Light, Brightness, and Distance

Description:

Does light seem brighter the closer you are to the origin? Dimmer when you are farther away? Closer and closer, the amount of light that enters your eye increases. The measure of brightness, the amount of penetrating light, is called illumination, which is measured in lux. This lab will explore how illumination differs in distance, and take theoretical data to compare with an actual mathematical model.

Purpose:

To understand the relationship between intensity and distance from a light source, and correlate newfound knowledge to derive a mathematical formula.

Results:

After moving Light Sensor away from Light Source, first by 1 cm then 10 cm increments, we collected data points that when connected resembled a rational graph (AD^B).

Equations / Calculations:

When fitting a graph to the collected data, the equation that fit best was a rational graph (AD^B) where:
A=5.633E+004 B=-1.782

And as D increased, the ration (A/D) got smaller.

Analysis / Description of what we learned:

WRAP-UP QUESTIONS

1. Suppose a small light source is placed at the center of 2 transparent spheres. One sphere has a radius R, and the other a radius 2R. Energy in the form of light leaves the source at a rate P. The same power P passes through the surface of the inner sphere and reaches the outer sphere. Intensity is the power per unit area. The intensity at each sphere is...

a) The power passing through the inner sphere is stronger/more intense than the power reaching the outer sphere.
b) Surface area of inner sphere < surface area of outer sphere
c) Using the derived equation, in accordance with the data graph, intensity decreases with increased distance from light source.

2. Since most light bulbs used are not true point sources of light, the answer to Question 1 would change. If a typical light bulb was used, yes, the light intensity contacting with the inner sphere is still greater than the outer sphere's light intensity; however, the difference in intensity would be less because the light bulb, a non-concentrated source of light, would emit light rays that cover more of the surface area, spreading the same amount of light intensity over a greater amount of surface.

The Square Inverse Law

(P/(4)(pi)(r^2)) = I

As distance between light source and light sensor increases, the intensity/illumination of light decreases.