Intensity of Light

How to measure the Intensity of Light

Joachim Köppen Strasbourg March 2010

We do have a good sense for the brightness of the light. Our eyes can cover the enormous range from the bright summer sunlight to the faint light of the Milky Way seen in a dark night from a really dark location. Only when we take photographs and we have to set the exposure times from 1/1000th seconds to several minutes, we can realize how vast this range is. Let us measure this brightness in a more quantitative way!

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

photoelements or solar cells produce electricity when light shines on them. They can be found in small battery chargers and the small lamps that we may employ to illuminate a garden path in the night while the internal battery is charged during the day. The great advantage of these photocells is that the electrical current they deliver increases strictly with the light intensity. The image below shows two examples, and another small photoelement in shown in the image after this:

photoresistors are small components whose electrical resistance goes down when light shines on them. They are used to increase the brightness of a display when the ambient light increases. Photoresistors often are made to have the same spectral sensitivity as the human eye. However, the relationship between resistance and light intensity is usually non-linear and therefore requires calibration. The image below shows a large one on the left and two small ones (about 5 mm across) at upper right. At bottom right there is a small photoelement.

photodiodes and phototransistors are very small components which allow a greater electric current to pass though when light shines on them. They are found in various applications, for instance they sense the movement of a computer mouse. Photodiodes and especially phototransistors can be very sensitive, but they are usually more sensitive in the infrared, which makes them less suitable to measure the intensity of the visible light, which may be of greater interest to us! The image below shows a photodiode from a computer mouse. The device is about 5mm across, and the light-sensitive chip is seen through the small plastic lens as the dark-blue area, with a gold wire to make the electrical connection.

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.

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last update: March 2010 J.Köppen