Physical Principles: Inverse square law

Student Prerequisites: For this demonstration, students need to be familiar with the following concepts - a.) the nature of light as electromagnetic waves, b.) energy transfer in wave motion.

Introduction: A general law of wave propagation that applies to all types of waves is the inverse square law. Students will apply this law to make quantitative predictions about the intensity of a light source at various distance from the source. The primary objective of this interactive demonstration is to help students comprehend this law as a consequence of conservation of energy.

Description of the Demo: For waves that travel in three dimensions, we define the intensity (denoted by I) to be the time average rate at which energy is transported by the wave, per unit area, across a surface perpendicular to the direction of propagation. That is, intensity I is average power per unit area. If waves spread out equally in all directions from a point source, the inverse square law states that the intensity of a wave decreases inversely as the square of the distance from the source,

,

... (1)

where the power output of the source is P with the average intensity through a sphere of radius r. The law follows directly from energy conservation,

.

... (2)

The greater the distance from a wave source, the greater the area over which the wave power is distributed and the smaller the wave intensity. 

Instructions: This demostration uses a light meter to measure the intensity of light falling on its sensor from a 25W bulb at various distances. The meter readings will be taken at equal intervals, for example, 40cm, 80cm and 120cm.

Note to the Instructor: Darken the room to eliminate excess light.

Possible CPS Questions:

1. When the light meter is 40 centimeters from the light, the light intensity is 0.41 (unit)... [Question] [Answer]

2. At what distance does the intensity decrease to one half of 0.41 (unit)? [Question] [Answer]

3. Decide which following factors cause this experiment to deviate from the inverse square law? [Question] [Answer]