Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

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?

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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

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.

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.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Geometric sequences and powers of √2; Area of a circle and how light scales with diameter
AA HL	Fits, but add an HL technique	Geometric sequences and powers of √2; Area of a circle and how light scales with diameter
AI SL	Good fit	Geometric sequences and powers of √2; Area of a circle and how light scales with diameter
AI HL	Fits, but add an HL technique	Geometric sequences and powers of √2; Area of a circle and how light scales with diameter

Level: Accessible. A good first extended piece of maths, with room to go deeper. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: automatic settings changing exposure; and jPEG processing distorting brightness — use RAW if possible. Say how each one affects your answer.

Use of mathematics (E)

SL: 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, each explained in your own words and carried out correctly.

How art & music explorations reach the top bands in general: Art, music & design IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

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

Extending it for HL

Add an HL technique the question genuinely needs: what an HL art & music exploration adds.

See a complete IA, marked

Is a hanging chain a parabola? Comparing catenary and quadratic models (AA SL) is a complete art & music exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AA SL, AI SL, AA HL and AI HL. We rate it Accessible: a good first extended piece of maths, with room to go deeper.

What mathematics does this IA use?

Geometric sequences and powers of √2, area of a circle and how light scales with diameter, logarithms base 2 (exposure value) and testing with measured pixel brightness.

Where can I get data for this IA?

Take photos of a fixed scene at different aperture/shutter combinations and measure average pixel brightness with software. Checked sources and tools: Desmos graphing calculator.

Turn this idea into your IA

The planner opens with “Why are camera f-stops 1.4, 2, 2.8, 4, 5.6?” filled in: the question, the maths and the data sources.

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