# Classical Fun with Polarisation

Look what Dad brought back from his trip to Germany!

Apollo Optik. An expensive, and an unknown brand to me. But to my delight, I discovered that they were polarized!!

For the uninitiated, light is a self-propagating electromagnetic field disturbance. I'm tempted to call it sourceless, but fact is, that all light is generated by charges in acceleration somewhere in the universe. Physics limits the speed with which the field values of said charges update themselves to the "current" position of the charges. So these disturbances seem to travel uncorrelated from their creators, into ths distant reaches of the universe to restore the balance. Hmm, so whats all this polarization nonsense?!

The shabby diagrams section:-

Sadly, the exact quantum treatment is beyond the scope of this post. Read a book.

The reason we call light "WAVES" is because if you manage to isolate any particular frequency of the "disturbance", the way this phenomena seems to interact with matter (such as measuring instruments) leads us to conclude that it consists of synchronised and oscillating electric and magnetic fields in mutually perpendicular planes. And the direction of propagation at any instant of time happens to be the cross product of the Electric and Magnetic Field.

So with the direction of propagation fixed, there is an extra degree of freedom in the perpendicular plane, i.e. the orientation of the Electric (or Magnetic) field. If you know how Euclidean geometry works, you'll realise that one can define two special perpendicular polarisation states and express any other state as a linear combination of these two.

Now, the way these waves interact with matter (other charges) is similar to the way they were produced (refer Feynman Lectures in Physics, Vol. I, Chapter 28 "Electromagnetic Radiation", equation 28.3). Any charge in an electric field will experience a force along its direction (or opposite if the charge is negative). So when an incoming EM wave is "classically" "absorbed" by an classical atom (the electron cloud version), it tends to push the negatively charged cloud to one side and the positively charged nucleus to the other (actually, given the mass ratios between electrons and nuclei, it is mostly the electrons that move. Now that the centers of charge of the positive part and the negative part are not on top of each other, they attract each-other, causing the atom to oscillate. But they won't go on for ever since accelerating charges transmit light, thus losing energy. So our atom has become a fresh source of light, re-radiating what energy it absorbed (albeit at lower strength since it re-radiates in all directions). So in a polarisation filter (such as my shades), heterogeneous molecules are arranged relative to each other such that the oscillation along one particular direction is easier than the other. Or in some cases, in one direction all oscillations translate to re-radiated light, but in another, they may couple to vibrations of molecules and become heat. This can also be achieved with certain anisotropic crystal lattices (charge oscillations along certain bond orientations). So any polarisation filter has a defined direction of polarisation, and all the light that comes through it is polarised in that direction. So when I put two filters one behind the other, the light that comes through the first one will not get through the second one if their polarisation angles are perpendicular to each other (as can be seen in the pic). Now my particular glasses are vertically polarised. How do I know that?

Brewsters Law :-

Again, classically, if we take the case of radiation by an oscillating charge, the radiation pattern is that of a dipole. What that means is that the strength of radiation will be different when measured at different angles from the plane perpendicular to the oscillation line.

So, if I can create an object whose charges will significantly oscillate in a given plane, I know that they can't radiate anything polarised in the normal direction. Creating a crude approximation to said object was simply a matter of creating a reflective water surface. Light reflection from a water surface occurs due to incident light being "absorbed" and "re-emitted" by charged particles in the water. The oscillations induced in the charged particles are in a plane perpendicular to direction of incident light. So, if the direction of the reflected rays is predetermined by the laws of reflection (refraction?), at a particular special angle of incidence (which depends on water's refractive index relative to that of air), the reflected rays will propagate at a right angle to the incident ray, and will thus be polarised horizontally (parallel to the water surface). Using this, I could easily deduce the plane of polarisation of my shades.

The reflection intensity from the water is maximum when my shades are tilted vertical (and consequently, the other pair of shades kept on the table seem dark). The result flips if my shades are made horizontal. This simple high-school level semi-classical viewpoint makes gargantuan predictions. For example, did you know that sky light (the scattered blue) is polarized?

Skylight is basically sunlight being scattered ("absorbed" and "re-emitted", classically speaking) by air molecules. The reason its blue is because higher frequencies of oscillation get scattered more. The density of Earth's atmosphere (and its extent) is such that more than half the scattered skylight would have suffered a single scattering event (as opposed to being scattered by multiple molecules). Now, Sunlight is not polarised. But, if one were to observe the sky in a direction perpendicular to sun-rays, a large chunk of the skylight was emitted by charges, whose oscillations were induced by the sur-rays in a plane perpendicular to the sun-ray propagation direction. So if we were to use polarisation filters, and tilt our head, we can artificially increase the contrast between the clouds, and the sky background.

The image is imperfect because I'm using an over-user-friendly digital camera that self-adjusts its aperture and exposure time, and I'm fresh out of analogue film. For more on this, refer: "Clouds in a Glass of Beer" by Craig F. Bohren. Now excuse me while I show-off my new shades outside . . . .