Matter and radiation
I = I0 e−μx
Exponential attenuation describes an ideal monoenergetic narrow beam. Real broad-beam and polyenergetic conditions require care.
Free printable learning reference
FRCR Physics: Formulas, Units and Relationships
Important equations are only useful when you know what they describe, which units belong in them, and where the assumptions break. This four-page sheet brings the core relationships together without turning revision into a wall of symbols.
Updated 11 October 2026 · Four printable A4 pages · Free, no sign-in needed.
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Seven areas, one habit: state the conditions
The sheet labels idealised or approximate relationships in context. These examples are a preview of the printable reference; each entry in the PDF also gives the units or physical interpretation.
Radiography and fluoroscopy
M = SID / SOD
The ideal geometric magnification factor; source-image distance divided by source-object distance. Practical unsharpness also depends on focal spot size.
Radionuclide imaging
A(t) = A0 e−λt
Activity is measured in Bq (decays per second). Effective half-life also depends on biological clearance where applicable.
Radiation safety
D = energy deposited / mass
Absorbed dose is in gray (Gy). Equivalent and effective dose use protection weighting and are expressed in sievert (Sv).
CT
DLP = CTDIvol × scanned length
DLP is in mGy cm. CTDIvol is a standard scanner output index, not the absorbed dose to an individual patient.
MRI
f0 = (γ / 2π) × B0
The Larmor relationship uses the angular gyromagnetic ratio. For protons, f₀ is about 42.58 MHz per tesla.
Ultrasound
Δf = 2 f0 v cos(θ) / c
This backscattered Doppler relation depends on beam-flow angle; pulsed systems also face a Nyquist sampling limit.
How to revise with this sheet
- 1. Say the relationship aloud. Describe what changes when a variable increases and what is held constant.
- 2. Check units. Verify that the dimensions match, especially for CT dose indices, radioactivity, gyromagnetic ratio and Doppler frequency.
- 3. Challenge the assumption. Ask whether the equation is exact, a simplified imaging model, or an approximation for specified conditions.
- 4. Apply it to a stem. Work the physics principle in question practice, then explain what made each true/false statement correct or incorrect.
References: RCR Part 1 Physics candidate guidance and the IAEA Diagnostic Radiology Physics handbook. Independent educational material; not affiliated with or endorsed by the RCR. Clinical protocols and safety regulations take precedence over condensed formula sheets.
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When ready to test a mixed paper, take the free FRCR Physics mock with a complete review after submission.