By Rudolf Kingslake
A wide a part of this ebook is dedicated to a research of attainable layout approaches for numerous forms of lens or replicate structures, with totally labored examples of every. The reader is recommended to keep on with the common sense of those examples and be certain that he is aware what's occurring, noticing really how each one to be had measure of freedom is used to regulate one aberration. no longer all sorts of lens has been thought of, after all, however the layout recommendations illustrated right here can quite simply be utilized to the layout of different extra advanced structures. it's assumed that the reader has entry to a small computing device to assist with the ray tracing, in a different way he may well locate the computations so time-consuming that he's prone to lose music of what he's attempting to accomplish
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Additional resources for Lens Design Fundamentals
Example text
649 Note that in this table of computation the sine of the ray slope is written above the angle U itself, since it is required twice more, for the transfer and again for the calculation of sin / at the following surface. It is also worth recording the cos U below the angle since it is required for the G calculation. The X and Y values have been added at the end of each surface, although they are not always required. Data relating to the surfaces appear in the columns, while data referring to the spaces between surfaces appear on the vertical dividing lines between the surface data.
Then Y = W/(n cos U) = W'/(ri cos U). If the last surface is a plane, the closing equation becomes L = W'l(ri sin U). III. M A G N I F I C A T I O N A N D T H E L A G R A N G E T H E O R E M A. TRANSVERSE MAGNIFICATION Consider first a single refracting surface as in Fig. 20. Let B, & be a pair FIG. 20. The Lagrange relationship. of axial conjugate points, their distances from the surface being / and /', respectively. We now place a small object at B and draw a paraxial ray from the top of the object to the vertex of the surface.
D — \X2 approximately, remember ing that each X must have the same sign as its r. Example. As an example, consider the lens sketched in Fig. 12 having M FIG. 12. The volume of a lens. 32 2. MERIDIONAL RAY TRACING rl = 20, r2 = 10, diam. = 16, and edge thickness = 6. 00. r Convex cap: Cylinder: Concave cap: Volume The error in the approximate calculation is only 3%, even for a very deeply curved lens such as this. E. SOLUTION FOR LAST R A D I U S TO GIVE A STATED V In some cases we need to determine the last radius of a lens to yield a specified value of the emerging ray slope U\ given the Q and U of the incident ray at the surface and the refractive indices n and ri.