Irradiance

The Irradiance of light I is defined as the 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. 

Note - When working with Irradiance, the radius of the sphere is usually referred to as the distance to point source, and is given the symbol d. 

If the following experimental setup is used, data showing how irradiance changes with distance from the point source can be gathered : 

In order to make the light source as close as possible to a point source, the smallest available bulb should be used. In order to prevent reflections from the tabletop interfering with the results of the light meter, a black cloth should be placed on the bench below the kit. 

The following graphs show how the Irradiance varies with both d and 1/d2 : 

As a straight line is found using 1/d2, this means that the Irradiance is inversely proportional to d2.

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 : 

Where : 

I = Irradiance (Wm-2) 

d = Distance from point source (m) 

k = constant

This relationship can also be written as : 

Where : 

I₁ = Irradiance at first location (Wm-2) 

d₁ = Distance from point source at first location (m) 

I₂ = Irradiance at second location (Wm-2) 

d₂ = Distance from point source at second location (m)