Fresnel’s equations explain the phenomenon of total internal reflection (TIR) by showing how the transmission and reflection coefficients behave when light travels from a denser medium (higher refractive index) to a rarer medium (lower refractive index) at increasing angles of incidence.
As the angle of incidence increases, the amount of reflected light increases, and the transmitted light bends further away from the normal. At a specific angle known as the critical angle, the transmitted light travels exactly along the boundary between the two media. According to Fresnel’s equations, beyond this angle, the transmission coefficient drops to zero — meaning no light is transmitted into the second medium.
Instead, all of the light is reflected back into the denser medium, and this is called total internal reflection. Fresnel’s equations confirm this by yielding a reflection coefficient of 100%, indicating that complete reflection occurs.
Although no real energy passes into the rarer medium, Fresnel’s equations also predict the presence of an evanescent wave just beyond the interface. This wave doesn’t carry energy away but decays exponentially into the rarer medium.
Thus, Fresnel’s equations provide the mathematical foundation for understanding how and why TIR occurs, based on the refractive indices and the angle of incidence.