You have n polarising filters stacked one on top of another, and you know each axis angle. How much light gets passed through the filter bank? For more information, see Polarizer (Wikipedia).
>> n = [0, 90];
>> polarised([0, 90])ans = 0
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two filters with orthoganol orientation 0 & 90 degrees block all light. The last solution tests x = 5 + (1:5)*22.5; which is a filter set with two orthogonal filters. How come not all light is blocked for that case?
@margreet: that is a good question, indeed. The following minutePhysics video talks about that: "Bell's Theorem: The Quantum Venn Diagram Paradox" https://www.youtube.com/watch?v=zcqZHYo7ONs
Thank you @Alfonso for the link it really helped me understand a bit more on the topic of stacked filters.
Could some one help point me in the direction to understand the last 2 test cases?
I currently have a solution that is correct for all the test cases except the last 2. Is there something special for these cases that would be causing me to be not quite converge. I am currently not meeting the tolerance, the difference of my result and the assertion test are:
9. 0.0019000
10. 0.056585
Thanks in advance.
@Alfonsi: thanks.
[0,45,90] is also a nice test (instead of twice the randi solution)
@Nabor: also have a look at the law of Malus (http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polcross.html), mind the difference between amplitude and intensity.
besides law of Malus (http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polcross.html), also have a look at what happens to a third polarizing filter (http://alienryderflex.com/polarizer/)
Tip: In this problem, the first polarizer is always equated to 0.5 (since I_0 = 1 and the light comes from all directions): we should calculate the integral of the function cos(x)^2 from 0 to 2pi divided by 2pi (Mean Value Theorem). The remainder is Malus's Law.
This is actually a problem of physics, rather than programming.