Phenomenon of total internal reflection

The total internal reflection is described, as a rule, by the Fresnel formulas (derived from the basic equations of the classical electrodynamics on condition that the wave vectors of the incident and refracted waves are real). In the case of the total internal reflection, this condition is not fulfilled. In this connection, the formal use of the Fresnel formulas with complex wavevectors leads to correct final results but during the formulas derivation, the geometrical meaning of the product of the wavevector and a value of the refraction angle cosine as a projection of the vector onto the considered direction is lost. This does not allow us to believe that the obtained results are valid. The required results are derived without using complex values of trigonometric functions and without violations of the geometrical sense of the performed calculations, which fully substantiated the physical-mathematical model of total internal reflection. It is shown that during the electromagnetic wave period at the interface between two dielectrics, the balance of electromagnetic energy fluxes perpendicular to the interface surface is fulfilled at each moment of time.

References

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