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How does Band Gap and Refractive index relate to Wavelength?

  1. Nov 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Nobel prize for physics for blue laser diode using Gallium Nitride with band gap of 3.4 eV and a refractive index of 2.429.
    Explain how these parameters determine at what wavelength a Gallium Nitride semiconductor will laser at.

    2. Relevant equations
    [itex] E=\frac{hc}{\lambda} [/itex]
    Blue wavelength ## \approx 445 nm ##

    3. The attempt at a solution
    This equation will give the energy band gap wavelength. But how does the refractive index factor into this? I know it changes the velocity that the light moves through the medium.
    I found this article: https://www.quora.com/Whats-the-relation-between-bandgap-the-extinction-coefficient-and-the-index-of-refraction [Broken]
    But I'm still not sure how to answer the question.
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Nov 10, 2015 #2

    Simon Bridge

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    When light goes from one medium to another, it's wavelength changes.
     
  4. Nov 10, 2015 #3
    Using the equations I can get:
    [itex]E=\frac{hc}{\lambda}[/itex]
    [itex]\lambda=\frac{hc}{E}=\frac{1240~eV~nm}{3.4~eV} \approx 365~nm[/itex]
    The velocity of the light changes in the medium by [itex]v=\frac{c}{n}[/itex] replacing c in the above by the velocity in the medium gives
    [itex]\lambda=\frac{hv}{E}=\frac{hc}{nE}=\frac{1240~eV~nm}{(2.429)(3.4)~eV} \approx 150~nm[/itex]

    I don't see how this gives blue light of 445 nm.
     
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