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Paraxial Rays and Lenses
Published in Ajawad I. Haija, M. Z. Numan, W. Larry Freeman, Concise Optics, 2018
Ajawad I. Haija, M. Z. Numan, W. Larry Freeman
Figure 3.2 illustrates essential quantities that relate to the lens properties. Alongside, we present definitions of the most prominent ones.Center of curvature: For each surface of the lens, the center of curvature is the center of the sphere of which the lens surface is cut.Optic axis: It is the line of symmetry that passes through the centers of curvature of the two (lens) surfaces.The center of the lens is defined at the middle of its width halfway between V1 and V2.
Further differentiation
Published in C.W. Evans, Engineering Mathematics, 2019
The circle centred at c with radius ϱ is called the circle of curvatureand the point c is called the centre of curvature. It is worth observing that if ϱ is negative this means that the curve is bending towards the x-axis (concave to the x-axis) and so in the opposite direction to the way shown in the diagram (convex to the x-axis).
Spherical Mirrors
Published in Abdul Al-Azzawi, Light and Optics, 2018
In Figure 9.9, the object is located at the centre of curvature, C, of the concave mirror. The mirror forms an image at the centre of curvature. The image is real, inverted, and the same size as the object.
Influence of Recess Dimensions and Jacking Oil Flow Rate on the Performance of Tilting Pad Journal Bearings with Jacking Oil Mechanism
Published in Tribology Transactions, 2022
Syed Muntazir Mehdi, Sung Yun Jeong, Tae Ho Kim
Figure 1a is a schematic of a typical four-pad TPJB with machined recesses at the loaded pads for the jacking oil supply, and Fig. 1b shows a single-pad simplified and exaggerated model of the TPJB. The journal’s center with spinning speed Ω covers a displacement denoted by e from the bearing center Ob, the origin of the inertial coordinates X (horizontal axis) and Y (vertical axis). The pad with the radius of curvature Rp resting on the pivot tilts by a magnitude of δ, shifting the pad’s center of curvature from Op to Op′ when subjected to load. The pad’s pivot located at an angular location θp from the X-axis deflects in the radial direction with a magnitude equal to ζ. The film thickness h is dependent upon the preload (Rp − Rb), journal eccentricity e, pivot deflection ζ, pad tilting angle δ, and recess depth Dr:
Corner inspection method for L-shaped composite structures using laser ultrasonic rotational scanning technique
Published in Advanced Composite Materials, 2021
Young-Jun Lee, Seong-Chan Hong, Jung-Ryul Lee, Sung-Jin Hong
As described in Section 2, when inspecting a curved surface using the raster scanning method, the SNR decreases as the incidence angle and stand-off distance are outside of a certain range. For corner sections, the angle changes rapidly from 0 to 90 degrees within a small radius of curvature, only a few centimeters, so the SNR decrease is obviously more severe. The rotational scanning method is proposed to solve the problems caused by the changes in incidence angle and stand-off distance. The principle of the rotational scanning method is as follows. A corner section generally has the shape of a quadrant, part of a circle, with a certain radius of curvature. The circle is a set of points at the same distance from the center, and the tangent lines at all points of the circle are normal to the center. Therefore, if a laser is located at the center of curvature of a corner section and scans while rotating along the corner section, the stand-off distance between the laser and the target surface is constant, and the incidence angle is always normal. However, considering the radius of curvature of the corner section is only a few centimeters, a laser that is only several tens of centimeters large cannot be placed at the center of curvature of the corner section. Conversely, by rotating the target structure about the radius of curvature while the laser head is stationary, the same effect as the laser head scanning with a rotation can be implemented. Figure 3 shows the configuration of the rotational scanning method in pulse-echo mode and through-transmission mode.
A Fusion Reactor Scheme Using Magnetic Mirrors
Published in Fusion Science and Technology, 2020
where n is the normal unit vector from the center of curvature to a point on the magnetic line, and R is the radius of curvature. The first term is from the particle drift under the centrifugal force, and the second is from the radial gradient of the magnetic field. When the magnetic field lines are convex outward, the charge separation from the opposite drifts of ions and electrons will cause an drift resulting in an enhancement of the perturbation with grow rate . In the opposite case, when the lines are concave outward, the plasma is stable. In other words, the plasma is stable when the magnetic field increases outward, the so-called “minimum-B condition” for stability.