Huygens construction

It follows that a family of trajectories may be obtained by constructing the normals to S, each one distinguished by its starting point x0. This description of particle motion is equivalent to the classic Huygens construction of elementary waves and their envelopes, with mechanical action taking the role of the phase in wave formalism. 

Fig. 6. Huygens construction for Cerenkov radiation showing geometric relationship of the electromagnetic wave and the motion of the particle ...

Huygens construction (Huygens principle) Every point on a wavefront may itself be regarded as a source of secondary waves. Thus, If the position of a wavefront at any instant is known, a simple constmction enables its position to be drawn at any subsequent time. The constmction was first used by Christiaan Huygens. 

If we allow monochromatic X-rays to pass through a crystal, each atom scatters a very small fraction of the incident wave and each becomes an emitter of secondary wavelets similar to the elements of the wave front in the Huygens construction for the propagation of light waves. The scattered wavelets reinforce in a given direction only if they are in phase. 

The distribution of light intensity in Figure 13 can be computed by application of Huygens principle which allows us to calculate the shape of a propagating wavefront provided the wavefront at an earlier instant is known. According to this principle, every point of a wavefront may be considered as a source of secondary waves (often called a wavelet) which spread out in all directions, i.e., all points on a wavefront are point sources for the production of spherical secondary wavelets. The new wave front 2 is then found by constructing a surface tangent to all the secondary wavelets as shown in... 

Figure 14a. Provided the wavefront is not interrupted, it moves out uniformly in a radial direction in accordance with the accepted notion of the rectilinear propagation of light. Suppose we now have a series of plane wavefronts incident on a slit with each successive wavefront being constructed from the envelope of secondary wavelets from the preceeding wave-front as shown in Figure 14b. If the width of the slit is small relative to the wavelength of light, then the portion of the wavefront at the slit may be considered as a single Huygens source radiating in all directions to produce...

Figure 14. (a) Schematic of Huygens Principle showing construction of a new wave front 2 from the preceeding wave front S 0>) plane wave front incident on a slit of width b (c) diffraction for case where b < (d)... 

The ray model of light is of limited usefulness. If we are to understand the fundamental processes involved in the formation of an image by a lens, we must consider the wave nature of light. The simplest form of the wave theory of light is based on a geometrical construction known as Huygens principle, which is usually stated as follows ... 

We will test the consistency of our solution by evaluating the diffraction field of a Gaussian beam from a reference plane defined by 2 = 0. We will use the Huygens-Fresnel construction (Born and Wolf, 1980, pp. 370-386), where we treat each point on the wavefront in the reference plane as the source point for a secondary wavefront of the form exp(tk r)/r and sum over all source points. If the diffracted field has the same functional form as the incident field, then we will have demonstrated that our solution is useful even in the presence of diffraction. 

We may write an integral expression for the Huygens-Fresnel construction that embodies these considerations as follows (Anan ev, 1992) ... 

The Cassim-Huygens spacecraft consists of two parts. Cassini is the orbiter, designed to attain orbit around Saturn, while Huygens is a space probe, designed to be released into the atmosphere of the planet s moon, Titan. NASA was responsible for the design and construction of the Cassini orbiter, while ESA was responsible for the Huygens probe. 

The very first attempt to construct a simplified kinematical description of a rotating spiral wave has been done in the classical paper of N. Wiener and A. Rosenblueth [33]. This description is based on the assumption that wave fronts propagate in a uniform and isotropic medium with equal velocity from any stimulated points into a region where the medium is in the rest state. Due to Huygens principle, successive wave fronts are perpendicular to a system of rays which represent the position which may be assumed by stretched cords starting from the stimulated point. The back of the wave is another curve of the same form, which follows the wave front at a fixed distance Ag measured along these rays. 

As a result, the angles cpt become complex. It is not expedient to undertake doubtful attempts to interpret the complex angles of incidence and refraction they should simply be considered as mathematical representations. The real angle of refraction of the beam in an absorbing medium is calculated on the basis of the Huygens-type construction via the effective (real) refractive index of the medium, which is not equal to either , or n, [9, 52]. 

Christiaan Huygens (1629-1695), Dutch mathematician, physicist and astronomer. Huygens was the first to construct a usefui penduium ciock. 

Rodrigue, C. M. (1999). Social Construction Of Technological Hazard Plutonium On Board The Cassini-Huygens Spacecraft (narrative for a proposal resubmitted to the Decision, Risk, and Management Science Program. National Science Foundation. January 14-... 

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