Introduction — Understanding the Relationships Between Camera Settings
Aperture, shutter speed, and ISO are three fundamental concepts in photography.
Their basic meanings are explained in the following article:
▶ Camera Basics for Beginners ★ Aperture, Shutter Speed, and ISO Explained
This article takes the next step by examining how these concepts relate to one another.
The central question is simple:
How do camera settings determine the amount of light recorded in a photograph?
To answer it, we need to distinguish three stages:
- The settings selected by the photographer
- The physical amount of light received during the exposure
- The resulting image and its brightness
Understanding these stages as a sequence of cause and effect explains why different camera settings can produce photographs with similar brightness.
For clarity, we will assume that the brightness of the subject and other optical conditions, including lens transmission, remain constant.
1. The Fundamental Relationship Between Aperture and Shutter Speed
Let’s begin with the central conclusion.
Under constant lighting and comparable optical conditions, the exposure received by film or an image sensor is proportional to the inverse square of the f-number multiplied by the exposure time.
This relationship can be expressed as:
Exposure ∝ (1 / f-number)² × Exposure time
Using symbols:
H ∝ t / N²
where:
- H represents the amount of light exposure per unit area.
- t represents exposure time.
- N represents the f-number.
ISO sensitivity does not appear in this equation.
Aperture and exposure time determine how much light reaches the recording medium. ISO describes the relationship between that exposure and the photographic response or image output.
Why does the equation take this particular form?
The explanation begins with the physical meaning of exposure.
2. Exposure as a Physical Quantity
In photographic physics, luminous exposure describes the total amount of light received per unit area over a period of time.
For constant illumination, it is calculated as:
Luminous exposure = Illuminance × Exposure time
Or, symbolically:
H = E × t
Here, E is the illuminance at the image plane.
Illuminance describes the amount of light arriving at a surface per unit area per unit of time.
Luminous exposure describes how much light has accumulated over the entire exposure period.
For example, when illuminance remains constant:
- Doubling exposure time doubles luminous exposure.
- Halving exposure time halves luminous exposure.
Similarly, when exposure time remains constant:
- Doubling illuminance doubles luminous exposure.
- Halving illuminance halves luminous exposure.
This is the basic structure behind photographic exposure.
The next question is how aperture affects illuminance.
3. Why the f-Number Appears in the Equation
What Does an f-Number Actually Represent?
An f-number is defined as:
f-number = Focal length / Entrance pupil diameter
The entrance pupil is the apparent opening of the lens when viewed from the front.
The f-number therefore expresses the relationship between the focal length and the size of the opening through which light enters.
A smaller f-number corresponds to a larger opening relative to the focal length.
A larger f-number corresponds to a smaller opening.
This explains why the numerical direction of f-numbers seems opposite to the size of the aperture.
Why Does the Relationship Involve a Square?
Light passes through an opening that can be treated approximately as circular.
The area of a circle is proportional to the square of its diameter.
Because the f-number is inversely related to the entrance pupil diameter relative to the focal length, the illuminance at the image plane is approximately proportional to the inverse square of the f-number.
Illuminance ∝ 1 / (f-number)²
For example:
- Doubling the f-number reduces illuminance to approximately one-quarter.
- Halving the f-number increases illuminance by approximately four times.
The square appears because light passes through an area, and area depends on the square of a linear dimension.
This is the geometric foundation of the relationship.
4. Why f-Numbers Follow a √2 Sequence
Camera lenses commonly use the following sequence of f-numbers:
f/1.4 → f/2 → f/2.8 → f/4 → f/5.6 → f/8 → f/11 → f/16
At first glance, these numbers may appear irregular.
Their pattern follows directly from the relationship between aperture area and illuminance.
Suppose we want to reduce the amount of light reaching the image plane per unit of time by half.
Because illuminance is proportional to the inverse square of the f-number, we must multiply the f-number by √2.
The square root of 2 is approximately 1.414.
For example:
4 × √2 ≈ 5.66
This is why f/5.6 follows f/4 in the standard sequence.
Each full step, or one stop, represents a doubling or halving of the light delivered per unit of time.
- Moving from f/4 to f/5.6 reduces illuminance by approximately one stop.
- Moving from f/5.6 to f/4 increases illuminance by approximately one stop.
The f-number sequence is therefore a practical expression of a simple geometric relationship.
5. How Shutter Speed Affects Exposure
Shutter speed controls exposure time.
Once the illuminance at the image plane has been determined, the total exposure depends on how long that illumination continues.
For constant illuminance:
Exposure ∝ Exposure time
Consider the following changes:
- Changing from 1/250 second to 1/125 second doubles the exposure.
- Changing from 1/125 second to 1/250 second halves the exposure.
Just as with aperture, doubling or halving the exposure corresponds to one stop.
We can now identify the distinct functions of aperture and shutter speed:
Aperture controls the intensity of light reaching the image plane, while shutter speed controls the duration for which that light is collected.
