Why does reflectivity suddenly change around critical angle? For example, consider the situation when incident light travel in dielectrics A and go in to dielectric B. Assume the dielectric constant $\epsilon_A=2.25$ and $\epsilon_B=1.25$. Total internal reflection occur when incident angle is around 46,7 degree. I'm wondering why reflectivity arise so sharply and suddenly? The reflectiviy is almost 0 when incident angle < 30 degree. And suddenly arise around critical angle. This is weird.

P.S Sorry. I only focus on TM wave unconsciously.

  • $\begingroup$ Beyond the critical angle, refraction out of the medium is impossible. $\endgroup$ Sep 14, 2018 at 13:15
  • 1
    $\begingroup$ Because the equations require it. $\endgroup$
    – Jon Custer
    Sep 14, 2018 at 13:15
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    $\begingroup$ It doesn't. To first order in the difference between the incidence angle $\theta_i$ and the critical angle $\theta_c$, the reflectivity increases linearly, $R \approx k |\theta_i-\theta_c|$ for some constant $k$. $\endgroup$ Sep 14, 2018 at 13:19

1 Answer 1


you can see the Fresnel coefficients for reflectivity and phase-change behavior below for dense to light-medium propagation that cause TIR (total internal reflection): TE polarization: enter image description here TM polarization: enter image description here

As a mathematical answer, near critical angle phase matching forces boundary to have to mirror-like behavior so reflection has to jumps to 1.

  • $\begingroup$ Thank you for answering. What is theta B in the phase changing graph of TM wave? $\endgroup$
    – Koreyuki
    Sep 15, 2018 at 5:18
  • $\begingroup$ it's Brewster angle. in this angle, TM mode gets removed from reflection. $\endgroup$ Sep 15, 2018 at 8:26

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