# Diameter of a spherical cavity at temperature 500K necessary to make deep red light at 100 cd/m²

This is a thinking experiment, I'd just like some help in reasoning.

When a cavity is heated it emits electromagnetic radiation depending on its temperature.

Say the cavity C is made of a white, heat-resistant material that reflects lambertially 100% of electromagnetic radiation.

C is heated uniformly at 500K.

C has a tiny window and one can look inside.

I want to measure 100 cd/m² when I point a spectrophotometer at the window of the cavity.

What should be the diameter D of the cavity for the intensity of light to be 100 cd/m²?

• Interesting question. Some clarifying questions: 1) is that total power across all wavelengths or just the deep red? 2) is the outside white or or it the inside walls white? 3) if yes to latter, it's not a black body right? Commented Jan 18, 2022 at 0:53
• Realize the inside surface of the sphere is in equilibrium with the radiation inside. So how does the intensity of radiation inside change with D?
– Dan
Commented Jan 18, 2022 at 2:20
• @dllahr yes you are right it's not a black body. The material is white, you could think of it as a white ceramic hollow sphere Commented Jun 3, 2022 at 15:48
• @Dan no the inside is not in equilibrium. Imagine it as an oven where most of the heat is emited inside, the outer part of the object being strongly isolated from the inside Commented Jun 3, 2022 at 15:50