Together, they determine luminous exposure.
6. Why Different Settings Can Produce the Same Exposure
We can now combine the two relationships.
Closing the aperture by one stop halves the illuminance at the image plane.
Doubling the exposure time compensates for that reduction.
The resulting exposure remains approximately unchanged.
For example, consider these combinations:
| Aperture | Shutter speed | Relative exposure |
|---|---|---|
| f/2.8 | 1/250 sec | 0.000510 |
| f/4 | 1/125 sec | 0.000500 |
| f/5.6 | 1/60 sec | 0.000531 |
| f/8 | 1/30 sec | 0.000521 |
| f/11 | 1/15 sec | 0.000551 |
The relative exposure values are calculated using:
Relative exposure = Exposure time / (f-number)²
The numerical differences arise from rounding in the commonly used f-numbers and shutter speeds.
For practical purposes, these combinations provide approximately the same exposure under identical lighting and optical conditions.
This explains an important feature of photography.
There are multiple combinations of aperture and shutter speed that produce the same amount of exposure.
The photographer can therefore change one setting while compensating with the other.
This freedom has creative consequences.
Aperture also affects depth of field, while shutter speed affects how movement is recorded.
Two photographs can receive approximately the same exposure while looking quite different.
7. Where ISO Fits into the Relationship
ISO sensitivity concerns the relationship between the amount of exposure and the photographic response.
In film photography, sensitivity is a characteristic of the light-sensitive material.
In digital photography, the ISO setting is associated with signal amplification and the camera’s image-output characteristics.
For example, in a digital camera, increasing ISO from 100 to 200 while keeping aperture and shutter speed constant will generally produce a brighter rendered image, depending on the camera’s processing.
The exposure received by the sensor remains determined by the optical conditions, aperture, and exposure time.
Alternatively, a photographer can raise ISO and use a faster shutter speed to obtain a photograph of similar brightness with less exposure.
This distinction is fundamental:
- Luminous exposure describes the accumulated light received per unit area.
- ISO sensitivity relates the amount of exposure to the photographic response or the resulting image brightness.
The two concepts operate at different stages of the photographic process.
Understanding this distinction makes the relationship between aperture, shutter speed, and ISO much easier to follow.
8. Exposure and Correct Exposure
The word exposure is used in several closely related ways in photography.
It can describe the act of exposing film or a sensor to light, the amount of light received, or the camera settings used to produce an exposure.
Photographers also speak of an image being underexposed or overexposed.
These expressions introduce another concept: correct exposure.
Correct exposure is a judgment about whether the chosen exposure produces an appropriate result for the subject and the photographer’s intentions.
For example, consider two situations:
A photographer may want a person’s face to appear bright against a backlit background.
Another photographer may want to preserve the darkness of an evening landscape.
The desired image brightness differs because the intentions differ.
A camera’s light meter provides a reference for determining exposure, but the photographer may deliberately choose a brighter or darker rendering.
This places two kinds of reasoning in different categories.
The calculation of luminous exposure is a physical problem. The selection of correct exposure is also a photographic judgment.
The physical relationships establish what the settings do. The photographer decides how those effects should be used.
9. Returning to the Fundamental Equation
We can now summarize the entire process as a sequence of causes and results.
Stage 1 — Camera Settings
The photographer selects the aperture, shutter speed, and ISO setting.
Stage 2 — Physical Exposure
For a given subject brightness and comparable optical conditions, aperture and exposure time determine the amount of light received per unit area.
H ∝ t / N²
Stage 3 — Photographic Response and Image Brightness
The exposure interacts with the film’s sensitivity or the digital camera’s signal amplification and output processing.
This contributes to the brightness and tonal characteristics of the recorded image.
Stage 4 — Evaluation
The photographer evaluates the result against the intended subject representation.
That judgment determines whether the exposure is appropriate for the photograph.
Conclusion — From Memorizing Settings to Understanding Cause and Effect
Photography involves many numerical settings, but the relationships underlying those settings follow a relatively simple structure.
Aperture controls the intensity of the light delivered to the recording medium.
Shutter speed determines how long that light is collected.
Their combination determines luminous exposure.
ISO relates exposure to the resulting photographic response and image output.
The photographer then evaluates the result according to the desired photograph.
Once these relationships are understood, camera settings become part of a coherent system rather than a collection of numbers to memorize.
That is the value of understanding photographic exposure through cause and effect.
Related Articles
1. Start with the Three Basic Terms
A beginner-friendly explanation of aperture, shutter speed, and ISO.
▶ Camera Basics for Beginners ★ Aperture, Shutter Speed, and ISO Explained
2. Understand Camera and Lens Specifications
Learn how sensor size, megapixels, focal length, and maximum aperture affect the characteristics of photographic equipment.
▶ Camera Basics for Beginners ★ Sensor Size, Megapixels, Focal Length, and Maximum Aperture
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