What is the Intensity of Light 12m from a Bulb Shining in All Directions?

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The discussion focuses on calculating the intensity of light from a 20W bulb at a distance of 12 meters. The correct formula involves using the surface area of a sphere, not a circle, which is 4πr². The initial attempts at calculating intensity were incorrect, as they did not account for the three-dimensional nature of light distribution. The final correct calculation yields an intensity of 0.011 W/m². Understanding the geometry of light distribution is crucial for accurate intensity calculations.
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Homework Statement


The light from a bulb shines equally in all directions. If 20W of light is given off, what will the intensity be 12m from the lamp to 2 significant figures? (Consider the shape of the region illuminated if the light hits this surface after traveling 12m in all directions.)

Homework Equations


The Attempt at a Solution


20 / pi * 122 = 0.044 W/m2. Incorrect. I suppose this value would give me the average intensity over the entire area. Halving it should then give me the furthest intensity. 0.022 W/m2, still incorrect.
 
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What's the total area of the surface at a radius of 12 m? (hint: the surface is not a circle).
 
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gneill said:
What's the total area of the surface at a radius of 12 m? (hint: the surface is not a circle).

Argh, I was considering it shining over a one-dimensional circle.
20 / (4 * pi * 122) = 0.011, correct answer. Thanks!
 
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