Lens equation

For a symmetric magnetic sector field, the entrance slit and the exit slit at A and A", respectively, are at the same distance from the magnetic field boundary. From the lens equation of a symmetric magnetic sector field with Iff = Iff Equation (3.6) is vahd... 

The passage of electrons or other particles with charge q and mass m through an electrostatic lens system is governed by their motion under the action of the electric field. In the case considered here, cylindrical symmetry around the optical axis (z-axis) and paraxial rays will be assumed. Of the cylindrical coordinates only the transverse radial coordinate p and the distance coordinate z are of relevance, and the electrostatic potential of the lens is given by q>(p, z). As shown in Section 10.3.1, in the paraxial approximation the potential q>(p, z) is fully determined by the potential symmetry axis. Hence, the equations of motion and the fundamental differential equation of an electrostatic lens depend only on this potential. The fundamental lens equation is given by (see equ. (10.38))... 

In order to derive the full properties of a lens system, the fundamental lens equation has to be solved for individual rays subject to the influence of the given potential d>(z). However, without going into the details for such a procedure, some aspects, which are important for axial-symmetrical electrostatic lenses with paraxial rays, can be listed by using results from light optics ... 

The extension of the lens equations to a cosmological context raises some technical difficulties because the background in which the objects are embedded is not flat. In particular one must pay attention to the distances that should be employed. The other change is that lenses will now have extended mass distribution. 

In the lens equation the distance to use is the angular distance. This can be unambiguously established by the geometric optic equations. 

For refraction at a single spherical interface of radius R that separates two media of refractive indices n2 and n2, the lens equation is... 

For mirrors, the equation is usually written 1/s + 1/s = 2/R = 1/f. A diverging mirror is convex to the incoming light, with negative f. From this fact we conclude that R is also negative. This form of the equation is consistent with that of the lens equation, and the interpretation of sign of focal length is the same also. But violence is done to the definition of R we used above, for refraction. 

The optics of optical instruments can be calculated in good approximation by the lens equation , assuming thin lenses (Sec. 3.3.2) ... 

The imaging properties of a lens are most simply described by the lens equation (see Fig. 3.3-3) ... 

Newton derived an alternate form of the lens equation. 

FIGURE 4 A thin lens, showing the parameters x and x used in Newton s formulation of the lens equation. 

The so-called lens equation expresses the quantitative relationship between the object distance a. 

The location of the focus can be calculated from the lens equation... 

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