01 Therapy
Inverse square law
Intensity or dose rate versus distance from a point source.
Listen
Listen · English
Simulation
Inverse square law — Change the numbers; the scene follows.
Where it works
Linear accelerator
Isocenter
At isocenter, on the central axis through the patient (or a phantom in the same place).
Open this machineFormula
Variables
Results
I₂
Intensity at d₂
156.25cGy/min
I₂/I₁
Ratio
1.5625
Curve
Explanation
What it means
Intensity (or dose rate) from a point source falls as 1/d² because the same energy is spread over a sphere of area 4πd². Doubling distance quarters the intensity. This is the geometric backbone of SSD changes, HDR dwells, and protection calculations. This is a working relation in Radiotherapy.
Where it is used
Clinically it sits on the Linear accelerator — Isocenter. At isocenter, on the central axis through the patient (or a phantom in the same place). Radiotherapy equations sit at the console and in the bunker: output, depth dose, equivalent square, and the monitor units that treat the patient. Hand-calc them beside the TPS, never instead of a commissioned plan.
Linear accelerator · Open this machineHow to use it
Enter the known rate I₁ at d₁ and the new distance d₂. Typical check: 100 cGy/min at 100 cm becomes 156 cGy/min at 80 cm. Use the curve to see how rapidly output rises as you move toward the source. Change one input and watch the curve and the simulation follow.
Symbols
- I₁Intensity at d₁100 cGy/min
- d₁Reference distance100 cm
- d₂New distance80 cm
Worked example
A typical case from the default values: I₁ = 100 cGy/min (Intensity at d₁); d₁ = 100 cm (Reference distance); d₂ = 80 cm (New distance). Substituting into the relation gives I₂ = 156.25 cGy/min; I₂/I₁ = 1.5625. These are teaching numbers — align them with your machine.
Typical values give
- I₂ = 156.25cGy/min
- I₂/I₁ = 1.5625
Where it comes from
The displayed formula is the working relation. Intensity or dose rate versus distance from a point source. Usual reference: Khan, The Physics of Radiation Therapy. Derive it in the specialty lesson, then return here to pin the numbers.
Reference: Khan, The Physics of Radiation Therapy
Assumptions & limits
Point source in air or vacuum — no attenuation, scatter, or finite source size. Inside a patient you must add tissue attenuation. Very near an extended source (brachytherapy) use TG-43 geometry instead.
Pitfalls
Never mix PDD from one SSD with TMR from another without converting. Field size at the surface is not the size at isocentre. A hand MU is a check, not a treatment. Point source in air or vacuum — no attenuation, scatter, or finite source size. Inside a patient you must add tissue attenuation. Very near an extended source (brachytherapy) use TG-43 geometry instead.
Keep this
Valid for a point source in air. In tissue, add attenuation and scatter.
In this specialty