How to measure the Intensity of Light

Joachim Köppen Strasbourg March 2010

There are several readily available electronic components that are light-sensitive and permit us to measure the intensity of light:

Experiment: How the light intensity diminishes with distance from the light source

Material needed

• photoelement
• analog or digital multimeter to measure electric current
• measuring tape or long ruler
• small light source in a dark room

What we do

Connect the multimeter - set to measure electric current, perhaps a few mA - to the photoelement. The light source could be a desk lamp with no or but a small lamp screen, a naked clear bulb or the small low-voltage lamps would be fine. Place the photoelement at some (measured) distance from the light source and measure the current. Repeat this for several distances, always holding the photoelement oriented towards the source. You might rotate it a bit in order to get the maximum current.

If you plot the current values against the distance, you will notice that the current decreases with distance. In fact it decreases with the square of the distance. You can show this by entering the data in Excel and overplotting a curve y = A/distance with some suitable value A.

There is an even nicer way to prove this relation: plot the currents against the square values of the distance, and the measured points will form a straight line!

A quick way, for a demonstration, would be to see that the current increases by a factor four everytime you half the distance!

Interpretation

The reason why the measured brightness decreases with the square of the distance is rather simple but fundamental: The light source radiates its power in all directions. If we imagine a spherical surface with some radius r around the source, the power flowing through the entire surface will always be the total power of the source, whatever the radius of the sphere. But since the surface area of the sphere increases with the square of its radius, each square centimetre of the sphere receives a portion of this total power which diminishes with the square of the sphere's radius. Thus, the power picked up by the photoelement - which has a given fixed area - goes down with the square of its distance from the source.

This law is the reason why more distant stars appear to be less bright.

last update: March 2010 J.Köppen