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Not a homwork problem, Fresnel Equations

  1. Oct 30, 2016 #1
    1. The problem statement, all variables and given/known data
    I was just curious, I know you can derive the critical angle using Snell's law..but could you use it using the Fresnel Equations of reflection, both of them?

    2. Relevant equations
    |r|=1 internal reflection of light
    r(tm)=(n1cos(theta-i)-n2cos(theta-t))/(n1cos(theta-i)+n2cos(theta-t))
    r(te)=(n2cos(theta-t)-n1cos(theta-t))/(n1cos(theta-t)+n2cos(theta-i))
    I'm putting theta-t and theta-i to denote incident angle and transmittance angle

    supposed to arrive at crit angle=arcsin(n2/n1)

    3. The attempt at a solution
    r(te)=
    [(n2cos(theta-t)-n1cos(theta-t))/(n1cos(theta-t)+n2cos(theta-i))]^2=1


    r(tm)=
    [(n1cos(theta-i)-n2cos(theta-t))/(n1cos(theta-i)+n2cos(theta-t))]^2=1
     
  2. jcsd
  3. Oct 30, 2016 #2

    Charles Link

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    Homework Helper

    ## R=1 ## at the critical angle because ## cos(\theta_t) =0 ## since ## \theta_t=90 \, degrees ##. I think it is necessary to use Snell's law to compute the critical angle ## \theta_i=\theta_c ##. For ## \theta_i ## greater than the critical angle, ## \theta_t ## does not exist. ## \\ ## Note: In your very first equation of part 3, I think the first "theta-t" should be a "theta-i". ## \\ ## Additional note: To get Latex, you need to put " ## " on both sides of the expression.
     
    Last edited: Oct 30, 2016
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