![]() In the original Recommendation of 1983, the symbol c was used for this purpose. ^ Current practice is to use c 0 to denote the speed of light in vacuum according to ISO 31.In addition, for a valid solution, the wave vector and the angular frequency are not independent they must adhere to the dispersion relation: As a result, and based on the theory of Fourier decomposition, a real wave must consist of the superposition of an infinite set of sinusoidal frequencies. In practice, g cannot have infinite periodicity because any real electromagnetic wave must always have a finite extent in time and space. size 12 by a liquid crystal and then passed by a polarizing filter that has its axis perpendicular to the original polarization direction.∇ ⋅ E = 0 ∇ ⋅ B = 0 įor virtually any well-behaved function g of dimensionless argument φ, where ω is the angular frequency (in radians per second), and k = ( k x, k y, k z) is the wave vector (in radians per meter).Īlthough the function g can be and often is a monochromatic sine wave, it does not have to be sinusoidal, or even periodic. Let us call the angle between the direction of polarization and the axis of a filter θ. Only the component of the EM wave parallel to the axis of a filter is passed. When the axes are perpendicular, no light is passed by the second. If the second polarizing filter is rotated, only the component of the light parallel to the second filter’s axis is passed. When the axes of the first and second filters are aligned parallel, then all of the polarized light passed by the first filter is also passed by the second. The first filter polarizes the light along its axis. The direction of polarization of an EM wave is defined to be the direction of its electric field.įigure 10.41 shows the effect of two polarizing filters on originally unpolarized light. The axis of a polarizing filter is the direction along which the filter passes the electric field of an EM wave (see Figure 10.40).įigure 10.40 A polarizing filter has a polarization axis that acts as a slit passing through electric fields parallel to its direction. Thinking of the molecules as many slits, analogous to those for the oscillating ropes, we can understand why only light with a specific polarization can get through. Polarizing filters are composed of long molecules aligned in one direction. Polarized materials, invented by Edwin Land, act as a polarizing slit for light, allowing only polarization in one direction to pass through. Such light is said to be unpolarized because it is composed of many waves with all possible directions of polarization. The sun and many other light sources produce waves that are randomly polarized (see Figure 10.39). Vertical slits pass vertically polarized waves and block horizontally polarized waves. The first is said to be vertically polarized, and the other is said to be horizontally polarized. Thus, we can think of the electric field arrows as showing the direction of polarization, as in Figure 10.37.įigure 10.38 The transverse oscillations in one rope are in a vertical plane, and those in the other rope are in a horizontal plane. For an EM wave, we define the direction of polarization to be the direction parallel to the electric field. Waves having such a direction are said to be polarized. This is not the same type of polarization as that discussed for the separation of charges. Polarization is the attribute that a wave’s oscillations have a definite direction relative to the direction of propagation of the wave. There are specific directions for the oscillations of the electric and magnetic fields. ![]() As noted earlier, EM waves are transverse waves consisting of varying electric and magnetic fields that oscillate perpendicular to the direction of propagation (see Figure 10.37). ![]() Light is one type of electromagnetic (EM) wave. Polarizing sunglasses are particularly useful on snow and water. As a result, the reflection of clouds and sky observed in part (a) is not observed in part (b). Part (b) of this figure was taken with a polarizing filter and part (a) was not. Figure 10.36 These two photographs of a river show the effect of a polarizing filter in reducing glare in light reflected from the surface of water. ![]()
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