Impedance Matching Using Quarter Wavelength Medium

Light wave falling on a glass surface suffers reflection
because of impedance mismatch. If Z_g = 250 Ohms (typical), the fraction
of power reflection is

[(Z_g - Z_0)/(Z_g + Z_0)]^2 = [(250-377)/(250+377)]^2 = 0.04 =
4 %,
where Z_0 = sqrt(mu_0/epsilon_0) = 377 Ohms is the impedance of free
sapce.

The first animation shows reflection and transmission
of sinusoidal wave of unit amplitude at a boundary between Z_1 = 1 and
Z_2 = 1/4. Because of reflection, (partial) standing waves are formed.
Power transfer is evidently not very smooth.

If a third medium having an impedance Z_3 = sqrt(Z_1*Z_2)
(geometric mean of Z_1 and Z_2) and thickness of quarter wavelength (wavelength
in the medium to be inserted) is inserted, wave reflection can be avoided
entirely. The second animation shows this case. The red portion in the
waveform corresponds to the inserted quarter wavelength medium. Note that
there are no standing waves (no reflection) and all of the incident wave
energy is transferred to the medium 2.

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