Electromagnetic waves (3/4)
So far we have examined the field quantities E and B. What is now
the intensity of light
seen with the eye of an observer, measured with a photodetector or taken as an image with a camera?
Light detection, visually or with an optical instrument, is not done with E and B directly. It is the energy
of the electric and magnetic field which determines the intensity. The field energy is proportional to the squared fields, i.e.
E2 and B2. Both the field quantities and their squares have very high frequencies,
in the order of 500 terahertz with visible light. These frequencies are much too high to be seen by the photoreceptors of
the eye.
Therefore, the eye and all electronic detectors for visible light perform a time-averaging over the squared field quantities.
It is this average which is related to the intensity of light.
Frame rate of motion pictures ↓ ↑
Films on television are composed of a sequence of individual images. The eye stores a single
image for a short time so that a sequence of images appears to the viewer as a moving image:
the human eye performs a smooth averaging of the individual images. For this to be possible,
the frame rate, specified as frames per second (fps), must exceed a value of around 18.
Lower refresh rates lead to jumpy or flickering films. Cinema films are shot at 24 frames
per second or 48 frames per second for newer films. Earlier CRT television sets used 25
frames per second (European PAL and SECAM signal encoding) or 30 fps (American NTSC signal
encoding); half-frame images were superimposed, which is why the refresh rate appeared to
the eye to be 50 or 60 frames per second. New LCD devices have refresh rates of up to 800
frames per second.
Please calculate the period of an individual TV image, and compare it with period of a light wave
having 500 THz frequency. Verify from the result that the frequency of light waves and the fps of motion pictures belong to completely
different physical phenomenena.
This is shown in the following graph with the electric field E. For simplicity, we consider its time-dependence only:
(thin blue curve)
Its square corresponds to a sine function with half amplitude and half period T, shifted by 0.5 to positive values:
(red curve)
Trigonometric relations ↓ ↑
The following transformations hold for an angle α and the square of its sine and cosine:
Equations ↓ ↑
Mathematical equations are shown using the
Mathematical
Markup Language (MathML), which is supported by Mozilla Firefox
and Safari. It may not be available for other browsers.
We use brackets to denote a signal average over time of E2(t). Since E2(t)
is symmetric around E2(t)=0.5, it follows:
(green line)
It is this constant signal (as long as the wave amplitude remains constant) which is seen by the eye as the intensity of light.
Read more about the energy density and intensity of electromagnetic waves in supplement 1.4.
