Fresnel equations - 1.0 Basics - Optical Waveguides and Fibers

Derivation of Fresnel equation for TE modes. I also show you a derivation of a phase shift that light undergoes during reflection form the boundary of two media.

[@alipedram5720]

Best explanation ever!

[@avral4148]

I wonder why the sqrt(n1^2/n2^2*sin(alpha)-1) at 13:55 takes a negative value, is there something going wrong?

[@ayushigarewal]

thank you

[@theodorstaffas7348]

Thank you for your video. But I'm confused about why cos(beta) is imaginary when we are dealing with total internal reflection?

[@SalaScience]

In case of total internal reflection when the angle of incidence is greater than the critical angle there is no refracted beam. In such case there is no real solution to the Snell's law, but still there can be an imaginary solution. Using Pythagorean identity we can introduce an imaginary solution on cos(beta).

[@adrianjuandelgado6326]

Hello, thanks for this serie. One query: the boundary condition states the continuity of the normal component of B field (since \vec{n}_{ij} \dot (\vec{B}_{j}-\vec{B}_{i}) = 0, where \vec denotes vector notation and i,j denote medium i and j). However, in the derivation of the Fresnel coefficients you use the continuity of the parallel component of B field. Could you help me in the point that I am missing here?

[@SalaScience]

In optics you can assume that permeabilities of both media are equal to 1, so also the parallel component of the B field is continuous. I am not sure, but I think you can also try to derive the equation taking perpendicular component of the B field instead of parallel.

[@adrianjuandelgado6326]

@@SalaScience Ok, a lot of thanks!

[@pradumkumar6712]

Thank you sir 😘

[@lowfreqx]

These are very good series. Thank you very much for your work!

[@Rolfi-0815]

Were u got the B = n/c*E from? Best regards

[@SalaScience]

You can prove this for a plane wave. The ratio of the electric and magnetic field is a wave impedance Z. In a free space it is a vaccuum impedance Z_0.

[@nick45be]

Why in 8:13 you say that cos(beta) is complex? Shouldn't be cos(0°) in the total reflection case?

[@SalaScience]

Nope, cos(beta) is complex because in case of TIR (total internal reflection) there is no transmitted beam. Only for the critical angle you have beta=pi/2. When you have TIR the Snell's law still holds, but the angle becomes complex.