Use factors of two to trade aperture and time without treating ISO as extra light.
By the end: Calculate a change in exposure and distinguish compensation from a creative choice.
One stop more light means twice the exposure. One stop less means half. Two stops mean a factor of four, not three. Three mean eight. This language works because photographic scenes span ratios much larger than a small linear scale conveniently describes.
A stop count is the base-two logarithm of a positive ratio. You need not know logarithms to use whole stops: count doublings or halvings. Fractional stops interpolate multiplicatively. Three one-third-stop increases together double exposure; they do not add three equal quantities of light.
Begin with 80 arbitrary exposure units in a fixed sensor area. One stop more means 160 units because 80 multiplied by two is 160. Another stop means 320, and a third means 640. Going backward halves the current value, giving 320, 160, then 80 again. The intervals in ordinary units grow as exposure grows, but every adjacent pair has the same ratio. Stops describe proportional change. They do not assign a fixed extra quantity of light independent of where you start.
Negative stop counts work the same way. Two stops less than 80 is 40 after the first halving and 20 after the second. To compare 20 with 640, count 20, 40, 80, 160, 320, 640. There are five doublings between six values, so the difference is five stops. Dividing 640 by 20 gives 32, and five successive multiplications by two also give 32. This checks the count without logarithms. Count the gaps rather than the number of values you wrote down.
The starting value can disappear from a comparison because stops concern ratios. An increase from 5 to 20 and one from 80 to 320 are both factors of four, hence two stops. Their added quantities, 15 and 240, differ. This is useful when the absolute light level is unknown but the change in time or opening is known. It does not mean the scenes are equally bright. A dim scene increased by two stops may still deliver less exposure than a bright scene decreased by one.
| Stops relative to 80 | Exposure units | Ratio to 80 |
|---|---|---|
| −2 | 20 | 1/4 |
| −1 | 40 | 1/2 |
| 0 | 80 | 1 |
| +1 | 160 | 2 |
| +2 | 320 | 4 |
| +3 | 640 | 8 |
A half stop must be a factor which, applied twice, makes two. A factor of 1.5 cannot be exact because 1.5 times 1.5 is 2.25. The needed factor is about 1.414, whose square is about two. Starting at 100 units, half a stop gives about 141.4 and a second half stop gives about 200. The second increment is larger in ordinary units than the first. Equal fractional stops divide a ratio equally, rather than dividing an added amount into equal pieces.
For thirds, the factor is about 1.260 because three successive multiplications give about two. Starting at 100, the sequence is approximately 126, 159, and 200. One third of the increase from 100 to 200 would instead give 133.3, which is not the same operation. Camera labels and displayed times may round these intermediate values. Treat an intended one-third-stop sequence as proportional steps, but use actual ratios when precision matters. Do not infer a hardware fault from a small discrepancy caused by rounded labels alone.
Practice by starting at 40 and making one stop more followed by two stops less. First obtain 80, then 40, then 20. The net change is one stop less than the start, consistent with adding positive one and negative two. Reversing the order gives the same final value because multiplying by two and dividing by four commute. This arithmetic applies to positive exposure ratios. It cannot rescue zero recorded signal by multiplication, and it says nothing by itself about whether a camera has already clipped a measurement.
| Step from 100 units | Half-stop sequence | Third-stop sequence |
|---|---|---|
| Start | 100 | 100 |
| First step | 141.4 | 126.0 |
| Second step | 200 | 158.7 |
| Third step | Not needed for one stop | 200 |
For a fixed scene, exposure is proportional to time divided by the square of the f-number. Double the time and collection doubles. Multiply the f-number by the square root of two, about 1.414, and the opening area halves. Printed f-numbers such as 2.8 and 5.6 are rounded.
Moving from f/4 to f/8 loses two stops. Extending 1/100 s to 1/25 s gains two, giving the same ideal exposure. The resulting pictures need not match: depth of field and motion blur can differ. Lens transmission and close-focus effects also limit exact equality between real lenses.
