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Light Transmittance

  1. Apr 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Light of wavelength 5000 angstroms is incident normally on a series of two transparent plastic disks separated by a distance large compared with the wavelength. If the index o refraction of the disks is n=1.5, what fraction of the light is transmitted? Neglect absorption, internal multiple reflections, and interference effects.


    2. Relevant equations
    T = 1+R
    R = (n1-n2)/(n1+n2), where n is the index of refraction depending on the material

    Itotal is proportional to |Etotal|^2 = Etot * (Etot*) where (Etot*) is the complex conjugate.



    3. The attempt at a solution
    R = (1-1.5)/(1+1.5) = -0.20: going from air to the disk1
    Similar calculations for air to disk1, disk1 to air, air to disk2, and disk2 to air.

    I tried to calculate Etotal as:
    Etotal = -0.20*E0 + 0.20E0* e^(i*delta)
    delta = 2kd = 2*(2pi/lambda)*d where d = thickness of the disc
    but I am not given a thickness...

    Am I missing an equation I need to use? Approaching this from the wrong angle?
    Any advice would help! Thank you.
     
  2. jcsd
  3. Apr 2, 2009 #2
    You've got an error in your equation for reflectivity. It should be ((n1 - n2)/(n1 +n2))^2

    which gives me an r = 0.04 or 4%. So that means 96% of light incident on each plate will transmit through... work from there:)

    Also for this thickness won't matter too much but remember that there is an interface at the front and the back of the plate... so really you've got 4 interfaces to find the transmission through.
     
  4. Apr 2, 2009 #3
    Thanks lambduh! I think I figured it out. :)
     
  5. Jun 8, 2010 #4
    is not it R+T=1 giving T=1-R?
     
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