The intensity of a 120-W lightbulb observed from a distance 2 m away is 2.4 W/m $^{2}$ . What would be the intensity if this distance was doubled?

Solution

If we move twice as far away, then the answer will change according to the inverse square of the distance, so the new intensity will be $\left(\frac{1}{2}\right)^{2}=\frac{1}{4}$ of the original intensity, or 0.6 W/m $^{2}$ .

Check Your Learning

How many times brighter or fainter would a star appear if it were moved to:

twice its present distance?
ten times its present distance?
half its present distance?

Answer:

a. $\displaystyle \left(\frac{1}{2}\right)^{2}=\frac{1}{4};$ b. $\displaystyle \left(\frac{1}{10}\right)^{2}=\frac{1}{100};$ c. $\displaystyle \left(\frac{1}{\text{1/2}}\right)^{2}=4$

Bibliography

This example is a derivative work of the Creative Commons source in [1].

[1] Andrew Fraknoi, David Morrison, and Sidney Wolff, “Example 5.2: The Inverse Square Law for Light,” in “5.1 The Behavior of Light,” Astronomy 2e. Houston, Texas: OpenStax, 2022. Licensed CC BY 4.0 in the original 2022 release (https://creativecommons.org/licenses/by/4.0/). Changes: converted to LaTeX for PhysicsLibrary and separated from section 5.1 as a standalone example. Access for free at https://openstax.org/books/astronomy-2e/pages/1-introduction. Section source: https://openstax.org/books/astronomy-2e/pages/5-1-the-behavior-of-light.

"example of behavior of light: inverse square law for light" is owned by bloftin.
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