∙Predict/Calculate In the following, assume that lightbulbs...

$\bullet$ Predict/Calculate In the following, assume that lightbulbs radiate uniformly in all directions and that 5.0$\%$ of their power is converted to light.(a) Find the average intensity of light at a point 2.0 $\mathrm{m}$ from a $120-\mathrm{W}$ red lightbulb $(\lambda=710 \mathrm{nm}) .$ (b) Is the average intensity 2.0 $\mathrm{m}$ from a $120-\mathrm{W}$ blue lightbulb $(\lambda=480 \mathrm{nm})$ greater than, less than, or the same as the intensity found in part (a)? Explain. (c) Calculate the average intensity for part (b).

$\bullet$ Predict/Calculate In the following, assume that lightbulbs
radiate uniformly in all directions and that 5.0$\%$ of their power is
converted to light.(a) Find the average intensity of light at a point
2.0 $\mathrm{m}$ from a $120-\mathrm{W}$ red lightbulb $(\lambda=710 \mathrm{nm}) .$ (b) Is the average intensity 2.0 $\mathrm{m}$ from a $120-\mathrm{W}$ blue lightbulb $(\lambda=480 \mathrm{nm})$
greater than, less than, or the same as the intensity found in part
(a)? Explain. (c) Calculate the average intensity for part (b).

Key Concepts

Wavelength Considerations

While wavelength determines the color of the light and influences other optical properties like photon energy and interactions with matter, it does not directly affect the spatial distribution of intensity, provided the effective power output in the light is constant. Therefore, differences in wavelength do not change the average intensity calculated using the inverse-square law.

Power Conversion Efficiency

Power conversion efficiency refers to the fraction of the total power output that is effectively converted into the desired form of energy, such as light. Many practical sources do not convert all the input power into light; instead, only a certain percentage contributes to the observable spectrum. This concept is essential when determining the effective power used in intensity calculations.

Intensity

Intensity is defined as the amount of power per unit area. It is a measure of how concentrated the energy radiated from a source is when it reaches a particular location. This concept is crucial when determining how bright or how strong the energy from a source will be at a given distance.

Inverse-Square Law

The inverse-square law describes how the intensity of light or any point-source radiation decreases with increasing distance from the source. Specifically, for a source that radiates uniformly in all directions, the intensity is inversely proportional to the square of the distance. This law is fundamental in radiation and optics when calculating the distribution of energy across a spherical surface.

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