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Frequency and other properties from E-field

  1. Feb 9, 2010 #1
    1. The problem statement, all variables and given/known data

    A plane, harmonic, linearly polarized light wave has an electric field intensity given by
    [tex]{E}_z[/tex] = [tex]{E}_0[/tex] cos pi*[tex]10^{15}[/tex]*(t - x/.65c)

    while traveling in a piece of glass. Find
    (a) The frequency of the light.
    (b) Its wavelength.
    (c) The index of refraction of the glass.

    3. The attempt at a solution

    I'm still confused about the argument of the cosine, but I assume that what was within the parenthesis was the real argument. Under this assumption, it fits the form (kx-wt) with some tweaking. The angular frequency w will give me the frequency. I'm pretty sure I need the velocity in order to get the wavelength, and am unsure as to how to find it. Once I get the velocity it will be easy to find the index of refraction.

    The problems I ran into:
    w=-1 in this case, and so 1/2pi gives me the frequency.
    finding velocity of the wave: I used [tex]w^{2}[/tex]/[tex]k^{2}[/tex] = v, however this gives me a value much larger than the speed of light.

    Should I just distribute the stuff before the argument? I've never seen a cosine like that. I think that it would be better if it was cos(pi*10^15*(t-x/.65c)) and am confused as to why they didn't do that if that is really what they meant.

    Thanks for any help you can provide!
  2. jcsd
  3. Feb 9, 2010 #2
    Is there a 2 in front of th e"pi" in the formula?

    The wave is in the form
    [tex]E_z=E_0 cos(\omega t -kx) =E_0 cos(2\pi f t -\frac{2\pi}{\lambda}x) = [/tex]
    [tex]=E_0 \cos2\pi f ( t -\frac{x}{v}) [/tex]
    where I used
    [tex]\omega=2\pi f, k=\frac{2\pi}{\lambda}, \lambda=c/f[/tex]
    So v=0.6 c, f=10^15 Hz
    Last edited: Feb 10, 2010
  4. Feb 9, 2010 #3
    Nope, it's just pi. Thank you so much!!! I didn't know what k equaled. Thanksthanksthanks.
  5. Feb 10, 2010 #4
    Then 2f =10^15.
  6. Feb 10, 2010 #5


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    Staff: Mentor

    Please do not post solutions to homework questions.
  7. Feb 10, 2010 #6
    Sorry if I posted more that I was supposed to.
    I am aware that the forum policy requires that the poster shows some work and ideas.
    I considered that in this case he showed some start and he is only confused about the math manipulation of the formula.
    I'll be more careful in the future.
  8. Mar 19, 2010 #7
    What is K and lambda, can anyone explain please
  9. Mar 19, 2010 #8


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