After refreshing my memory with much needed research, the explanations are so fascinating that I wanted to share it here at KHP Family too! There are three main areas of mathematics in photography, including:
- Camera Exposure Settings
- Compositional Rules
- Studio Lighting
Camera Exposure Settings
The first thing that might come to mind is Camera Exposure Settings. Professionals are expected to work in “Manual” mode (instead of “Automatic”), meaning the photographer decides how much light enters the camera via each setting. There are three settings that control light intake:
- Shutter Speed
Aperture (sometimes also referred to as F-Stop)
Your most common Apertures look something like this:
f/1.4 f/2 f/2.8 f/4 f/5.6 f/8 f/11 f/16 f/22
The number on our apertures, i.e. 2.8, 4, 5.6, etc… are all fractions. As an example of this concept, on a 50mm lens, an aperture of f/2 is 1/2 of the length of the focal length of the lens, so the actual opening of the aperture is 25mm wide (50/2=25). At f/4, the opening is 12.5mm wide. As the aperture decreases, the opening gets smaller. At f/22, the opening of a 50mm lens is only 2.3mm wide. (REFERENCE)
Your most common Shutter Speeds look something like this:
30″, 15″, 8″, 4″, 2″, 1″, 2, 4, 8, 15, 30, 60, 125, 250, 500, 1000, 2000, 4000, 8000
If you take any number on the scale, the number to its left captures twice as much light because the shutters open twice as long. If you take any number on the scale, the number to its right captures half as much light because the shutters open half as long. For example, if we look at 1 second, the number to the left is 2″, or 2 seconds which is twice as long as one second, and the number on its right is 2, or 1/2 a second, which is half as long as one second. (REFERENCE)
ISO (sometimes also referred to as ASA)
Your most common ISOs look something like this:
50, 100, 200, 400, 800, 1600, 3200, 6400
When you reduce the ISO it makes the sensor less sensitive to light. When you increase the ISO it makes the sensor more sensitive to light. To halve how sensitive the sensor is to light, you move one number on the scale to the left. To double the sensitivity, you move one number to the right. (REFERENCE)
If you adjust any one of these three settings UP or DOWN (or LEFT or RIGHT), that is considered 1 Stop of Light. When one setting is changed, the light intake must be balanced by adjusting another setting. Many cameras also allow for adjustments of a fraction of a stop as well (one half or one third), allowing for more precise creativity.
A photographer is making mathematical adjustments, likely by memory. Memorizing these settings allows a photographer to focus on what is really important – the creative aesthetic of the image they want to produce. Controlling and understanding these three settings allows a photographer to turn a photograph into a piece of artistry by controlling the depth, how motion is captured in a scene, and determining the graininess (or smoothness) of the resulting photograph.
“The Rule of Thirds” is a simplified method to frame the main subject to create eye-pleasing balance in a resulting photograph. In all honesty, The Rule of Thirds is meant to encourage beginners to break free from centering all of their subjects.
Most people have heard of The Rule of Thirds. The concept is the break up the composition into nine equal sections, horizontally and vertically (like a tic tac toe game board). In doing so, four cross points are created to position a main subject, while the lines are used to position a horizon line. The Rule of Thirds looks like this:
THE RULE OF THIRDS
The Rule of Thirds creates a 1:2 ratio. But did you know that 1:2 is not the IDEAL ratio?
The idea ratio is actually 1:1.618. And this is called The Golden Mean. In nature the Golden Mean occurs everywhere… from the classic example of a Nautilus shell to the formation of galaxies, from the relative size and arrangement of bones in your arms and hands to the growth and shape of trees and forests, it is also used in complex economic equations and it is claimed that its even found in the very structure of your DNA. (REFERENCE) Fascinating, right??
In visual art, The Golden Mean is applied by subdividing your image by the 1:1.618 ratio. The resulting image can look like this:
THE GOLDEN MEAN
I think the most fascinating and complicated concept in photography mathematics is the Inverse Square Law.
Intensity of Light = 1 / Distance2
This law, when applied to photography, is used to determine “Light Fall Off”. When using artificial lights (flashes, studio lights, continuous lights, etc.), understanding light fall off gives a photographer greater understanding of light, and how it will fall upon our subjects and backgrounds. Very simply, light fall off – or drop in intensity of light – is huge over initial distances. For example, the change between 1-foot and 2-feet. When you apply the formula, it becomes easier to calculate how much light power must be pumped out in order to get a decent exposure. (REFERENCE)
But the Inverse Square Law is much more than figuring out the light power necessary to get the right exposure. It also helps photographers control the look and feel of the light applied.
Are you after contrasty light or soft light on the subject? The closer a light is to the subject, the more contrasty the light will be, creating sharp bright highlights and deep dark shadows. The further a light is to the subject, the softer the light will fall, creating more even tones and gradations between highlights and shadows.
Are you after a darker background / backdrop, or a lighter background / backdrop (within a controlled environment)? A single light close to a subject will result in a brighter subject with a darker background as compared to a single light further away from a subject, in which case, the light fall on the subject will be lessened, but the background will appear brighter.
Math found in Day to Day Business
As with any profession, there is math in the every day routine. From writing proposals and paying taxes to determining what time I have to leave the house be set-up on time at a client’s office. Math even comes into play during my annual goal setting.
And let’s get real… most of the math we do as adults is adding, subtracting, dividing, and multiplying. We have memorized a great variety of simple mathematics because we practiced it so much over the years. I don’t have to pull out a pencil and paper (or my smartphone calculator) to feel confident in my answer (most of the time). Remind your kids that practicing math will make the rest of their lives easier, both professional and personal.
Next time you do just about anything, consider the breadth of math involved, and thank your Math Teachers for their dedication and hard work!