Inverse Square Law: 3D Radiation Physics
Medical Physics Training - Surface Area & Attenuation Effects
INVERSE SQUARE LAW & GEOMETRY
I₂ = I₁ × (d₁/d₂)² = I₁ × (A₁/A₂)
Surface Area of Sphere: A = 4πr²
Same radiation spread over increasing surface area
Distance (d₁):
1.00 m
Surface Area:
12.57 m²
Count Rate (I₁):
0 ± 0 cpm
Distance (d₂):
2.00 m
Surface Area:
50.27 m²
Expected I₂:
0 cpm
Observed I₂:
0 ± 0 cpm
Geometric Ratio:
0.250
Distance (d₃):
3.00 m
Surface Area:
113.10 m²
Expected I₃:
0 cpm
Observed I₃:
0 ± 0 cpm
Geometric Ratio:
0.111
Drag detectors to explore distances. In 2D view, detectors represent cross-sections through a spherical
radiation field. Switch to 3D view to visualize the spherical surface area expansion that creates the
inverse square relationship.
🎯 Geometric Insight: In 3D view, observe how the yellow radiation sphere expands.
At distance r, the surface area is 4πr². At 2r, the area is 4× larger (16πr²),
diluting the radiation intensity to 1/4. This is the fundamental origin of the "square" law.
The Three L's of Radiation Protection:
Length (distance - inverse square law),
Lead (shielding - exponential attenuation), and
Low-time (minimize exposure duration).
Notice how combining distance with shielding provides multiplicative protection.