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

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SUMMARY

The intensity of light from a 20W bulb shining in all directions at a distance of 12 meters is calculated using the formula for the surface area of a sphere. The correct calculation is 20W divided by the total surface area of a sphere with a radius of 12 meters, which is 4π(12^2). This results in an intensity of 0.011 W/m², confirmed as the accurate answer after correcting initial miscalculations.

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  • Understanding of light intensity and its measurement in watts per square meter (W/m²).
  • Familiarity with the concept of spherical surface area.
  • Basic knowledge of algebra for manipulating equations.
  • Ability to apply the formula for intensity in a three-dimensional context.
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  • Study the formula for the surface area of a sphere and its applications in physics.
  • Learn about the inverse square law in relation to light intensity.
  • Explore the concept of luminous flux and its relationship to intensity.
  • Investigate practical applications of light intensity calculations in real-world scenarios.
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Students studying physics, educators teaching light and optics, and anyone interested in understanding the principles of light intensity and its 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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