|Cosine square law
in Polarised light
||This is a simple (and
cheap) experiment/demonstration showing the cosine-squared
dependence of light transmission throught a pair of polarising filters.
It uses cheap equipment, (total cost approx 60 euro), and is easy to perform in daylight (-- it uses daylight)
The accuracy is good (a few percent)
||This is an essential
experiment in physics, and students must see it, either as a lab
experiement, or at least as a demonstration.
Indeed it illustrates:
|link to QM
are used as the standard analogy in the DIRAC formulation of quantum mechanics, (at the basis of quantum field theory),
see for instance the classical ref :
Alternatively, cheap linear polarising filters (plastic) can be obtained from standard physics suppliers.
||using a photographic
filter, the only real work consists in attaching a paper tape around
one of the filters, after graduating it in angles.
The zero setting may be chosen arbitrarily, but as a matter of elegance, it is convenient to fix it using the Brewster angle (see below)
||light reflecting from
a non-conducting (dielectric) surface (tradition calls for a piece of
black glass) is polarized. At the Brewster incidence angle, reflected
light cannot be polarised with the electric vector in the incidence
plane (it must thus, in case of a flat surface be both
perpendicular to the direction of the light ray, and parallel to the
This is easily realised on the optical bench, by placing the polariser in its rotating mount on the light source, and fitting a piece of black glass on a goniometer.
It is however very easily demonstrated in the class room by looking at a set of windows from a nearby building (in the horizontal plane). One window will likely be close to the Brewster angle, and rotating the filter will kill the reflected light: at this moment, the filter is only allowing the light polarised in the incidence plane. (the Brewster angle for glass is about 56 degrees from the normal incidence).
|mode of operation
||It is obviously
tempting to use a spreadsheed to plot the results.
However, care should be taken if an automatic line fitting (least squares) is used. Many programs indeed assume equal errors (and often neglect the error on x in x-y plots). This is certainly not the case here: the error on the light measurement is typically a fraction of the measurement + a constant, while, if the cosine squared is used as a variable, the error on this quantity is proportional to 2 * sin* cos* Delta(theta) . The error is thus maximal for 45 degrees, and vanishes (at first order) for 0Â° and 90Â° , which are both local extrema of cos squared in terms of the angle.
A precise chi-squared treatment is of course possible (see http://homepages.vub.ac.be/~frere/ , under the heading general physics)
To avoid entering these more elaborate discussions for this elementary measurement, and more specifically in the framework of a demonstration, I suggest to present:
||the meter (VELLEMAN
DVM1300) is a cheap model, and its accuracy is listed as 5% of reading
+ 10 LSD. This applies to the absolute reading,
the linearity is probably much better, and will be checked in separate experiment testing the 1 over R squared behaviour.