Use a 48 mm focal length so the opening arithmetic is simple. At f/4 the entrance-pupil diameter is 48 divided by 4, or 12 mm. At f/8 it is 6 mm. The diameter ratio is one half, and the circular area ratio is one quarter. The f-number doubled, but exposure at unchanged time fell by two stops. F-number is focal length divided by pupil diameter. The pupil is the opening as seen through the lens front.
For a one-stop reduction in area, diameter must fall by a factor of about 1.414, not two. Starting at f/4, multiply the f-number by 1.414 to get about f/5.657, normally labeled f/5.6. At 48 mm its pupil is approximately 8.49 mm, compared with 12 mm at f/4. Squaring 8.49 divided by 12 gives about one half. This explains the familiar f-number progression. Printed decimal values are rounded conventions.
Now start at f/4 and 1/200 second. Changing to f/8 multiplies collection by one quarter. Changing time to 1/50 second multiplies it by four because 1/50 is four times 1/200. Together the factors multiply to one, preserving ideal exposure. Intermediate reasoning matters here. The larger shutter denominator means a shorter duration, whereas the larger f-number means a smaller opening. Compare actual durations and areas rather than assuming that increasing either displayed number has the same physical meaning.
Consider a different pair of changes from that same start. Move to f/8 but lengthen time only to 1/100 second. Time doubles, aperture area quarters, and the combined factor is one half. That is one stop less physical exposure. If ISO rises from 100 to 200, the lesson's simple output proxy can return to its starting value, but collection remains halved. If illumination instead doubles while ISO stays fixed, physical collection returns to its starting value. Both scenarios can match brightness while differing in what changed before measurement.
The arithmetic assumes equal scene light, transmission, and sensor area. Two lenses with the same f-number can transmit different fractions of light through their glass. A very close subject can also require corrections outside this simple distant-scene model. Consequently, equivalent settings are a prediction under stated conditions, not proof that two real files must have identical pixel values. Automatic tone curves can further disguise small collection differences. Use the calculated ratios to organize a comparison, then identify which assumptions the real situation does not hold constant.
For a paper check, replace the compensated time of 1/50 second with 1/25 while keeping f/8. Relative to the original 1/200, time is now eightfold, not fourfold. Multiplying eight by the quarter-area factor gives two, so the final exposure is one stop greater than the start. The table preserves each intermediate case for comparison. These settings do not guarantee equal sharpness, since changing time changes motion integration and changing aperture changes ray geometry. Exposure equivalence answers one question, not every question about the picture.
| Setting | Time factor | Area factor | Exposure; stops |
|---|---|---|---|
| f/4; 1/200 s | 1 | 1 | 1; zero |
| f/8; 1/100 s | 2 | 1/4 | 1/2; −1 |
| f/8; 1/50 s | 4 | 1/4 | 1; zero |
| f/8; 1/25 s | 8 | 1/4 | 2; +1 |
t is time in seconds; N is f-number. Old and new distinguish the two settings. ISO is not part of collected light.
Going from f/4 to f/8 quarters exposure; four times the time restores it.
| Change | Exposure factor | Stops |
|---|---|---|
| 1/100 to 1/50 s | 2 | +1 |
| f/4 to f/8 | 1/4 | −2 |
| Both together | 1/2 | −1 |
Choosing settings requires a reason to change them. Suppose a moving label travels at 800 pixels per second in the output. At 1/100 second it travels 8 pixels. Suppose, for this task, that travel of at most 2 pixels is acceptable. Dividing 2 pixels by 800 pixels per second gives 1/400 second. This is a chosen motion criterion for this output, not a universal definition of sharpness. Focus, optical blur, and sampling still contribute.
Shortening 1/100 to 1/400 second quarters collection at fixed aperture and light. The two-stop loss can be offset by changing f/8 to f/4, which doubles pupil diameter and quadruples area at the same focal length. In the ideal model, quarter-duration times fourfold area gives the original exposure. The moving label's travel nevertheless falls from 8 to 2 pixels. The physical benefit is a shorter integration interval. The cost may be less acceptable depth or different lens behavior at the wider opening.
If the lens is already at its widest available opening, that compensation may not exist. Do not assume an f/4 setting is available on a phone or any particular lens. Raising ISO fourfold can restore the simple brightness proxy but leaves collection at one quarter. Adding four times the steady illumination can restore physical collection, although that may be impractical or alter reflections. Accepting a darker rendering does not restore collection either. Equipment, subject, and intention determine possible responses.
Changing the intended output can change the motion requirement. Suppose the same source image is reduced to half its width and half its height. A path spanning 8 source-image pixels then spans about 4 output pixels. The requirement of at most 2 output pixels would now permit about 1/200 second at that reduced scale, assuming uniform resizing and the same framing. Compared with 1/400 second, that doubles collection. This is not extra captured detail. It is a less demanding presentation of the existing spatial information.
A stationary object produces a contrasting decision. If its important parts occupy different distances, a smaller opening may reduce defocus enough to matter, while longer time may cause no subject-motion penalty. Stable support can make that trade practical, though it cannot stop wind or people. The correct calculation could then run in the opposite direction, from f/4 at 1/100 to f/8 at 1/25. Both examples conserve exposure through a fourfold trade, but they serve different tasks and do not predict identical rendered pictures.
On paper, impose both limits at once: time no longer than 1/400 second and aperture no wider than f/8 because the scene needs depth. Relative to f/8 at 1/100, collection must fall to one quarter unless illumination increases. No rearrangement of stop arithmetic removes that conflict. You must change a requirement, alter physical conditions, or accept reduced collection. This is why an exposure recommendation can be mathematically consistent yet unsuitable. A table of constraints helps distinguish unavailable compensation from a mistake in the ratio calculation.
| Choice from f/8, 1/100 s | Collection ratio | Consequence |
|---|---|---|
| f/8; 1/400 s | 1/4 | Meets time and aperture limits |
| f/4; 1/400 s | 1 | Violates aperture limit of f/8 |
| f/8; 1/100 s | 1 | Violates time limit of 1/400 s |
| f/8; 1/400 s; ISO ×4 | 1/4 | Matches simple brightness proxy only |
| f/8; 1/400 s; light ×4 | 1 | Requires changed illumination |
A reflected-light meter sees light arriving from the scene. It cannot know whether a pale wall should look pale or a dark room should remain dark. Modern evaluative metering uses additional scene heuristics, but a recommended exposure is still not a guarantee of the intended rendering.
In aperture priority, you choose aperture and the camera usually chooses time; shutter priority reverses those roles. Manual mode lets you choose both, though Auto ISO can still adjust ISO. Exposure compensation asks an automatic exposure system to depart from its meter recommendation. Which parameter changes depends on the mode and Auto ISO settings. In fully manual capture with fixed ISO, compensation may merely shift the meter indication. Inspect actual settings, the image, and highlight warnings rather than trusting the compensation label alone.
A reflected-light meter measures arriving light, not the intended identity of each subject. Imagine filling the frame first with pale paper and then with dark cloth under unchanged illumination. If an automatic system tries to bring both toward a similar middle lightness, it may reduce exposure for the paper and increase it for the cloth. Their output values can become more similar than their real reflectances suggest. Modern metering may recognize more context, so this is an explanatory case, not a prediction that every camera makes that exact decision.
Suppose aperture priority selects f/8, 1/250 second, and fixed ISO 100. Positive one-stop compensation could change time to 1/125 second while aperture and ISO stay fixed. The duration doubles, so physical collection doubles. Positive two stops could instead reach roughly 1/60 second, the conventional rounded label near 1/62.5. That may better preserve the intended lightness of the pale paper, but the longer time may worsen movement. The compensation request does not separately guarantee highlight preservation or motion sharpness.
