Could someone provide an equation for calculating frustrated internal reflection? Like for a partially reflective laser mirror or a beam splitter. I believe that it depends on the refractive indexes of a first medium and a third medium if a second medium separating the two (like a mirror) is thin enough that evanescent wave coupling allows light to be transmitted through to the third if it's in a certain angle range. However, I couldn't find an equation to calculate this. I found one for total internal reflection but not for this. I could use some help on this, or otherwise something that explains this. Thank you.

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    $\begingroup$ Try googline "Frustrated total internal reflection". I am not sure an equation is what you want. Probably more an explanation of what it is and what it is good for. See physics.ohio-state.edu/~dws/class/570/notes/p036.pdf $\endgroup$
    – mmesser314
    Nov 20, 2016 at 1:32
  • $\begingroup$ See this question. In my answer, I derive an equation for power transmitted by frustrated total internal reflexion $\endgroup$ Oct 10, 2017 at 0:25
  • $\begingroup$ This could also help : photonics.ethz.ch/fileadmin/user_upload/Courses/NanoOptics/… p.23 $\endgroup$
    – EigenDavid
    Feb 20, 2018 at 11:52
  • $\begingroup$ David, could you help me clarify something in the paper you linked? Are the angles theta_3 and theta_1 equal in figure 2.7? The equation provided above the picture doesn't allow for the calculation of theta_3 $\endgroup$
    – Francis L.
    Nov 2, 2018 at 22:34

1 Answer 1


Frustrated total reflection obviously means that the usual total reflection at a surface to a medium with lower refractive index $n$ becomes less than total because the thickness of the lower $n$ medium becomes comparable to the evanescent wave damping length penetrating the lower $n$ medium.

This can be calculated by using the Fresnel equations with multiple surfaces. See Fresnel equations


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