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?
A) It has decreased by a factor of two.
B) It has increased by a factor of two.
C) It has decreased by a factor of four.
D) It has increased by a factor of four.

Answer 1

From my new perspective, the new intensity of the
light source has decreased by a factor of four.

Answer 2

Answer:

The new intensity of the wave has decreased by a factor of four.

(C) is correct.

Explanation:

Given that,

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.

Using inverse square law,

The intensity is inversely proportional to the square of the distance from the source.

It is defined as:

$I\propto\dfrac{1}{r^2}$

The intensity at 10 m distance,

$I\propto\dfrac{1}{100}$....(I)

The new intensity at 20 m distance,

$I'\propto\dfrac{1}{400}$.....(II)

The ratio of the equation (I) and (II)

$\dfrac{I}{I'}=\dfrac{400}{100}$

$\dfrac{I}{I'}=4$

$I'=\dfrac{I}{4}$

Hence, The new intensity of the wave has decreased by a factor of four.