Reflection phase change

A phase change sometimes occurs when a wave is reflected.^[1][2] Such reflections occur for many types of wave, including light waves, sound waves, and waves on strings.

Optics

Light waves change phase by 180° when they reflect from the surface of a medium with higher refractive index than that of the medium in which they are travelling.^[1] A light wave travelling in air that is reflected by a glass barrier will undergo a 180° phase change, while light travelling in glass will not undergo a phase change if it is reflected by a boundary with air. For this reason, optical boundaries are normally specified as an ordered pair (air-glass, glass-air); indicating which material the light is moving out of, and in to, respectively.

"Phase" here is the phase of the electric field oscillations, not the magnetic field oscillations.^[3] Also, this is referring to near-normal incidence—for p-polarized light reflecting off glass at glancing angle, beyond the Brewster angle, the phase change is 0°.

The phase changes that take place upon reflection play an important part in thin film interference.

Sound waves

Sound waves in air, in a tube

Sound waves in a solid experience a phase reversal (a 180° change) when they reflect from a boundary with air.^[2] Sound waves in air do not experience a phase change when they reflect from a solid, but they do exhibit a 180° change when reflecting from a region with lower acoustic impedance. An example of this is when a sound wave in a hollow tube encounters the open end of the tube. The phase change on reflection is important in the physics of wind instruments.

Strings

Standing waves on a string

A wave on a string experiences a 180° phase change when it reflects from a point where the string is fixed.^[2] Reflections from the free end of a string exhibit no phase change. The phase change when reflecting from a fixed point contributes to the formation of standing waves on strings, which produce the sound from stringed instruments.

Electrical transmission lines

Reflections of signals on conducting lines can exhibit a phase change from the incident signal. The voltage wave reflection on a line terminated with a short circuit is 180° phase shifted. This is analogous (by the mobility analogy) to a string where the end is fixed in position, or a sound wave in a tube with a blocked off end. The current wave, on the other hand, is not phase shifted. A transmission line terminated with an open circuit is the dual case; the voltage wave is shifted by 0° and the current wave is shifted by 180°. In both cases the full amplitude of the wave is reflected.

A transmission line terminated with a pure capacitance or inductance will also give rise to a phase shifted wave at full amplitude. The voltage phase shift is given by

$\varphi = 2 \tan ^{-1} {Z_0 \over X}$^[4]

where

Z₀ is the characteristic impedance of the line

X is the susceptance of the inductance or capacitance, given respectively by ωL or −1/ωC

L and C are, respectively, inductance and capacitance, and

ω is the angular frequency.

The phase shift will be between 0 and 180° and will be respectively positive or negative for inductors and capacitors. The phase shift will be exactly 90° when X = Z₀.

For the general case when the line is terminated with some arbitrary impedance, Z, the reflected wave is generally less than the incident wave. The full expression for phase shift needs to be used,

$\varphi = \tan ^{-1} \left ( \frac {2|Z| \sin (\angle Z) Z_0}{Z^2 - Z_0^2} \right )$^[5]

This expression assumes the characteristic impedance is purely resistive.

References

1. Nave, C.R. "Reflection Phase Change". Hyperphysics. Georgia State University. Retrieved 2016-03-28.
2. Nave, C.R. "Reflection of Sound". Hyperphysics. Georgia State University. Retrieved 2016-03-28.
3. Byrnes, Steven J. (2016). "Multilayer optical calculations". arXiv:1603.02720. Appendix A
4. B. I. Bleaney, Brebis Bleaney, Electricity and Magnetism, volume 1, p. 275, Oxford University Press, 2013 ISBN 0199645426.
5. Bleaney &Bleaney, p. 273