Red light of vacuum wavelength 650 nm is travelling in non-magnetic glass with refractive index nG = 1.50, then meets an interface with air at an angle of incidence of 75 degrees, and total internal reflection occurs. Calculate the tangential component of the wavevector kG in glass; state two conditions on the transmitted wavevector kA on the air side; and show that this leads to an evanescent wave with amplitude decaying exponentially away from the boundary. Calculate the distance over which the E-field amplitude drops by a factor of 1/e.

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Red light of vacuum wavelength 650 nm is travelling in non-magnetic glass with refractive
index nG = 1.50, then meets an interface with air at an angle of incidence of 75 degrees,
and total internal reflection occurs.
Calculate the tangential component of the wavevector kG in glass; state two conditions
on the transmitted wavevector kA on the air side; and show that this leads to an evanescent wave with amplitude decaying exponentially away from the boundary. Calculate the
distance over which the E-field amplitude drops by a factor of 1/e.

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