ao/(2si) = 1.22/aoao2 = (2)1.22siao = (2.44si) = 1.56(si)For 0.5 m light, ao (in m) = (1.1) (si).The minimum size of the aperture is a function of the wavelength of light. If the wavelength of light approached zero, then minimum aperture diameter would be zero. At aperturediameters greater than ao (at a given si), the image again blurs due to the greater overlap of the circles of confusion emanating from each point on the object. While this problem can be overcome by using a perfect lens that focuses the rays emanating from each given point, the size of the aperture, which may be the size of the lens itself, will always influence the fidelity of the image.I have been discussing diffraction patterns of objects illuminated with plane waves, and the diffraction patterns are viewed an infinite distance from the object. This is known as far-field or Fraunhöfer diffraction. If we were to reduce the wavelength of light to zero, the Fraunhöfer diffraction pattern would turn into a shadow or an image that exactly reproduced an opaque or transparent object, respectively. Fresnel diffraction occurs when an object is illuminated with plane waves and the diffraction pattern is observed a short distance away from the object. This is known as near-field or Fresnel diffraction. The diffraction pattern is clearly recognizable as an imperfect and somewhat fuzzy image of the object. Young realized that, as long as the wavelength of light was not infinitely short, the image of a specimen would be affected by diffraction. That is, slits will appear as fringes, squares will appear as crosses, and circles will appear as Airy discs. Young (1803) wrote: “The observations on the effects of diffraction and interference, may perhaps sometimes be applied to a practical purpose, in making us cautious in our conclusions respecting the appearances of minute bodies viewed in a microscope. The shadow of a fibre, however opaque, placed in a pencil of light admitted through a small aperture, is always somewhat less dark in the middle of its breadth thanin the parts on each side. A similar effect may also take place, in some degree, with respect to the image on the retina, and impress the sense with an idea of a transparency which has no real existence: and, if a small portion of light be really transmitted through the substance, this may again be destroyed by its interference with the diffracted light, and produce an appearance of partial opacity, instead of uniform semitransparency. Thus, a central dark spot, and a light spot surrounded by a darker circle, may respectively be produced in the images of a semitransparent 73and an opaque corpuscle; and impress us with an idea of a complication of structure which does not exist.”In the early part of the nineteenth century, Young, as well as Arago and Fresnel considered light to be, in part, a mechanical longitudinal compression wave. Mechanical waves, be they longitudinal or transverse, cause the particles in a gaseous, liquid or solid medium to be displaced as the waves propagate though it at a speed whose square is proportional to the elasticity of the medium and inversely proportional to the density of the medium. As we will see, the idea of the longitudinal component of light dropped out of favor with the discovery of polarization (chapter 8) and the success of Maxwell's equations. While FitzGerald (1896) and Roentgen (1899) proposed that electromagnetic radiation might have a longitudinal component, since the beginning of the 20th century, electromagnetic waves have not been considered to be mechanical waves, and thus did not need a medium through which to propagate. In the following discussion, we will only consider the transverse components.3. James Clerk Maxwell and the Wave Theory of LightNewton was held in high regard in England as can be seen by the following epitaph written for Newton by Alexander Pope:Nature and Nature's laws lay hid in night:God said, "Let Newton be!" and all was light.Thomas Young was viciously attacked anonymously in the Edinburgh Review for being "Anti-Newtonian" (Anonymous, 1804,1805; Young, 1804; Peacock, 1855; Wood and Oldham, 1954; Klein, 1970). The anonymous reviewer (1804), most likely Lord Brougham, wrote about Young and his theory: “A mere theory is in truth destitute of all pretentions to merit of every kind,except that of a warm and misguided imagination. It demonstrates neither patience of investigation, nor rich resources of skill, nor vigorous habits of attention, nor powers of abstracting and comparing, nor extensive acquaintance with nature. It is the unmanly and unfruitful pleasure of a boyish and prurient imagination, or the gratification of a corrupted and depraved appetite.” He went on to say: “We take our leave of this paper with recommending it to the Doctor to do that which he himself says would be very easy; namely, to invent various experiments upon the subject. As, however, the season is not favourable for optical observation, we recommend him to employ his winter months in reading the ‘Optics’, and some of the plainer parts of the ‘Principia’, and then to begin his experiments by repeating those which are to be found in the former of these works.”Young decided that academia was no place for original thinkers and left the Royal Institution. However, his work has held up over time, and it is an essential aspect of understanding image formation in the microscope. In the mid nineteenth century, however, a more mathematical treatment of diffraction by Jean Fresnel (1827-1828), as well as work done byJean Foucault and James Clerk Maxwell led to such an acceptance of the wave theory of light, that it came to be known as the classical theory of light.In 1850, Foucault (1850,1862) measured the speed of light in air and in water and found that the speed of light was slower in water than it was in air (appendix 5). This finding was inconsistent with the corpuscular theory of light (Newton, 1730), but consistent with the wave theory of light (Huygens, 1690).74Faraday was looking for the relationship between electricity, magnetism and light and eventually found that he could influence the plane of polarization of a light beam when he placed the glass through which the beam traveled in a magnetic field. Other nineteenth century scientists,including Weber were also interested in unifying electricity, magnetism and optics. Maxwell was working on electricity and magnetism,