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wavefront serves as the source of spherical secondary wavelets, such that the wavefront at some later time is defined by the envelope covering these wavelets. Further, if wave propagation occurs in an isotropic medium, the secondary wavelets have the same frequency and velocity as the original reference wavefront. The geometrical construction of Huygens wavelets is a useful device for predicting the locations of wavefronts as modified by both refraction and diffraction; however, Huygens theory does not account for many wave-optical phenomena of diffraction, which require the application of newer approaches in physical optics. When applied to the diffraction grating, we can use the construction of Huygens wavelets to determine the location of the diffraction spots and the diffraction angle. Take a moment to study the construction for a diffraction grating with spacing d in Figure 5-11, which emphasizes the concept that the diffraction spots occur at angles where the optical path lengths of constituent waves are an integral number of wavelengths . At locations between the diffraction spots, waves vary by a fraction of a wavelength and destructively interfere. Although Huygens wavelet construction accounts for the locations of diffraction spots, it does not account for all aspects of the diffraction process. For example, the sum of all of the energy present in the luminous regions of the diffraction pattern is known to equal the energy incident on the grating. This is inconsistent with ray particle models and predictions from the geometrical construction of wavelets that photons are distributed uniformly on the diffraction screen, being annihilated where there is destructive interference. We enter here a murky area where the wave and particle natures of light are difficult to reconcile.

4.76 4.19 2.88 1.48 3.96 3.70 2.88 5.68

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The DIC image has a relieflike quality, exhibiting a shadow-cast effect as if the specimen were a three-dimensional surface illuminated by a low-angle light source. It must be remembered that the shadows and highlights in the shadow-cast image indicate the sign and slope of phase gradients (gradients in optical path length) in the specimen and do not necessarily indicate high or low spots. The direction of optical shear is obvious and is defined by an axis connecting regions having the highest and lowest intensity. Finally, the direction of the apparent shadow casting reverses for structures with refractive indices that are lower and higher than the surrounding medium. Thus, dense nuclei, mitochondria, and lysosomes might have the appearance of raised elevations, while less dense pinocytotic vesicles and lipid droplets look like sunken depressions. The degree of contrast and extent of three-dimensionality depend on the amount of bias retardation between wavefronts imparted by the objective prism. The axis of optical shear cannot be changed by changing a setting on the microscope. However, the orientation of bright and dark edges can be reversed 180 by moving the DIC prism to place the optic axis of the microscope on the other side of the null position of the prism. This has the effect of reversing the relative phase retardation of the O and E wavefronts. Therefore, the only way of changing the shear axis relative to the specimen is to rotate the specimen itself. For certain symmetric specimens such as diatoms, specimen rotation can be used to highlight different features (Fig. 10-8). A precision-rotating specimen stage is very useful in deducing the direction of phase gradients in complex structures.

Table 9.2 Death sentencing and race in Florida 1973 1979, full table. For white victims the hypothesis that the two other attributes are independent can be rejected with an error probability less than 0.01% (according to a 2 test).

What CCD is mounted in the camera What are the pixel dimensions Indicate the magnification of the objective you typically use, and then calculate the radius ( m) of the diffraction disk in the image plane produced by this lens at 550 nm. Do the pixel dimensions on the CCD meet the Nyquist limit for preserving spatial resolution If not, how would you solve this problem Indicate the binning modes available (2 2, 3 3, 4 4, etc.). Remember that binning reduces spatial resolution, but reduces the exposure time and helps protect live cell preparations.

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