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Studying for an exam and came across this question that appear on a previous paper. I thought I knew what I was doing here.
My approach was to get two simutaneous equations: one at when then incident ray first hits the medium, and next when the ray inside the medium hits the wall. Using geometry, we can deduce the incident angle during the second hit.
Now using Snells Law and critical angle, we can get two the two equations:
Substituting them, we get the 3rd equation. Now the problem I have now is that Er is unsolvable due to multiple asin, well.. at least i cant.
Is my method wrong? Did I make a mistake somewhere? This is an electromagnetic course so it may somehow involve some waveguide theory but I doubt it.
Any help is appreciated.
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Calculator solved for Er = 1.75.
I can't remember much about Snell's Law so I can't tell if your method is right.
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1.75 seems like a suitable answer. I still dont understand how to solve for it in the last equations though.
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I'm guessing you need some trig identity trickery which I've never been any good at.
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I got 3.482 for Er through a bunch of algebra.
get the inverse sines together then reverse them by taking the sine of each side.
From there it is just manipulating roots.
It took about 10 lines of math to solve. Try it and if you do not get 3.482 let me know and I will show you what i did.
edit: fuck it here
90=arcsin (sqrt(1/Er) + arcsin)[.866/sqrt(Er)]
take the sin of the arcsines to get rid of them and transfer it to the 90 on the other side.
sin(90) = [sqrt(1/Er)] + [.866/sqrt(Er)]
you can break up quotients of square roots into a fraction of square roots.
sin(90) = 1/(sqrt(Er) + .866/(sqrt(Er)
sin(90) = 1.866/SQrt(Er)
so Er = (1.866)^2 = 3.482
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using your notations
substituting first and second into the third we get Er=7/4
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On November 08 2009 04:03 15vs1 wrote:using your notations substituting first and second into the third we get Er=7/4
Or that. I must have ruined a step or did something illegal sorry 
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Aren't there enough hard problems in Emag that they don't have to throw geometrical optics at you too?
lol
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@op: I'm curious to what class this is. I see that electromagnetics is in my physics book, but the section seemed to be more closely related to the nature and propogation of light, and having nothing to do with electromagnetism.
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This class is an introductory course to the fundamentals of electromagnetic fields and waves. The course focuses on the theory of transmission lines, application of Maxwell's equations on wave properagation and plane waves, guiding structures (waveguides, slabguides), and radiation and antennas. I must agree that this question is fairly basic, as it only involves the simple concepts of light propogation (material for guiding structures). Thanks for the help guys.
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