Calculating the brightness of a beam

Power in the beam is determind by the energy of each photon and the number of photons emitted per second

The power switched to the heating by radiation pathway is set by the energy of each photon and the number of photons emitted per second. If the beam is not monochromatic, then you'll have to sum across all the frequencies of photons present in the beam, working out the product of activity and energy shifted for each frequency present. This is complex and time consuming but clear and simple in principle.

This power will ultimately fill a store, but the mechanisms will vary over the huge range of frequencies. Remember that lighting is just a part of what the radiations that make up the electromagnetic spectrum do. Heating (microwaves, infrared) is another significant process that is important to humans, as are the carrying of radio and television signals, as in episode 01. The photon description applies right across the range of radiations that make up the electromagnetic spectrum.

Beams can be pictured as directed streams of photons, but remember that this is only a picture – it's only on departure or arrival where we can be certain of the granularity. The intensity of a beam is just the power for each square metre of cross-section of the beam. So intensity is measured in watt metre^-2. The greater the intensity, the brighter the beam, as more energy per second is detected by the absorbers placed in the beam (power = intensity × collision area of detector).

Streams of photons plot the evolution of the beam

Beams have a history in travelling from source to detector. They may spread; be refracted; be reflected; or be partially absorbed. Each of these may have an effect on the intensity.

These effects can be accounted for in terms of the stream of photons picture. It's easy and perhaps helpful to speak as if the photons actually make the journey. If the beam goes through a fog, for example, you can describe the resultant reduction in intensity as a fraction of the photons being absorbed by each metre of fog traversed. This gives rise to an important pattern in radiation protection, which is met again later. A certain thickness of absorber is needed to reduce the chance that a photon makes it through: high up on mountains the ultraviolet photons have traversed less atmosphere to reach you, so there is a greater chance of each one making it through. Multiplied across a whole stream, this increased chance leads to more ultraviolet photons striking your skin. More chance of sunburn.

Spreading is a matter of geometry. For the beam, the same power is spread across increasing areas (measured at right angles to the beam); for the stream, the same number of photons intersects an increasing number of square metres.

Reflection at surfaces can be partial or complete: you can model both by altering the chance that each photon is reflected. Multiply across the whole stream to predict the behaviour of the beam. You can predict the angle of reflection by considering what each photon might do, and we come back to that in episode 03.

Refraction is again a matter of considering the chance that each photon takes a particular path. Again, there is more on that in episode 03.