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.

  • Beyond the critical angle, refraction out of the medium is impossible. – probably_someone Sep 14 at 13:15
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    Because the equations require it. – Jon Custer Sep 14 at 13:15
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    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 $k$. – Emilio Pisanty Sep 14 at 13:19

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.

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

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