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April 6th, 2010, 08:57 AM   #1
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I need help with this calculation

Hello this is the equation of fabri-perot interferometer.... I think I should use eulero's formulas but I'm not able to find the final result.

The books starts with this relation Ecav = A/(1-R*exp(-j2kL))
Then, in order to find the intensity of field, it does (Ecav)^2 writing that is ugual to = I / (1 + R^2 - 4*R*cos(2kL)) = I/[(1-R)^2 +4*R*sin^2(kL)] .... where I = A^2.
What are the passages?
Please help me
diegosened is offline  
 
April 6th, 2010, 11:42 AM   #2
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Re: I need help with this calculation

That looks like a pretty hairy problem...I can tell they want you to show the steps of squaring that nastly looking denominator to make it look like what you are trying to get.

Whenever you have exponents changing into sin and cos, then the exponents must be complex numbers.

e^(ix) = cos x + (i)sin x, for all real values. This can be represented in the generic complex number form a + bi, where a = cos x and b=sinx.

Notice that some of the exponents in the first equ. end up with cos... I see that there is no sin to go along with the cos, therefore
in your case, (i)sin x= 0 for some reason. You would also have to relate R in terms of e (can't remember it, but there is an algebra rule for this).

I'm definitely not sure how to guide you, but I thought it might help. Someone else may be able to take it from here or shoot me down

Make sure you typed it in right as well.
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April 7th, 2010, 05:53 AM   #3
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The usual name is "Fabry–Pérot interferometer". The equations have at least one error (in copying, presumably), since by elementary trigonometry one has 1 + R˛ - 2R*cos(2kL) = 1 + R˛ - 2R(1 - 2sin˛(kL)) = (1 - R)˛ + 4R*sin˛(kL), so the coefficient 4 in the denominator of the expression initially given for (Ecav)˛ should have been 2.

Unfortunately, I don't see how the book was progressing from Ecav = A/(1-R*exp(-j2kL)), and I can't find sufficiently similar theory using Google to let me work out what the book must be doing. How does the book obtain its equation for Ecav?
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