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The transfer-matrix method is based on the fact that, according to Maxwell's equations, there are simple continuity conditions for the electric field across boundaries from one medium to the next. If the field is known at the beginning of a layer, the field at the end of the layer can be derived from a simple matrix operation.
The signs are reversed for the back surface of the lens: R 2 is positive if the surface is concave, and negative if it is convex. This is an arbitrary sign convention; some authors choose different signs for the radii, which changes the equation for the focal length. For a thin lens, d is much smaller than one of the radii of curvature (either ...
For the purposes of ray tracing, this is equivalent to a series of identical thin lenses of focal length f = R/2, each separated from the next by length d. This construction is known as a lens equivalent duct or lens equivalent waveguide.
In weak lensing by large-scale structure, the thin-lens approximation may break down, and low-density extended structures may not be well approximated by multiple thin-lens planes. In this case, the deflection can be derived by instead assuming that the gravitational potential is slowly varying everywhere (for this reason, this approximation is ...
The points that span conjugate planes are called conjugate points. [ 3 ] For a thin lens or a curved mirror , 1 u + 1 v = 1 f , {\displaystyle {1 \over u}+{1 \over v}={1 \over f},} where u is the distance from the object to the center of the lens or mirror, v is the distance from the lens or mirror to the image, and f is the focal length of the ...
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 optic equation of the crossed ladders problem can be applied to folding rectangular paper into three equal parts. One side (the left one illustrated here) is partially folded in half and pinched to leave a mark. The intersection of a line from this mark to an opposite corner, with a diagonal is exactly one third from the bottom edge.
In most cases, two thin lenses are combined, one of which has just so strong a positive aberration (under-correction, vide supra) as the other a negative; the first must be a positive lens and the second a negative lens; the powers, however: may differ, so that the desired effect of the lens is maintained. It is generally an advantage to secure ...