Complete destructive interference is obtained (resulting wave vanishes) when the maxima of one of the component waves coincide with the minima of the other, i.e., when the two waves are in phase opposition. The wave drawn at the bottom (bold line) shows the result of the interference, which has maximum amplitude when interfering waves overlap, i.e. Possible states of interference of two waves shown at the top, having identical amplitude and frequency. For an easy mathematical treatment to keep track of the relations between phases of the wave components, these terms are usually expressed in an exponential notation, where the exponential imaginary unit i means a phase difference of + \(\pi\)/ 2. We speak of waves being in phase if the difference between the phases of the components is an integer multiple of 2\(\pi\), and we say that the waves are in opposition of phase if that difference is an odd multiple of \(\pi\). T and r are, respectively, the time and the position vector with which we measure the disturbance, and \(\alpha\)is the original phase differencerelative to the other components of the wave. In the full electromagnetic spectrum (ie in the distribution of electromagnetic wavelengths) the hard X-rays (the high energy ones) are located around a wavelength of 1 Angstrom in vacuum (for Cu the average wavelength is 1.5418 Angstrom and for Mo it's 0.7107 Angstrom), while visible light has a wavelength in the range of 4000 to 7000 Angstrom. ν, which measures the number of repetitions per radian (180/π degrees) of the cycle. We give the name pulse to the magnitude given by: 2\(\pi\). Νis the frequency (the inverse of the period), that is, the number of repetitions (or cycles) per unit of time. Thus, K is the number of repetitions per unit of length. In the expression of the phase ( \(\phi\)), K is the so-called wave vectorwhich gives the sense of progress of the wave ( the ray), and is considered with an amplitude 1/ λ. The intensity is a measure of the energy flow per unit of time and per unit of area of the wavefront (spherical or flat, depending on the type of wave).Ī wave is a regular phenomenon, ie it repeats exactly in time (with a period T) and space (with a period λ, the wavelength), so that λ = ν. The intensity of an undulatory disturbance, at any point of the wave, is proportional to the square of the disturbance value at that point, and if it is expressed in terms of complex exponentials, this is equivalent to the product of the disturbance by its complex conjugate. The solutions to this equation are usually combinations of trigonometric terms, each of them characterized by: 1) an amplitude ( A), which measures the maximum (or minimum) of the disturbance with respect to an equilibrium value, and 2) a phase \(\phi\): Undulatory phenomena (waves) propagate at a certain speed ( v) and can be modeled to meet the so-called wave equation, scalar or vectorial, depending on the nature of the disturbance. Transverse wave propagation of vibrating longitudinal and circular movementsĪnimations originally taken from Waves are usually represented graphically by a sinusoidal function (as shown at right), in which we can determine some general parameters that define it. However, to describe the phenomenon, it is advisable to first introduce some physical models that (as all models) do not fully explain reality (as they are an idealization of it), but can be used to help understand the phenomenon.Ī wave is an undulatory phenomenon (a disturbance) that propagates through space and time, and is regularly repeated. X-ray diffraction is the physical phenomenon that expresses the fundamental interaction between X-rays and crystals (ordered matter). Depending on the rotation of the polarizer, one of components of the incident beam (coming from the right) is filtered Animations originally taken from Right: Polarization of light passing through a polarizer. Depending on the wavelength (color) of the incident beam (coming from the left), the angle of refraction varies, ie: it is scattered TIR = "Total Internal Reflection"Ĭenter: Refraction of light after passing through a glass prism. Left: Reflection and refraction of light in the interface between glass with a refractive index 1.5 and air with a refractive index 1.0. In the context of this chapter, you will also be invited to visit these sections.Įlectromagnetic radiations (such as visible light) can interact among themselves and with matter, giving rise to a multitude of phenomena such as reflection, refraction, scattering, polarization.
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