Light Intensity in 2D Flatland · CAP 2017 #4
Physics · optics
Problem
The creatures of flatland inhabit a 2-dimensional world. Square, a man of good standing in flatland, holds a hot candle which emits light of intensity 36 Watts. 3 metres away, a detector feels: a) W/m b) W/m² c) W/m² d) W/m e) WIntuitive explanation
In flatland's 2D world, light spreads differently than in our 3D reality. Instead of spreading over a sphere's surface (proportional to ), the intensity spreads over a circle's circumference (proportional to ). You need to apply the inverse-square law's 2D cousin: intensity falls off as , and the "area" receiving light is actually a 1D line segment. This shifts which answer has which units—think carefully about what "intensity per unit length" means in a flat world.
Intuitive explanation
In flatland's 2D world, light spreads differently than in our 3D reality. Instead of spreading over a sphere's surface (proportional to ), the intensity spreads over a circle's circumference (proportional to ). You need to apply the inverse-square law's 2D cousin: intensity falls off as , and the "area" receiving light is actually a 1D line segment. This shifts which answer has which units—think carefully about what "intensity per unit length" means in a flat world.