The Exposure Equation

In Lesson 4 we studied aperture — the variable opening that controls how much light passes through the lens at any instant. In Lesson 5 we examined the shutter — the timed gate that determines how long that light falls on the film. Now we bring these two controls together with a third variable, the film's sensitivity, to build the complete framework for exposure. This framework is not a loose set of guidelines. It is an equation, and once you internalize it, every exposure decision becomes a matter of simple arithmetic.

Exposure Is Light Multiplied by Time

The fundamental insight is this: the total amount of light energy that reaches the film during an exposure is the product of two quantities — the intensity of the light falling on the film (controlled by aperture) and the duration of the exposure (controlled by the shutter). Physicists call this the reciprocity law, and in photographic notation it is written:

This equation was first described by Robert Bunsen and Henry Roscoe in 1862, working not with cameras but with photochemistry experiments. Their insight was that the chemical effect of light depends on the total dose — twice the intensity for half the time produces the same result. This principle is so central to photography that it governs nearly every decision you make with a camera.

The Three Variables

In practice, exposure involves three interrelated controls:

Aperture (the f-number) governs the intensity of light passing through the lens. As we saw in Lesson 4, each stop change — for example, from f/5.6 to f/8 — halves the light. Opening from f/8 to f/5.6 doubles it.

Shutter speed governs the duration of the exposure. As we saw in Lesson 5, each stop change — for example, from 1/125 to 1/250 — halves the time the film is exposed to light, and therefore halves the total light received.

Film speed (ISO or ASA) describes the film's sensitivity to light. A higher number means more sensitive: ISO 400 film needs half as much light as ISO 200 film to produce the same density on the negative. Each doubling of the ISO number is one stop.

These three variables form a system. For any given lighting condition, there is a specific amount of light that will produce a well-exposed negative. You can deliver that amount through any combination of aperture, shutter speed, and film speed that satisfies the equation. Change one variable, and you must compensate with another.

The “Exposure Triangle” — and Why It Misleads

You will often see these three variables presented as an “exposure triangle.” The metaphor is popular in photography education, but it is somewhat misleading. A triangle implies three equal, symmetric sides, but the three exposure variables are not symmetric. Film speed is chosen before you shoot (when you load the roll) and remains fixed for all 12 frames on a roll of 120 film. In practice, you are adjusting only two variables — aperture and shutter speed — on a shot-by-shot basis. The relationship is less like a triangle and more like a seesaw: with film speed fixed, any change to aperture demands an equal and opposite change to shutter speed.

A more accurate mental model is a simple equation. If the light requires EV 13 (a bright overcast day) and your film is ISO 100, then any combination of aperture and shutter speed that sums to the correct total will work. The “triangle” label is not wrong, but it obscures the elegant simplicity of what is really just multiplication.

Stops: The Universal Unit

The genius of the photographic exposure system is that all three variables are calibrated in the same unit: the stop. One stop always means a doubling or halving of light. Open the aperture one stop: double the light. Slow the shutter one stop: double the light. Use film one stop faster: need half the light. Because everything speaks the same language, compensation is trivial — one stop taken away here is one stop added there.

This was not always the case. Before the standardized stop system was widely adopted in the early twentieth century, photographers had to juggle aperture ratios, exposure times in fractions of a second, and plate sensitivity ratings on incompatible scales. The universal stop system, fully mature by the 1950s, was one of the most important simplifications in the history of photographic technique.

Equivalent Exposures

The reciprocity law means that many different combinations of aperture and shutter speed will deliver the same total exposure. These are called equivalent exposures. Consider a scene that meters correctly at f/8 and 1/125 with ISO 100 film. All of the following combinations deliver exactly the same amount of light to the film:

• f/2.8 at 1/1000 — wide open, very fast shutter
• f/4 at 1/500 — shallow depth of field, fast action
• f/5.6 at 1/250 — moderate depth, good for handheld
• f/8 at 1/125 — the metered combination
• f/11 at 1/60 — deeper depth of field
• f/16 at 1/30 — maximum depth, needs steady hands or tripod
• f/22 at 1/15 — extreme depth, tripod recommended

Every time we close the aperture by one stop (letting in half the light), we compensate by slowing the shutter one stop (doubling the time). The product — total light on the film — remains constant.

The choice among equivalent exposures is not arbitrary — it is creative. A wide aperture like f/2.8 gives shallow depth of field, isolating a subject against a soft background. A small aperture like f/16 renders everything from foreground to infinity in sharp focus. A fast shutter like 1/1000 freezes motion; a slow shutter like 1/15 allows deliberate blur. The exposure equation gives you freedom: the physics constrains the total light, but you choose how to distribute it between aperture and time.

