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Homework Help: Phase shift arising from reflections of metal

  1. Jan 2, 2014 #1
    Dear All,

    I have a question about the optical properties of light in a metal.
    I need to solve a problem.
    1. The problem statement, all variables and given/known data
    a] Why is the phase shift in a metal neither 0 or pi?
    b] And calculate the phase shift of gold with a wavelength of 514 nm?
    n_real=0,5 and n_imaginary=1,85, R=0,647
    For problem b I can't find the proper equation to calculate the phase shift.

    I already read Optics of Hecht, but I can't find it in Hecht. They mention it on page 131 but they do not explain it.

    Thanks in advance!
  2. jcsd
  3. Jan 2, 2014 #2
    Hey! Let's be sure of what's going on, is the phase shift in the magnetic or the electric field?
  4. Jan 2, 2014 #3
  5. Jan 2, 2014 #4
    I think the phase shift is in an electric field.
    But that isn't mentioned in this problem. I only have a graph of the refractive index of gold with the real and imaginary part of the refractive index.
  6. Jan 2, 2014 #5
    Thanks for the link.
    I will take a look.
  7. Jan 3, 2014 #6


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    Was the question about the phase shift of the reflected light wave with respect to the phase of the incident wave?

    You need to know the amplitude reflection coefficient r in terms of the refractive index N. N is a complex number for metals, it has both real and imaginary components, which were given. So r is also a complex number. Find its phase.

    Last edited: Jan 3, 2014
  8. Jan 3, 2014 #7
    Yes, I need to calculate the phase shift of the relfected wave with respect to the incident wave.
    But the direction of the electric field with respect to the plane of incidence isn't given. So I don't which component I need to have of the amplitude reflection coëfficiënt. I already calculated the reflectance and the relation between the reflection coëfficiënt and the reflectance is R=r^2. I will take a look at the equations of hecht.
    And for my first question there have to be a more theoretical explanation for why the phase shift in a metal isn't 0 or pi?
    Thanks for the advice!
  9. Jan 3, 2014 #8


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    What phase shift do you speak about inside the metal? Phase shift of what with respect to what? And why should it be pi or zero?

  10. Jan 4, 2014 #9
    I mean the phase shift due to reflections. So the phase shift of the reflective wave with respect to the incident wave.
    In general for a dielectric if the component of the electric field normal to the plane of incidence undergoes a phase of pi upon reflection when the incident medium has a lower refractive index than the transmitting medium. Otherwise the phase shift is 0.
    But the phase shift due to reflections in a metal occur in both components(parallel and perpendicular). And in Hecht they mention it on page 131, "These phase shifts are generally neither 0 or pi, with a notable exception at
    teta_incidence=90 degrees".
  11. Jan 4, 2014 #10


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    So it is the phase upon reflection, not in the metal as you wrote.
    You certainly heard about Fresnel reflection coefficients, did you? And you learnt about Snell's Law and know what refraction index is.

    They can be derived from the Maxwell equations for the electric and magnetic fields, and also from the boundary conditions for the fields at the interface of two media. The components of both fields, parallel with the interface are the same at both sides of the interface, in both media.

    If the light arrives from a medium of refractive index n1 and incident normally onto a medium of refractive index n2, the ratio of the amplitude of the reflected wave to that of the incident wave is


    In case of real refractive indices, r is positive if n1>n2 and negative if n1<n2. In the first case, the reflected wave is in phase with the incident one (phase shift is zero), in the second case the reflected wave is in the opposite phase its phase shift is pi.

    The refractive index of the metals is a complex number, with both real and imaginary parts. The reflection coefficient is also a complex number, with magnitude and phase. The phase of r is equal to the phase shift between the reflected and incident waves.
    The refractive index of gold was given as N=0.5+1.85 i. The reflection coefficient of the air-gold interface is

    The imaginary part of the refractive index in the metals is consequence of their conductance.
    You might find this place useful http://farside.ph.utexas.edu/teaching/jk1/lectures/node58.html

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