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Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective (and hence its light-gathering ability and resolution), and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.
A geometrical arrangement used in deriving the Kirchhoff's diffraction formula. The area designated by A 1 is the aperture (opening), the areas marked by A 2 are opaque areas, and A 3 is the hemisphere as a part of the closed integral surface (consisted of the areas A 1, A 2, and A 3) for the Kirchhoff's integral theorem.
Visulization of flux through differential area and solid angle. As always ^ is the unit normal to the incident surface A, = ^, and ^ is a unit vector in the direction of incident flux on the area element, θ is the angle between them.
The mathematical representation of a radial wave is given by = (+) / where =, is the wavelength, is frequency of the wave and is the phase of the wave at the slits at time t = 0. The wave at a screen some distance away from the plane of the slits is given by the sum of the waves emanating from each of the slits.
This is the basic principle behind fiber optics in which light is guided along a high index glass core in a lower index glass cladding (Figure d). Ray optics only gives a rough picture of how waveguides work. Maxwell's equations can be solved by analytical or numerical methods for a full-field description of a dielectric waveguide.
Ray tracing of a beam of light passing through a medium with changing refractive index.The ray is advanced by a small amount, and then the direction is re-calculated. Ray tracing works by assuming that the particle or wave can be modeled as a large number of very narrow beams (), and that there exists some distance, possibly very small, over which such a ray is locally straight.
Physical optics is also the name of an approximation commonly used in optics, electrical engineering and applied physics.In this context, it is an intermediate method between geometric optics, which ignores wave effects, and full wave electromagnetism, which is a precise theory.
This is the Fresnel diffraction integral; it means that, if the Fresnel approximation is valid, the propagating field is a spherical wave, originating at the aperture and moving along z. The integral modulates the amplitude and phase of the spherical wave. Analytical solution of this expression is still only possible in rare cases.