Divergence angles

The value of the beam divergence angle given by equation 3 corresponds to that emerging from the laser. The beam may be collimated further by a telescope. The improvement of the coUimation is the inverse of the magnification of the telescope ... 

F = (H+ cosor) (wVe/g) + (Pe-P0)Ae where oc = half of the divergence angle of the nozzle, w - weight rate of proplnt flow, g = acceleration of gravity, Ve = exit flow velocity, Pe = nozzle exit pressure, PQ = external atm pressure, and Ae = cross section at nozzle exit plane. An effective exhaust velocity is defined by... 

Figure 8.2 Logarithmic spiral with superimposed mean planetary orbits. The circles in blue define the orbits of inner planets on a larger (self-similarj scale. The divergence angle of 108° causes those planets at angles of 5 x 108° apart to lie on opposite sides of the spiral origin. These pairs are Neptune-Mars, Uranus-Earth, Saturn-Venus and Jupiter-Mercury. The hypothetical antipode of the asteroid belt, a second, unobserved group of unagglomerated fragments, has been swallowed up by the sun...

Table 8.1 The orbital distances (astronomical units) at perihelion, mean and aphelion of the planets, compared to scaled intercepts, with divergence angle of 108°(3/10 x 360), on a golden spiral...

A powder specimen in the form of a rectangular plate has a width of 0.5 in., measured in the plane of the diffractometer circle, which has a radius of 5.73 in. If it is required that the specimen entirely fill the incident beam at all angles and that measurements must be made to angles as low as 26 = 10°, what is the maximum divergence angle (measured in the plane of the diffractometer circle) that the incident beam may have ... 

In hollow-optical fibers for laser delivery, usually only some low order modes are excited because of small divergence angle of incident laser beam. In contrast, many high order modes are excited in hollow-optical fibers for spectroscopic applications because usually an incoherent light source like an arc lamp is used as the light source. Therefore, ray optic theory that can handle a wide divergence beam is used for evaluation of optical properties in this section. 

Figure 4 shows theoretical losses of (1) silver hollow-optical fiber, (2) dielectric-coated silver hollow-fiber with coating thickness of 0.39 pm, and (3) d = 0.66 pm. The thickness of 0.39 pm is the optimized value for 2 = 3 pm and 0.66 pm is the one for 2 = 5 pm. Parameters used in the calculation are rii = 1.53, z = 1 m, 2T = 1 mm, and cr = 0 and complex refractive index of silver is taken from literature [11]. In the calculation, a Gaussian beam with the divergence angle of 6° in full-width-half-maximum is assumed as an input beam. As seen from the calculated spectra, one can obtain a low loss region around the optimized wavelength. 

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