Lamberts Cosine Law
Lamberts Cosine Law is used in solar engineering to determine the irradiance of a surface from a ray of sunshine. The irradiance is proportional to the cosine of the angle between the beam and the normal to the surface:
The angle between the beam and the normal to the surface is showin in the diagram below:
In solar calculations, z is often referred to as the zenith angle.
The diagram shows the radiation received by a surface for three values of z:
Cosine Response
The term "cosine response" is used to describe the behaviour of sensor which is irradiated by ray at an angle to its surface. A device with good cosine response is one which allows the Ibeam to estimated knowing the value of Isurface and the zenith angle. This is important in instruments that measure solar irradiance which are mounted in a fixed position and do not track the sun as it moves across the sky (Earth-centred explanation used for brevity!).
Experiment
Whilst determing if a low cost photocell could be used to estimate solar irradiance, an experiment was set up which involved blue-tacking a photocell to a vertical piece of plywood and pointing a torch at it from different angles whilst maintaing a constant distance between the torch and the photocell. The wires from the photocell were connected across an ammeter, effectively short-circuiting it, thus the output of the meter was directly proportional to the irradiance of the photocell. A diagram of the layout is shown below:
The photocell selected was a flat, crystaline device measuring approximately 65mm by 20mm which produces current in the range 0 - 250mA depending on the irradiance:
The results of the experiment are shown in the plot below:
There is a close agreement between the theory and the experimental results. Three sources of error would account for the deviations. The source was not a pure point, also, the cell was receiving some diffuse light from the surrounding room, not to mention some errors of measurement.