## Friday, June 02, 2023

### BeeDee Gave Me A Gentle Reminder To Get Back On Topic

wikipedia  |  In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater intensity (constructive interference) or lower amplitude (destructive interference) if the two waves are in phase or out of phase, respectively. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves as well as in loudspeakers as electrical waves.

The word interference is derived from the Latin words inter which means "between" and fere which means "hit or strike", and was coined by Thomas Young in 1801.[1][2][3]

The principle of superposition of waves states that when two or more propagating waves of the same type are incident on the same point, the resultant amplitude at that point is equal to the vector sum of the amplitudes of the individual waves.[4] If a crest of a wave meets a crest of another wave of the same frequency at the same point, then the amplitude is the sum of the individual amplitudes—this is constructive interference. If a crest of one wave meets a trough of another wave, then the amplitude is equal to the difference in the individual amplitudes—this is known as destructive interference. In ideal mediums (water, air are almost ideal) energy is always conserved, at points of destructive interference energy is stored in the elasticity of the medium. For example when we drop 2 pebbles in a pond we see a pattern but eventually waves continue and only when they reach the shore is energy absorbed away from the medium.

Constructive interference occurs when the phase difference between the waves is an even multiple of π (180°), whereas destructive interference occurs when the difference is an odd multiple of π. If the difference between the phases is intermediate between these two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum values.

Consider, for example, what happens when two identical stones are dropped into a still pool of water at different locations. Each stone generates a circular wave propagating outwards from the point where the stone was dropped. When the two waves overlap, the net displacement at a particular point is the sum of the displacements of the individual waves. At some points, these will be in phase, and will produce a maximum displacement. In other places, the waves will be in anti-phase, and there will be no net displacement at these points. Thus, parts of the surface will be stationary—these are seen in the figure above and to the right as stationary blue-green lines radiating from the centre.

Interference of light is a unique phenomenon in that we can never observe superposition of the EM field directly as we can for example in water. Superposition in the EM field is an assumed and necessary requirement, fundamentally 2 light beam pass through each other and continue on their respective paths. Light can be explained classically by the superposition of waves, however a deeper understanding of light interference requires knowledge of wave-particle duality of light which is due to quantum mechanics. Prime examples of light interference are the famous double-slit experiment, laser speckle, anti-reflective coatings and interferometers. Traditionally the classical wave model is taught as a basis for understanding optical interference, based on the Huygens–Fresnel principle however an explanation based on the Feynman path integral exists which takes into account quantum mechanical considerations.