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Argh - De Broglie and the wave equation

  1. Jan 29, 2009 #1
    This isn't a homework question, but something which has been bugging me. I can't figure it out. Maybe it's late, but it's probably a very stupid question

    If light shines onto a denser medium, the light slows down in this medium right? If the light slows down, then by the wave equation, v = fλ, since f is constant, the wavelength must decrease.

    So why is it that de broglie's equation λ = h/mv implies a decrease in velocity would increase the wavelength?

    I'm so confused...
     
  2. jcsd
  3. Jan 29, 2009 #2
    v is in the denominator
     
  4. Jan 29, 2009 #3
    eh?

    de broglie: λ = h/mv
    wave equation: λ = v/f
     
  5. Jan 30, 2009 #4
    if anyone has any insight, could someone please help me? It's sort of urgent. I'm taking an exam tomorrow and this uncertainty is really making me nervous.
     
  6. Jan 30, 2009 #5
    Well... the de broglie equation is [tex]\lambda=\frac{h}{p}[/tex]. I don't really think that [tex]p=mv[/tex] works for light, because photons have no mass.

    I don't really know what I'm talking about though.
     
  7. Jan 30, 2009 #6
    The equation [tex]p=mv[/tex] does not hold for photons (light quanta) since they have no rest mass. For a photon, its energy, [tex]E=h \nu[/tex] (Planck's constant multiplied by frequency) is equal to its momentum multiplied by the speed of light in vacuum (Generally, for relativistic motion, [tex]E^{2}=(pc)^{2}+(mc^{2})^{2}[/tex]; Since m is zero in the case of the photon [tex]E=pc[/tex]. In this case, de Broglie's equation becomes

    [tex]\lambda = \frac{h}{p}=\frac{hc}{E}=\frac{hc}{h \nu}=\frac{c}{\nu} \Rightarrow \lambda \nu =c[/tex]

    Which is your original equation. Contradiction resolved.
     
  8. Jan 30, 2009 #7
    Thank you!!! So for electrons use debroglie, for light, use the other..
     
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