. The Bell System technical journal . the relation (/2-^2Mi^^ Jl^ls (51) fidi \ V2 ^2 where k2 is a constant of the lens, given by 1/^2 = exp. r^. (52) By proceeding in the same manner with a particular solution X for aray leaving the lens parallel to the axis, we obtain a second relation (f^-ddd.^j^ jv^rj^ (53) fidi \viri where The differential equations of X and Y may also be subtracted andintegrated, and this gives a third relation f If - -^^ S. (55) A multiplication of the first two relations 51 and 53 gives (/2 - ^2)(/i - d,) = -^1-^2/1/2, (56) ELECTROSTATIC ELECTRON-OPTICS 17 which is on
. The Bell System technical journal . the relation (/2-^2Mi^^ Jl^ls (51) fidi \ V2 ^2 where k2 is a constant of the lens, given by 1/^2 = exp. r^. (52) By proceeding in the same manner with a particular solution X for aray leaving the lens parallel to the axis, we obtain a second relation (f^-ddd.^j^ jv^rj^ (53) fidi \viri where The differential equations of X and Y may also be subtracted andintegrated, and this gives a third relation f If - -^^ S. (55) A multiplication of the first two relations 51 and 53 gives (/2 - ^2)(/i - d,) = -^1-^2/1/2, (56) ELECTROSTATIC ELECTRON-OPTICS 17 which is one form of the equation relating the conjugate focal distancesof a lens. This equation may be converted into a more useful formby the following considerations. A combination of the three preceding relations gives -J- {di — Q!2) = X (^1 ~ ^l)^2 CLl where a =/i(l - ^i), ^2 = /2(1 — ^2). (57) (58) To interpret this equation, we erect two imaginary planes as shownin Fig. 10. The first plane is located at a distance ai from Zi. If the. Fig. 10—The principal planes. path of the incident ray is projected it intersects this plane at someradial distance R\. The second plane is erected at a distance 0:2 from22. The path of the exit ray intersects it at a radial distance equation says—from simple geometry—that the two radialdistances Ri and R2 are equal. The path of an electron through thelens is therefore the same as if the electron proceeded in a straight lineto the first plane, passed parallel to the axis to the second plane, andthen proceeded again in a straight line to the second conjugate focalpoint. These two planes are called the first and second principalplanes of the lens. The action of a thick lens is the same as if thespace between the principal planes were non-existent, leaving themin coincidence, and a thin lens were located at the plane of coincidence. The principal planes of a lens may lie either inside or outside ofthe lens. In most convergent lenses, ax i
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Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
