In summary, we find there are basically three advantages and three disadvantages in electronic computers. They are as follows:

Disadvantages

Limited Intelligence Limited Language Capability Cost

Advantages

High Speed

High Precision and Accuracy

Reliability

The advantages far outweigh the disadvantages in a great number of needs and applications in industry, government, education, and busi­ness. There are many activities that we could not accomplish without the computer. The nature and structure of the' electronic digital com­puter is such that it is helpful and beneficial to man.

Electron Optics

The conversion of a visual image — a two-dimensional distribu­tion of light and shade — into an electrical signal requires not merely a photosensitive element which translates differences in light intensity into differences in current or voltage, but also a commutator which successively causes the photoemission derived from different picture elements to actuate a common signal generator, or, as an alternative, successively derives the output signal from individual photoelements associated with the picture elements. Similarly, in picture reconstruc­tion, a commutator is needed to apply the received signal successively to elements in the picture frame corresponding to the picture elements at the transmitter from which the signal has originated.

In electronic television the commutators used for both purposes . are electron beams. In order that the reproduced picture may be a faith­ful replica of the original scene, these beams must be deflected in a precisely controlled manner; to realize sharp, high-quality pictures, they must be sharply converged. Electric and magnetic fields are the means used for accomplishing both purposes.

The design of electric and magnetic fields to focus and deflect electrons in a prescribed manner is commonly called electron optics. The term follows from the recognition that the paths of material particles subject to conservative force fields obey the same mathema­tical laws as light rays in a medium of variable refractive index. Later, it was shown, both theoretically and experimentally, that axially symmetric electric and magnetic fields act indeed on electron beams in the same manner as ordinary glass lenses act on light beams. The "refractive index" n for electrons in a field with electrostatic potential V and magnetic vector potential A can be written simply

where c is the velocity of light and 0 the angle between the path and the magnetic vector potential. The zero level of the potential V is made such that e V represents the kinetic energy of the electron. It is thus possible to derive the path equations of the electrons from Fermat's law of optics:

Fermat's law states that for the actual light ray (or electron path) from point A to point B the optical distance is a minimum or maximum as compared with any comparison path.

In any actual electron-optical system only the electrodes surround­ing the region through which the electrons move, along with their potentials, as well as external current carrying coils and magnetic cores can be determined at will. The fields in the interior, which enter into the refractive-index expression and the path equations, must be derived from a solution of Laplace's equation for the boundary conditions established by the electrodes and magnetics. For electro­ static systems Laplace's equation is simply:

The determination of electron paths within the system is thus normally carried out in two steps: the determination of the fields and the solution of the path equation in these fields. However, computer programs applicable for a great range of practical cases, have been written for carrying out both operations. With them, the computer supplies the electron paths if the point of origin and initial velocity of the electron as well the boundary potentials are specified.

Radiation

Radiation is the process by which waves are generated. If we con­nect an ac source to one end of an electrical transmission line (say, a pair of wires or coaxial conductors) we expect an electromagnetic wave to travel down the line. Similarly, if, as in the first Figure, we move a plunger² back and forth in an air-filled tube, we expect an acoustic wave to travel down the tube.

Thus, we commonly associate the radiation of waves with oscilla­ting sources. The vibrating cone of a loudspeaker radiates acoustic (sound) waves. The oscillating current in a radio or television trans­mitting antenna radiates electromagnetic waves. An oscillating electric or magnetic dipole radiates plane-polarized waves³. A rotating electric or magnetic dipole radiates circularly polarized waves.

Radiation is always associated with motion, but it is not always associated with changing motion. Imagine some sort of fixed device moving along a dispersive medium*. In the Figure below this is illustra­ted as a "guide" moving along a thin rod and displacing the rod as it moves. Such a moving device generates a wave in the dispersive medium. The frequency of the wave is such that the phase velocity v of the wave matches⁵ the velocity v of the moving device. If the group velocity is less than the phase velocity, the wave that is generated trails behind the moving device. If the group velocity is greater than the phase velocity, the wave rushes out ahead⁷ of the moving device. Thus, an object that moves in a straight line at a constant velocity can radiate waves if the velocity of motion is equal to the phase velocity of the waves that are generated. This can occur in a linear dispersive medium, as we have noted above. It can also occur in the case of an object moving through a space in which plane waves⁸ can travel.

Antennas and Diffraction

The Figure represents a beam of light emerging from a laser. As the beam travels, it widens and the surfaces of constant phase become spherical. The beam then passes through a convex lens made of a ma­terial in which light travels more slowly than in air. It takes a longer time for the waves to go through the centre of the lens than through the edge of the lens. The effect of the lens is to produce a plane wave over the area of the lens. When the light emerges from the lens, the wavefront, or surface of constant phase, is plane.

The next example represents a type of microwave antenna. A mic­rowave source, such as the end of a waveguide, is located at the focus of a parabolic (really, a paraboloidal) reflector. After reflection, the phase front⁴ of the wave is plane over the aperture of the reflector.

The light emerging from the lens of the first Figure does not tra­vel forever in a beam with the diameter of the lens. The microwaves from the parabolic reflector do not travel forever in a beam the dia­meter of the reflector. How strong is the wave at a great distance from the lens or the reflector?

A particular form of this question is posed in the Figure at the'; bottom of the text. We feed a power P_T into an antenna that emits a plane wave over an area At. We have another antenna a distance L away which picks up the power of a plane wave in an area A_R and supplies this power P_R to a receiver. What is the relation among Pt, Pr, At, Ar, and L? There is a very simple formula relating these quantities: