Why are camera f-stops 1.4, 2, 2.8, 4, 5.6?

AA SLAI SLAA HLAI HL Accessible Also in: Pure maths, Modelling

Research question

Why do f-numbers form a geometric sequence with ratio √2, and does the exposure of my own photographs follow the predicted relationship between aperture, shutter speed and brightness?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

The strange numbers on a camera lens are a geometric sequence chosen so each step halves the light. Deriving this and testing it with your own photos connects sequences, logarithms and area.

The mathematics you'll need

Geometric sequences and powers of √2
Area of a circle and how light scales with diameter
Logarithms base 2 (exposure value)
Testing with measured pixel brightness

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Take photos of a fixed scene at different aperture/shutter combinations and measure average pixel brightness with software.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Derive why each f-stop halves the light.
Explain rounding of the sequence (5.6, 11).
Define exposure value with logarithms.
Test with your photographs.
Reflect on sensor response and image processing.

Pitfalls that cost marks

Automatic settings changing exposure.
JPEG processing distorting brightness — use RAW if possible.
Not controlling lighting.

Showing personal engagement

Use your own camera or phone in manual mode.
Explain the rounding choices photographers use.
Compare lenses.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Model the sensor's response curve (brightness vs light) from your data.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).