Using the equation intensity = power/cross-sectional area

[John421]

Let's say we have the problem: A 100W lamp emits light in all directions. Assuming that the lamp is a point source, calculate the intensity of the radiation 1m away from the lamp.

The surface area of a sphere is :4*Pi*r²
intensity = power/cross-sectional area
The answer is intensity = 100w/4Pi = 7.96

Now what confuses me is that the answer is derived by intensity = power/surface area of the shape the wave makes when it spreads out.

Shouldn't cross-sectional area be the cross-sectional area of a sphere?
I don't see how 4*Pi*r² is the cross-sectional area in this case.

 

[mfb]

4 pi r² is the surface area of a sphere. Your light will be distributed uniformly over this area.

 

[John421]

But then why does the formula say cross-sectional area instead of surface area?

 

[mfb]

This is the cross-section of the light with your sphere. It happens to be the whole sphere as you have a point-charge radiating in all directions.

 

[Meesh]

If the question were to ask what the intensity of the light was at a screen 1m away from your light source, then you would use the surface area of that screen, not the surface area of your light source (just to be clear on what surface area you are using -- not the surface area of your light source). I just want to ensure you know that the equation uses the cross-sectional area (of the light) interchangeably with the surface area of the *thing* that the light is hitting.