Question

You are standing 10 meters from a light source. Then, you back away from the light source until you are 20 meters away from it. From your perspective, what has happened to the intensity of the wave?


It has decreased by a factor of two.

It has increased by a factor of two.

It has decreased by a factor of four.

It has increased by a factor of four.

Answer 1

The intensity of light (or any electromagnetic wave) diminishes with the square of the distance from the source, following the inverse square law. This means that if you double the distance from the source, the intensity decreases by a factor of \(2^2 = 4\).

Initially, you are 10 meters away from the light source. When you back away to 20 meters, you have doubled your distance. According to the inverse square law:

\[
\text{Intensity} \propto \frac{1}{\text{distance}^2}
\]

So, when your distance changes from 10 meters to 20 meters, the intensity at 20 meters will be:

\[
\text{Intensity at 20m} = \frac{1}{(20)^2} = \frac{1}{400}
\]

And the intensity at 10 meters is:

\[
\text{Intensity at 10m} = \frac{1}{(10)^2} = \frac{1}{100}
\]

Now, comparing the two intensities:

\[
\frac{\text{Intensity at 10m}}{\text{Intensity at 20m}} = \frac{1/100}{1/400} = \frac{400}{100} = 4
\]

This shows that the intensity has decreased by a factor of 4 when you move from 10 meters to 20 meters.

Thus, the correct answer is: **It has decreased by a factor of four.**