1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Snell's law with a complex refractive index

  1. Mar 14, 2008 #1
    hello everyone

    Consider extinction coefficient k, n becomes N=n-ik.
    the text book says NsinA=N'sinB still holds itself.

    But the sinB,for exmple, may be a complex number, i want to know
    how to get B?
    how to understand this situation, which is the refractive angle?
    the B's real part?
     
  2. jcsd
  3. Mar 14, 2008 #2

    pam

    User Avatar

    The electric field in a plane wave E~exp[i(kx-wt)], where k=w N/c.
    If N=n-ia, then E~exp[i(nw/c)x-wt)exp[-ax].
    This means n is still used by Snell.
    k is usually the wave number, so I used a for Im N.
     
  4. Mar 14, 2008 #3
    thank you
    and you mean that the refrective angle only depends on Re N--n
    and has nothing to do with Im N--a(using your signal), right?
     
  5. Mar 19, 2008 #4
    Why you write exp{i[(nw/c)x-wt]}*exp(-ax) and not exp{i[(nw/c)x-wt]}*exp(axw/c) ?
     
    Last edited: Mar 19, 2008
  6. Mar 20, 2008 #5

    pam

    User Avatar

    Sorry. That was a misprint. It should be axw/c.

    "and you mean that the refrective angle only depends on Re N--n"
    I'm afraid I oversimplified. The boundary conditions have to be applied at the interface, and the derivation done from scratch. It gets quite complicated.
     
  7. Mar 20, 2008 #6
    these days ,i thought further that maybe it's only a kind of appearance to describe the polirized light phase shift at the interface of different media.
    but i wonder which is the refractive angle if k ,ie absorption exist.
    for example. air/silicon,whose N is 1 and 4.4-0.8i, respectively.
    to Snell, 1*sin(AOI)=(4.4-0.8i)*sin(AOR),
    AOR will be a complex number, how to get the real AOR in experiments?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Snell's law with a complex refractive index
Loading...