## Mathematics Of PhotographyAlly Johnson

Photo of my cat Finn: Underexposed (Left) Perfect Exposure(Middle) overexposed (right)

#### How Does Capturing a photo Work?

We all have cameras. Both my grandma, who is 58, and my cousin, who is four, can easily maneuver a camera into taking a good picture. This is because today's cameras are so advance they do almost all the work for us. Before this, taking pictures was much more complex, and if someone wanted a good picture, he or she must know the math behind it.

The basis of photography comes down to one thing: Light. The Webster definition calls photography "the process of producing images by the action of radiant energy and especially light on a sensitive surface." This is because When the perfect amount of light hits the sensor of the camera, all the details are crisp and beautiful. Too much light or not enough light hitting the sensor results in details lost and a bad image (see photos above for reference).

So how does a camera work to ensure perfect light hits the sensor every time? Cameras use three key tools: f-number, shutter speed, and ISO. Together these functions form the photography triangle. Just like a triangle, each of the three sides depend on the other two to balance. When you adjust one, you must adjust the others so they will fit perfectly and the right amount of light hits the sensor.

F-number, shutter speed and ISO work very similar to the way eyes do. F-number is your pupil. It dilates and contracts, just like the pupil, to receive a lot of light or less light at one time. Shutter speed is your eyelid. It opens and closes at varying speeds to control the amount of light let in. Finally, ISO is the sensitivity of the eye.

In most photography cases, ISO is a preset number, where f-number and shutter speed are adjusted to the lighting. For My math, I will be breaking down what is shutter speed and f-number.

### F-Number

• Definition: A number that represents the ratio of focal length to the diameter, or how "wide open" a lens is (called aperture).
• The amount of light in a photo = area of lens opening. Therefore we can represent the amount of light captured with the equation L= π(½D)^2, where D is the diameter of our lens opening. This makes sense, because our lens is a circle.
• F-number =(Focal Length)÷(Diameter of lens opening)
• There exists a common series of F-stop settings that exists on every modern camera today. this series is : 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 44. right away I recognize this as a geometric series starting at 1 with a common ratio of approximately 1.4.
• I have represented this in summation notation:
• This 1.4 number is not random, it is actually the square root of 2. Each F-stop setting is multiplied by this number, because when you multiply a diameter by this, you double the area of the Lens, therefore doubling the amount of light hitting the sensor as well.
• I have worked out how this works below:

### Shutter Speed

• Definition: the time for which a shutter is open at a given setting.
• In Contrast with F-stop, Shutter speed is very simple.
• Shutter speed= 1÷( Focal Length)

Credits:

All By Ally Johnson