Physics laboratory: polarization-- Malus' Law?

Question

i would like to ask if the graphs i did for our laboratory activity is correct.

these are graphs made from data collected for a laboratory activity in physics (elementary optics and electromagnetism).

graph 1: intensity versus angle for the laser diode polarization setup

http://i337.photobucket.com/albums/n363/binibiningarki06/intensityversusangleforthelaserdiod.jpg

graph 2: intensity versus angle for the plain light source

http://i337.photobucket.com/albums/n363/binibiningarki06/intensityversusangleforplainlightso.jpg

More questions:

Is malus' law obeyed by these graphs? How can i qualify my answer?

Does the intensity of the light source determine whether Malus' Law is obeyed or not? How is this supported by the plot?

Answer 1

I think it would certainly help if you mentioned what the two colors are in each graph.  My guess is that the dark line is the intensity vs angle -- I have no idea what the light line might be.

Malus's law says that intensity goes as cos squared of the angle between E field and polarizer.

If you plot cosine squared, you will see that it starts at the maximum, goes to the minimum at 90 degrees, then goes to a max at 180 again.  Your first graph certainly shows this effect.  Qualitatively, you could plot 350 * cos(theta) * cos(theta) onto your graph, and show that it has the same form.  Quantitatively, you would fit the curve exactly (nonlinear least squares fit), then report the residual error.

The second curve, plain light source, does show some effect.  That surprises me -- were you using two polarizers?  Again, plot a cos^2 with a reasonable amplitude (1.8?) to see how it compares.  Since your signal is much lower, you'd expect more noise in this case.

The intensity of the source plays no real part to whether malus's law is obeyed -- although does play a part in your ability to measure it accurately.  For instance, you have to start worrying about room ambient lights.  Also, the divergence angle of the beam certainly plays a role, as your polarizer probably has some dependance on angle of incidence.  Also wavelength band of your source may play a role.