General Formula of Wave

The phenomena of interference and diffraction of light cannot be understood without introducing the wave concept. In fact, the wave properties of light were established precisely from these phenomena. Here, we will introduce the essential aspects of a propagating wave and the formulae needed to explain the optical effects described throughout this section. Let us first recall the one dimensional wave formula that we met for the first time during the physics classes in senior high school. 

Where A, A, v, t, and 0are the amplitude, wavelength, velocity, time, and phase, respectively. This equation describes the propagation of a cosine curve [A cos(2jt/A)x] along the x-axis. Introducing the frequency v = v/A, the general formula of wave can be written as  

If the phase difference 0 is neglected, Eq. (1.2) becomes Eq. (1.3) where we introduce the wave number k = 2JilX and the angular frequency w = 2jiv. This leads us to the simplest example of a three dimensional wave, the plane wave. 

A plane wave exists at a given time, when all the surfaces of constant phase form a set of planes, each generally perpendicular to the propagation direction. Under these conditions Eq. (1.3) becomes Eq. (1.4), defining the unit vector / in the direction perpendicular to the wave plane, that is, in the direction of the wave propagation. 

Assuming that the wave number vector k = k/, Eq. (1.4) becomes the general formula of a plane wave. As defined, the wave number vector k indicates that the direction of the vector k is the propagation direction of the plane wave. 

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Typically, books on optics explain the principles of the various optical experiments and instrumentation.1 41 The first section of this book, while dedicated to optics will be limited to a description of the general formula of wave and the phenomena of refraction, reflection, interference, diffraction, and polarization. An overview of the fundamentals of optics presented in this section is shown in Table 1.1. Most books on optics begin the explanation of the wave by stating Maxwell s equations, and this is most appropriate, no doubt. Here we tried to follow a different approach in order to set the stage for the description of the radiation theory in the next section. However in explaining optical phenomena, it is impossible to avoid the concept of wave. So, in this section, although reluctant to do so, we introduce the equation of the three-dimensional plane wave. 

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