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Need help solving an equation

  1. Mar 10, 2009 #1
    1. The problem statement, all variables and given/known data
    They ask me to solve the characteristic equation of a fiber optics glass. The equations I need to solve (separately) are:


    2. Relevant equations

    solve(2000000*Pi*sin(x)-2*arctan(.6666666667*(2.25*cos(x)^2-2.1904)^.5/sin(x)) = Pi, x):

    solve(2000000*Pi*sin(x)-2*arctan(.6666666667*(2.25*cos(x)^2-2.1904)^.5/sin(x)) = 0, x)

    That's how I tried to solve them in MAPLE.



    3. The attempt at a solution

    Maple is not giving me answers, I used my TI and it gave me some results but they were extremely similar and I don't think they are the real ones. How can I solve for the propagation angle x?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 11, 2009 #2

    Galileo

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    The expressions on the left look the same. How can the same expression be both Pi and 0 at the same time?

    And please try using tex or at least 2*10^6 and 2/3 instead of 2000000 and .6666666667
    More people may decide to help if you put effort in presenting your problem neatly.
     
  4. Mar 11, 2009 #3
    Well I'm Maple I used fractions, when I copy pasted them here they appeared as decimals. The equations are supposed to be different modes or propagation, so I need to solve for each angle individually.

    The equation (general) is:

    m*PI=2*PI*d/lambda -2 arctan(SQRT((n12Cos(x))^2 -n2^2)/n1*sin(x))

    Where N1=1.5
    n2=1.48
    lambda=1(10^-6)
    d=(3.192(10^-6)
    And m=0,1,2,3...... Where I only need the first (0 and 1)
     
  5. Mar 12, 2009 #4

    Galileo

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    If you define
    [tex]\alpha^2 =1-(n_2/n_1)^2[/tex]
    and let
    [tex]y=sin(x)/\alpha[/tex], then I think you can write the arctan as:
    [tex]arctan\left(\frac{\sqrt{1-y^2}}{y}\right)[/tex]

    Try some trig identities from there.
     
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