Figure 8-10 The effect of the size of a light source on spatial coherence. The interferometer fringe pattern produced by a second point source (point B) of light is shifted relative to the first point source (point A). Superimposing both patterns results in a new pattern with decreased fringe contrast. A small light source has high spatial coherence and produces high-contrast fringes. If a light source is too large (ie, consists of numerous point sources), no fringes will be seen.
(Illustration b y Edmond H. Thall, MD.)
Electromagnetic Waves
The corpuscular theory of light was abandoned after Young provided strong evidence that light is a wave phenomenon. The next question is, What type of wave? James Clerk Maxwell developed equations describing the behavior of electric and magnetic fields. Maxwell discovered that oscillating electric fields (ie, those that rhythmically reverse polarity) are inextricably linked to oscillating magnetic fields and that such electromagnetic (EM) fields can radiate as waves. In 1862, Maxwell calculated the speed of EM waves and found that they moved at the speed of light, and he thus concluded that light is an EM wave. Several phenomena can be explained by the EM wave theory.
Polarization
The electric field of an EM wave oscillates perpendicularly to its magnetic field, and both oscillate perpendicularly to their direction of propagation (Fig 8-11). Because the electric and magnetic fields oscillate in lockstep, for simplicity only the electric field is shown in most illustrations. The EM
plane of polarization is defined by the orientation of the electric-field oscillation (eg, vertical in Fig 8-11) and direction of propagation. In general, the plane of polarization of an EM wave may have any orientation (ie, horizontal, vertical, or oblique).
Figure 8-11 Light is polarized. The plane of polarization is specified with reference to the direction of propagation and the direction of the oscillating electric (E) or magnetic (H) field, which always oscillate perpendicularly to each other. In this view, the electric field is polarized vertically and the magnetic field horizontally, but they could be interchanged, or polarization could be in any oblique meridian. (Illustration b y Jonathan Clark.)
Note that there is no such thing as “unpolarized” light. Typically, the plane of polarization changes rapidly (about every 10–13 to 10–14 second) and randomly, resulting in light that is randomly polarized. Linearly polarized light, however, has a single unchanging plane of polarization. In circularly polarized light, the plane of polarization rotates, and the (maximum) electric-field vector traces a corkscrew pattern as the wave propagates. Viewed head-on, the field vector traces a circle. In elliptically polarized light, which represents a more general case of circular polarization, the plane of polarization rotates as the wave propagates, but the (maximum) electric-field vector traces an ellipse instead of a circle.
Refractive Index and Dispersion
EM waves travel fastest in a vacuum and slower in any transparent material medium. All EM frequencies travel at the same speed in vacuum, but in any transparent medium, each frequency travels at a different speed—a phenomenon called dispersion. The refractive index (n) is the ratio of the speed of light in a vacuum divided by its speed in a given material. Dispersion is measured using the refractive index at 3 different wavelengths. This measurement, the Abbe number (V), is defined as
where nd, nF, and nC represent wavelengths (in a vacuum) of 587.6 nm, 486.1 nm, and 656.3 nm, respectively. Larger Abbe numbers indicate lower dispersion.
Reflection, Transmission, and Absorption
Consider light striking the interface between 2 materials such as air and glass (Fig 8-12). Some light is reflected according to the law of reflection and some transmitted (refracted) according to Snell’s law.
Figure 8-12 At the interface of 2 transparent media, some incident light is reflected and some is refracted (transmitted). The amount of reflected light increases as the angle of incidence increases, and the amount of light refracted decreases commensurately. When, as in this case, the reflected and refracted rays form a right angle, all the reflected light is linearly polarized parallel to the interface (ie, perpendicular to the plane of incidence). (Illustration b y Edmond H. Thall, MD.)
The question is, How much light is reflected and how much transmitted? Applying electromagnetic wave theory, Fresnel demonstrated that the greater the difference in the refractive
indices or the greater the angle of incidence, the greater the degree of reflection and, consequently, the less light transmitted. For an air–glass interface, typically about 4% of light is reflected at low angles of incidence. Tears have a lower refractive index than glass, so an air–tear-film interface reflects even less light—about 2%.
Light reflected at the front and back surfaces of the cornea and the crystalline lens produces the 4 Purkinje images. The reader should be able to rank the Purkinje images from brightest to dimmest in both phakic and pseudophakic eyes.
Fresnel also showed that reflected light tends to be linearly polarized parallel to the interface. Reflected light is completely polarized if the angle of incidence equals the Brewster angle:
where nt and ni are the refractive indices of the transmitted and incident media, respectively. At the Brewster angle, all the reflected light is linearly polarized, but not all the linearly polarized light is reflected. Consequently, the transmitted light is a mixture of linearly and randomly polarized light.
When light moves from a higher to lower refractive index medium, it will be completely reflected
(total internal reflection [TIR]) if the angle of incidence exceeds the critical angle:
Note that the critical angle always exceeds the Brewster angle. TIR is what prevents visualization of the angle during slit lamp examination. In rare cases, the cornea might be so distorted that the angle is visible without gonioscopy, but usually some method must be employed to prevent TIR and make the angle visible.
Absorption is usually expressed as an optical density (OD). An OD of 1 represents a transmittance of 10%; an OD of 2, a transmittance of 1% (0.01); and an OD of 3, a transmittance of 0.1% (0.001). In general, the expression for optical density is
where T is the transmittance. (See Chapter 3 for a discussion of absorptive lenses.)
The Electromagnetic Spectrum
All EM radiation is fundamentally the same phenomenon, but its manifestations strongly depend on frequency. The frequency of EM radiation has no specific upper or lower limit. The spectrum is divided into regions in which the radiation is produced and detected by similar techniques; thus, various EM regions partially overlap (Fig 8-13).