Exposure Value: One Number for a Light Level

In 1954, the German engineer Friedrich Deckel — whose family firm manufactured the Compur shutter we discussed in Lesson 5 — patented a system that collapsed the aperture-shutter pair into a single number. He called it Exposure Value, or EV. The system was formalized as part of the APEX (Additive System of Photographic Exposure) framework adopted by ASA and later ISO.

EV is defined logarithmically. EV 0 corresponds to an exposure of f/1 at 1 second. Each increment of 1 EV represents a halving of the exposure (one stop less light). So EV 1 is f/1 at 1/2 second (or f/1.4 at 1 second), EV 2 is f/1 at 1/4 second (or f/2 at 1 second), and so on.

Mathematically, the formula is:

In everyday use, EV is most useful as a way to describe how bright a scene is, independent of camera settings. A sunny day is about EV 15 (at ISO 100). A brightly lit interior is about EV 8. A scene lit by candlelight is about EV 1. Knowing the EV tells you what combinations of aperture and shutter speed will work. This is exactly what a light meter gives you: an EV reading that you then translate into your preferred aperture-shutter pair.

Some cameras, particularly those designed in the 1950s and 1960s, have interlocked shutter speed and aperture rings that couple to an EV scale. Setting EV 13 locks the controls so that any change to the aperture automatically shifts the shutter speed to maintain the same total exposure. The Hasselblad 500C (1957) is a famous example of this design. Some Rolleiflex models also featured EV coupling on the shutter ring.

Reciprocity Failure

The reciprocity law — H = E × t — works beautifully across the range of shutter speeds most photographers use (from about 1/1000 to 1 second). But at very long and very short exposures, the law breaks down. This phenomenon is called reciprocity failure, and it was first described by the astronomer Karl Schwarzschild in 1899 (the same Schwarzschild who would later develop the first exact solution to Einstein's field equations in general relativity). It is sometimes called the Schwarzschild effect in his honor.

At the molecular level, the issue is this: creating a latent image in a silver halide crystal requires multiple photons to arrive at the same sensitivity speck within a short time window. When the light intensity is very low (as in long exposures), photons arrive so infrequently that some of the intermediate chemical states decay before the next photon arrives. The net result is that the film behaves as though it were slower than its rated ISO. To compensate, you must give more exposure than the reciprocity law predicts.

The severity of reciprocity failure varies by film stock. Some films are relatively resistant — Fujifilm Acros 100, for example, was specifically engineered for minimal reciprocity failure and requires no compensation for exposures up to about 120 seconds. Other films, such as Kodak Tri-X, begin to show significant failure at exposures beyond about 1 second. Kodak T-Max 100 is more resistant than Tri-X but less so than Acros.

Practical Compensation

Film manufacturers publish reciprocity failure data for their emulsions, usually as a table or chart showing the recommended actual exposure for each metered exposure. A rough general rule for films without published data:

Reciprocity failure also affects contrast. In the shadow areas of the image, where the light intensity is lowest, the failure is most severe. The highlights, receiving more light, are less affected. The result is increased contrast. Some photographers compensate by reducing development time (a technique we will explore in Lesson 18 on the Zone System).

Color films suffer an additional problem: the three emulsion layers may exhibit reciprocity failure at different rates, leading to color shifts in long exposures. This is one reason that long-exposure film photography tends to favor black and white.

Putting It Into Practice

Let us work through a practical example. You are standing in a park on a bright overcast day with a Yashica-Mat 124G loaded with ISO 400 film. Your light meter (perhaps the metergeist app on your phone) reads EV 13 at ISO 100. Since your film is two stops faster than ISO 100 (100 → 200 → 400), you need two stops less exposure, so the effective EV is 15.

EV 15 can be achieved with many combinations. A few options:

• f/8 at 1/500 — good general-purpose setting, moderate depth of field
• f/11 at 1/250 — deeper focus, still comfortably handheld
• f/16 at 1/125 — maximum depth, just fast enough for handheld with an 80mm lens
• f/3.5 at 1/2000 — not available on most TLR shutters, which top out at 1/500

The constraints of your specific camera shape the choice. A Yashica-Mat 124G has a maximum shutter speed of 1/500 and apertures from f/3.5 to f/22. Within those limits, you pick the combination that gives you the depth of field and motion control you want. That is the art that lives inside the math.

In the next lesson, we will explore how to measure the light in a scene — the crucial first step before any exposure calculation can begin. We will examine reflected and incident metering, the 18% gray standard, and the practical metering workflow for TLR photographers working without built-in meters.