The Three Corners

Mastering the exposure triangle is akin to solving a complex equation. Today we look at the exposure triangle - Aperture, Shutter Speed, and ISO - through a mathematician's lens, breaking down this fundamental concept into a precise, quantifiable formula.

The Three Variables of the Exposure Triangle

The exposure triangle can be thought of as a set of three interdependent variables, each determining the exposure and the resulting photograph. Each variable requires a very specific and precise number to create a working formula. The formula for a perfect exposure for the subject and the story you are telling.

Aperture (A): Light Control

Aperture is analogous to a variable in an equation, dictating the diameter of the lens opening. Measured in f-stops (f1.4, f2.8, f4, f5.6, etc.), it inversely relates to the amount of light passing through the lens. A smaller f-stop number means a larger opening and vice versa, following an inverse square law relationship. The lower the number the lower the depth of field. The higher the number the greater the depth of field.

Shutter Speed (S): The Time Variable

Shutter speed represents the time for which the camera sensor is exposed to light. Expressed in seconds or fractions of a second, it directly impacts the amount of light captured. A faster shutter speed (1/500s, 1/1000s) allows less light on the sensor, suitable for freezing motion, while a slower speed (1/30s, 1s) allows more time for the light to hit the sensor, often resulting in motion blur in dynamic scenes. The movement of the subject is the greater determining factor for shutter speed.

ISO (I): The Sensitivity Coefficient

ISO serves as a coefficient that amplifies the light received by the sensor. A lower ISO (100, 200) indicates lower sensitivity and is optimal for bright, well-lit conditions, while higher ISO levels (3200 and higher) increase sensitivity, useful in low-light scenarios but at the cost of increased noise, akin to the error term in a mathematical function.

Balancing the Equation

Achieving the perfect exposure is equivalent to solving a three-variable equation where changing one variable necessitates compensating adjustments in the other two. For instance, if the aperture is widened, and more light is allowed in, you might need to decrease the shutter speed or reduce the ISO to maintain the desired exposure level.

Practical Applications in Photography

Portrait photographers opt for a larger aperture (small f-number), equivalent to increasing one variable in the equation, to isolate the subject from the background using a narrow depth of field.

Landscape photographers use a smaller aperture (large f-number) to ensure a greater depth of field, akin to a balancing act in an algebraic equation.

Sports photographers prioritize a fast shutter speed to freeze motion, necessitating adjustments in the other two variables for correct exposure.

Night photography requires increasing ISO to capture more light in low-light conditions, understanding the trade-off with increased noise.

What’s Important

Approaching the exposure triangle with a mathematical mindset transforms photography into a precise, calculated act. Each adjustment is a step in solving an intricate equation, with the photograph as the final solution. As in mathematics, practice and experimentation lead to greater understanding and skill.

What’s Next?

Just as in mathematics, hands-on experimentation is key to understanding these concepts in depth. I prefer to use the scientific method and change just one of the three variables (aperture, shutter, ISO) at a time so I can see the direct result of the change no matter how big or small. Changing more than one variable will not give you an immediate answer. It will be more confusing.

Look at other photographer’s work and see how they have employed the Exposure Triangle formula.

Find a mentor who understands and is ready to explain the formula and exchange ideas and insights.

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