A PDF Download on Interference and Diffraction: The Phenomena that Reveal the Wave Nature of Light

We head back to the recording studio to study interference and diffraction of sound waves. We investigate qualitatively how diffraction affects sound waves of various frequencies. We also explore how constructive and destructive interference patterns are created and what that means for what we hear coming from a sound source.

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Solutions to Maxwell's equations at a semi-infinite plane and a double slit are used to construct lines of constant amplitude, constant phase and energy flow. The lines of energy flow show how the electromagnetic boundary conditions necessitate a particular undulation in the path of the light energy and that the consequent redistribution of energy corresponds with a diffraction or interference pattern. This interpretation complements the interpretation in terms of the interaction of secondary wavelets due to Huygens.

Generally the interaction of incident light with the slits is explained by using Fresnel's theory of diffraction which demands that diffraction patterns/effects are generated due to superposition of Huygens secondary wavelets starting from every point of space located in the aperture. Here it may be noted that Huygens proposed his theory based on the existence of aether (the material supposed to fill the region of the universe above the terrestrial sphere) so that aether particles were responsible for generation of secondary wavelets. But existence of aether has been ruled out long ago through Michelson-Morley experiment [12]. Thus, again interest is gaining towards Young's theory of diffraction [13-18]. According to Young's theory of boundary diffraction wave, diffraction patterns are a result of interference of a direct wave unaffected by the diffracting aperture and another wave generated by interaction of incident light with the edges of the diffracting apertures [19]. Recently the theory has been successfully applied to explain various phenomena [20-23].

To describe how the quasiparticle interference measured at the surface layer relates to the bulk electronic structure requires addressing what the correct mapping between surface and bulk reciprocal spaces for its description is. Figure 1b illustrates this point for a rocksalt crystal structure: the primitive cell in the bulk cannot be used to describe a (001) surface. The minimal unit cell required to describe the surface as well as its electronic structure is thus larger. As a consequence, the surface BZ in which the electronic structure is measured by QPI is not just a cut or projection of the bulk BZ, but a folded version of it.

Such a characteristic difference between these two orbital sets and their contribution to the QPI reveals a fundamental distinction in the orbital character of the underlying scattering processes. To further explain how they respond to the bias variation, we also need to consider the energetic alignment of the impurity states and their relative coupling to the host energy bands.

An opaque body placed midway between a screen and a point source casts an intricate shadow made up of bright and dark regions quite unlike anything one might expect from the rules of geometric optics. The effect is a general characteristic of wave phenomena occurring whenever a portion of a wavefront from either a mechanical wave or from an electromagnetic wave is obstructed in some way. If in the course of encountering an obstacle, either transparent or opaque, a region of the wavefront is altered in amplitude or phase, diffraction will occur. The various segments of the wavefront that propagate beyond the obstacle interfere to cause the particular energy-density distribution referred to as the diffraction pattern.

In the general sense, both interference and diffraction refer to effects resulting from the superposition of two or more waves at a given point in space. There is no essential mathematical difference between interference and diffraction. However, in more restricted usage, interference is used to describe effects that result from the superposition of two or more wave trains (as in the case of water-layer reverberations of seismic waves), and diffraction is used to describe interference effects caused by the presence of an aperture or an obstacle in the path of a wave (as in the bending of seismic waves around obstacles). In modern usage, the terms interference and diffraction still refer more or less to the types of problems studied by Hooke and Grimaldi, respectively.

This resource includes the following topics: microwaves (mw), interference: the difference between waves and bullets, demonstration: microwave interference, interference - phase shift, microwave interference, prs question: interference, two transmitters, two in-phase sources: geometry, interference for two sources in phase, the light equivalent: two slits, young?s double-slit experiment, prs question: double slit path difference, lecture demonstration: double slit, diffraction, single-slit diffraction, intensity distribution, prs question: two slits with width, babinet?s principle, experiment 13.

Newton's rings is a phenomenon in which an interference pattern is created by the reflection of light between two surfaces, typically a spherical surface and an adjacent touching flat surface. It is named after Isaac Newton, who investigated the effect in 1666. When viewed with monochromatic light, Newton's rings appear as a series of concentric, alternating bright and dark rings centered at the point of contact between the two surfaces. When viewed with white light, it forms a concentric ring pattern of rainbow colors because the different wavelengths of light interfere at different thicknesses of the air layer between the surfaces.

(Fig. 4a): In areas where the path length difference between the two rays is equal to an odd multiple of half a wavelength (λ/2) of the light waves, the reflected waves will be in phase, so the "troughs" and "peaks" of the waves coincide. Therefore, the waves will reinforce (add) and the resulting reflected light intensity will be greater. As a result, a bright area will be observed there.

(Fig. 4b): At other locations, where the path length difference is equal to an even multiple of a half-wavelength, the reflected waves will be 180 out of phase, so a "trough" of one wave coincides with a "peak" of the other wave. Therefore, the waves will cancel (subtract) and the resulting light intensity will be weaker or zero. As a result, a dark area will be observed there. Because of the 180 phase reversal due to reflection of the bottom ray, the center where the two pieces touch is dark. This interference results in a pattern of bright and dark lines or bands called "interference fringes" being observed on the surface. These are similar to contour lines on maps, revealing differences in the thickness of the air gap. The gap between the surfaces is constant along a fringe. The path length difference between two adjacent bright or dark fringes is one wavelength λ of the light, so the difference in the gap between the surfaces is one-half wavelength. Since the wavelength of light is so small, this technique can measure very small departures from flatness. For example, the wavelength of red light is about 700 nm, so using red light the difference in height between two fringes is half that, or 350 nm, about 1/100 the diameter of a human hair. Since the gap between the glasses increases radially from the center, the interference fringes form concentric rings. For glass surfaces that are not spherical, the fringes will not be rings but will have other shapes.

The phenomenon of Newton's rings is explained on the same basis as thin-film interference, including effects such as "rainbows" seen in thin films of oil on water or in soap bubbles. The difference is that here the "thin film" is a thin layer of air. 2ff7e9595c