Contrast shutter priority with fixed ISO. Starting at 1/250 second and f/8, a positive one-stop request could open the aperture to about f/5.6 while retaining time. Area approximately doubles, so collection rises without increasing motion duration. Depth behavior can change instead. If the lens cannot open farther, the request may not be fully satisfied. With Auto ISO active, either mode may change ISO as part of its response. The compensation number alone therefore does not identify which physical factor changed or whether collection doubled.
| Fixed ISO mode | Before request | Possible +1-stop response | Physical cost |
|---|---|---|---|
| Aperture priority | f/8; 1/250 s | f/8; 1/125 s | Twice the motion interval |
| Shutter priority | f/8; 1/250 s | About f/5.6; 1/250 s | Wider ray cone |
Manual exposure with fixed ISO is different again. If you set both time and aperture, a compensation control may only change the meter reference or may be unavailable. If Auto ISO is active, compensation may direct a change in ISO while leaving time and aperture fixed. That changes gain or rendering behavior without adding photons at fixed scene light. These are possible behaviors, not universal instructions. Inspect reported settings and device documentation before interpreting an unfamiliar control.
Practice with a written observation instead of a camera. The first file reports f/8, 1/250 second, ISO 100. The second reports f/8, 1/250 second, ISO 200 after positive one-stop compensation. At unchanged light, duration and opening are identical, so expected physical collection is unchanged. The simple brightness proxy doubles. If the second file instead reports f/8, 1/125 second, ISO 100, collection doubles. Those distinct explanations can correspond to the same requested compensation. The evidence table makes the hidden automatic choice explicit.
If your device offers compensation, you may repeat a stationary scene with two requests and record the reported settings. If it does not, use the written cases and predict which edges might blur or which depths might soften. Compare pictures at one intended size. A preview histogram is not a direct sensor measurement. A conclusion names the changed settings and assumptions, such as doubled time under steady illumination. An invalid conclusion infers extra light merely because the result looks brighter or the compensation label increased.
| Reported case | Aperture; time; ISO | Collection ratio | Brightness proxy ratio |
|---|---|---|---|
| Reference | f/8; 1/250 s; 100 | 1 | 1 |
| ISO response | f/8; 1/250 s; 200 | 1 | 2 |
| Time response | f/8; 1/125 s; 100 | 2 | 2 |
You change f/4 to f/8 while starting at 1/200 s. What time preserves exposure at fixed light?
The aperture loses a factor of four.
| Stage | Time | Relative exposure |
|---|---|---|
| Start at f/4 | 1/200 s | 1 |
| f/8, unchanged time | 1/200 s | 1/4 |
| f/8, compensated | 1/50 s | 1 |
Use 1/50 s, four times as long. The two-stop loss and two-stop gain cancel in collected light. A moving subject may become less sharp, so equal exposure does not make this a suitable choice for every scene.
Two successive one-stop increases start from 100 arbitrary exposure units. Is the result 300 or 400?
Apply the second doubling to the new value.
| Stage | Units |
|---|---|
| Start | 100 |
| +1 stop | 200 |
| +2 stops total | 400 |
It is 400: first 100 becomes 200, then 200 becomes 400. Stops describe ratios relative to the current value. The additive quantity is the stop count, not the number of exposure units.
The lessons and answers stand alone. These optional secondary references explain the optics and imaging concepts. Numerical examples are constructed, not measured camera specifications. Visual judgments depend on the intended image; the course does not claim a universal aesthetic score.
Secondary overview of exposure, time, aperture, and sensitivity conventions. Our light-collection and brightness ratios are simplified teaching models, not camera calibrations.
Definitions, light per unit area, transmission limits, and diffraction. Selected passages checked; the illustrations here are original geometric constructions.