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Irradiance and the Inverse Square Law

The Irradiance of light I is defined as the amount of light energy incident on every square metre of a surface per second or more simply power per square metre.

This allows Irradiance to be calculated using the following formula:-

    Where:-          I = Irradiance ( Wm-2 )

                            P = Power ( W ) 

                            A = Area ( m2 )

The video below demonstrates how the Irradiance of the Sun can be measured.

The above video made a large assumption about the Sun. 

In order to calculate the Irradiance in this way, we must assume that the Sun acts as a point source of Light.

A point source is one which irradiates equally in all directions.

Therefore  the volume that will be irradiated will be a sphere centered on that point.

To find the Irradiance of the Sun, we must find the surface area of a sphere with a radius equal to 1 A.U. (1.5x1010m) 

The surface area of a sphere is calculated using:-

This means that the area will increase proportionally with r2, not r. 

Therefore Irradiance is inversely proportional with r2. 

Using the kit provided:-

•  Measure the average Irradiance over a range of radii from a bulb.

• Convert the radii measurements into 1/r2.

• Plot a line graph of Irradiance ( Y-axis ) against 1/r2 ( X-axis ).

The following graphs show how the Irradiance varies with both r and 1/r2. 

As a straight line is found using 1/r2, this means that the Irradiance is inversely proportional to r2.

This allows us to calculate the Irradiance of point source at any position, as long as we know the Irradiance at a known radius using:-