kaveh1000 wrote:Dinesh, you are clearly a genius with maths, but you have to ask yourself why all that theoretical stuff is getting in the way of understanding a very simple principle that seems to be obvious to everyone else in this forum.

Genius, huh? Flattery will get you everywhere....well, at least it'll get you a beer at the MIT bar (they do have one, don't they?)

The problem is, Kaveh, that the the obvious is sometimes not so obvious. Many times, the obvious is wrong. I've seen too many situations where the "obvious" was assumed and proved to be not quite as obvious. There is a very well known holograpy company led by a very competent optical scientist who thought it was "obvious" that woodgrain was due to spurious reflections off the walls of the lab and would not believe it was a polarisation effect. We wasted an entire day covvering the walls of the lab with black velvet and still the woodgrain occurred! The very first dot matrix machines had some of the dots brighter than other dots. Everyone thought it was "obvious" that the laser was mode-hopping. I managed to prove mathematically that the cube in the dot matrix was twisted. Even though the mathematics was pretty compelling proof, it took quite a while for the company to act on it because the person in charge thought that it was "obvious" and "simple" that the laser was mode-hopping.

In this case, for instance, it seems "obvious" and "simple" that the beam is apparently both p and s polarised at the same time relative to both cube and mirror. This is simple, right? However, let's throw in a bit of complexity. Let's have a beamsplitter instead of a mirror. Let's then place a sheet of glass above the beamsplitter at an angle of 60 degrees odd. We're agreed that the beam is clearly s polarised when it exits the cube at the top. So, according to Brewster's law, the glass atop the beamsplitter will reflect some of the light (as you know, only p polarised at Brewster's angle does not reflect). Now, vary the beamsplitter's reflectivity. At some point, due only to the varying of the splitter, the beam now takes on the characteristics of both p and s. So, apparently, the reflectivity of the piece of glass atop the cube will now drop because of the p component, while simultaneously not drop because of the s component.

The problem is, people seem to accept truth based on a belief system and, when the belief system does not solve the problem, people add all sorts of spurious

*ad hoc* assumptions to the belief system to force fit the result into the belief system. When I was in school and in university, back in the bad ol' 60's, the educational system tried to teach us rational thinking and analytical skills. I was actually told by Dr Bondi (one of the proposers of the Steady State theory of cosmology and a lecturer at Kings) that the whole point of going to university was to teach you to think and analyse. If you simply wanted to learn physics, you could do a correspondance course! My apparent skill in mathematical manipulation is not that great; these are after all, simple algebraic equations. I'd like to believ my skill is in the analysis of a speculation or problem, the mathematisation is a fairly simple and straightforward process coming out from the analysis. But these days,I find that any analysis of any problem is frowned upon and deemed to be socially unacceptible. It seems that the socially correct thing to do, when presented with facts and/or speculation is to assume a "group think", "politically correct" stance such that analysis has a faint whiff of elitism. When did educational system get to the stage that the results of education in the analysis of a speculation become a shameful thing done in the dark. When did we deny the ability to analyse, and put down those who did analyse, and simply accept a "group hug" kind of mentality to problem solving?