Half-wavelengths

Therefore the cavity has been increased in length by 0.000 03 cm = 0.3 [im. This means that to tune the cavity to a half wavelength of the radiation requires an extremely accurate movement of one of the mirrors forming the cavity. 

Before going further, it may be noted that the flipping ratio does not depend either on the Lorentz factor or on absorption in the sample. Certain instrumental parameters such as the polarisation of the neutron beam for the two spin states, the half wavelength contamination of the neutron beam and the dead-time detector can readily be taken into account when analysing the data. On the other hand, the extinction which may occur in the scattering process is not so easy to assess, but must also be included [14]. Sometimes, it is even possible to determine the magnetisation density of twinned crystals [15]. 

Figure 5.7 shows the effects of the distance from the oscillator to the bottom of the reaction vessel on the rate of Au(III) reduction, where the distance is changed from 3.5 to 4.5 mm [29]. It is clear that the rates of reduction are affected by the position of the reaction vessel. The rate of reduction became the maximum at a distance of ca. 3.8 mm. This was almost the same as the half-wavelength of the ultrasound (3.71 mm) used in this study. It is suggested that ultrasound is effectively transmitted into the reaction vessel at 3.8 mm distance. It should be noted that the position of the reaction vessel sensitively affects the efficiency of the sonochemical reduction. 

The electron behaves as a standing wave with an integral number of half wavelengths fitting into the one-dimensional box, with boundary conditions... 

The second overtone has three half-wavelengths within the string. We can find the... 

Dauter, Z. (2002). Qne-and-a-half wavelength approach. Acta Crystallogr. D 58,1958-1967. 

As a simple example, we might impose a perturbation with a cosine distribution as illustrated in Fig. 10.4. If the uniform state is stable to such a perturbation, the amplitude will decay to zero if the uniform state is unstable, the amplitude will grow. We could ask this question of stability with respect to any specific spatial pattern, but non-uniform solutions will also have to satisfy the boundary conditions. This latter requirement means that we should concentrate on perturbations composed of cosine terms, with different numbers of half-wavelengths between x = 0 and x = 1. 

If P, n, and k are chosen suitably, this equation may have two real and positive solutions, ni and n+ say. The uniform stationary state is then unstable to perturbations which have n half-wavelengths where n is an integer lying in the range... 

Fig. 10.5. Representation of the conditions for which the uniform stationary state is unstable to perturbations with a particular number-of half-wavelengths (a) n = 2 (b) the loci for n = 1,2,3, and 4, showing how these overlap to create regions in which more than one spatial perturbation may cause departure from the uniform state.

Fig. 10.6. Division of the y-ji parameter plane into regions according to the different dominant spatial forms. For the zero-flux model, an odd number of half-wavelengths appears to be...

When the incident beam reaches the interface of a second medium with a greater refractive index, the beam, depending on the incident angle, will be totally reflected as on a mirror or partially reflected after penetrating the medium by approximately one half wavelength (2 to 10 pm for the mid IR). The sample absorbs part of this radiation. 

If v — 15 800cm-1, A = 0.633 pm. In passing from one minimum to the next the mirror must be displaced by a distance corresponding to a half-wavelength which is 0.316 pm. 

Half-way between these positions, the path length will differ by an odd number of half wavelengths, and destructive interference will occur. 

If this is a whole number of wavelengths, constructive interference will result. Unless the path length is exactly an odd number of half wavelengths,... 

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