Figure 8-5 A, According to the law of rectilinear propagation, light should not change direction after traversing an aperture. B, In reality, apertures do cause light to change direction—a phenomenon called diffraction. C, The smaller the aperture is relative to the wavelength of incident light, the more pronounced is the diffraction. (Illustration b y Edmond H. Thall, MD.)
Some scientists believed that the discovery of diffraction (c 1665) offered sufficient justification to abandon the corpuscular theory completely, and they concluded that light was fundamentally a wave. Sir Isaac Newton and others, however, believed that the corpuscular theory could explain diffraction. For the next 100 years, the nature of light—wave or particle—was an open question.
The Speed of Light
In 1687, Danish astronomer Ole Roemer noted an irregularity in the orbit of Jupiter’s moon Io that he attributed to light having a finite speed. Later laboratory measurements confirmed that the speed of light is finite.
By international agreement, a meter had been defined by the length of a metal bar kept in Paris, France. Because this standard meter bar might be damaged or destroyed by war or natural disaster, the international community adopted a standard of measurement based on natural phenomena that are readily accessible and indestructible. Hence, the speed of light became the measurement standard, and the meter is defined as the distance light travels in a vacuum during 1/299,792,458 second. Thus, the speed of light is by definition exactly 299,792,458 m/s. A useful approximation for the speed of light in a vacuum is 3 × 108 m/s (approximately 1 ft/ns).
The Superposition of Waves
The superposition principle states that when 2 or more waves overlap, their amplitudes will add or cancel. The superposition of 2 waves of differing frequencies produces a changing “interference” pattern of reinforcement and cancellation that, in the case of light, is much too fast to be observed (Fig 8-6). However, the superposition of 2 waves of identical frequency produces a stable interference pattern (Fig 8-7).
Figure 8-6 According to the principle of superposition, when 2 waves overlap, their amplitudes add, producing a single resultant wave. The 2 waves at top differ slightly in frequency and align peak to peak (blue band), reinforcing each other in some places, and peak to trough (red band), canceling each other in some places. In this example, complete cancellation does not occur because the waves differ in amplitude. In any case, the pattern alternates between reinforcement and cancellation about every 10–14 second—much too fast to be observed.
Figure 8-7 Overlapping waves of identical frequency and amplitude produce stable interference patterns. A, Waves overlap in phase—peaks coincide with peaks and troughs with troughs—producing a resultant wave of twice the amplitude. B, Waves overlap out of phase—the peak of one wave coincides with the trough of the other—and the waves cancel. C, Waves partially overlap—neither completely in nor out of phase—producing a wave of intermediate amplitude
(between zero and twice the amplitude). (Illustration developed b y Edmond H. Thall, MD, and redrawn b y C. H. Wooley.)
The result of 2 particles striking the same place simultaneously is always additive, whereas 2 overlapping waves may reinforce or cancel each other, as just described. In 1801, London physician Thomas Young demonstrated that light can produce patterns of cancellation and reinforcement, thus providing strong evidence that light is a wave phenomenon.
Coherence
Light from most sources consists of wave trains. Just as a train has many cars, a wave train consists of many sections, each having a dominant frequency (Fig 8-8). Temporal coherence is a function of the bandwidth of a light source (ie, the number of frequencies it is composed of). Wave trains from broadband light sources (ie, those radiating many frequencies) consist of short sections, whereas narrowband light sources consist of wave trains with longer sections. The length of one wave train section is the coherence length. The time required for light to travel one coherence length is the coherence time.
Figure 8-8 Each section of a wave train has a dominant frequency that changes randomly from one section to the next. The color of each section corresponds to its dominant frequency—eg, in A, the red section is lower in frequency, and the blue section is higher in frequency. The length of each section is the coherence length. A, Broadband wave trains have a short coherence length. B, Compared with A, the light represented in B has a narrower bandwidth and consequently a
longer coherence length. (Illustration b y Edmond H. Thall, MD.)
Consider a single section of a wave train from a broadband point source illuminating 2 small, closely spaced pinholes in an otherwise opaque screen (Fig 8-9A). Each section arrives at both pinholes simultaneously and is diffracted by the pinholes. The distance from each pinhole to point O
is identical, so both sections produce a bright spot by constructive (ie, additive) interference.
Figure 8-9 Schematic of Young’s experiment demonstrating that light is a wave phenomenon. A, Wave train sections arrive at the pinholes simultaneously, then diffract and arrive simultaneously at point O. They constructively interfere, producing a bright spot. B, To reach point P, one section travels slightly farther than the other, which lags behind by half a wavelength. The 2 sections interfere destructively, and point P is dark. C, At point Q, one section lags behind the other by 1 full wavelength. The 2 sections interfere constructively, producing a reduced bright spot. D, At point R, one section lags the other by more than 1 coherence length so there is no interference, but a superposition of noncorresponding sections produces an average uniform illumination. (Illustration b y Edmond H. Thall, MD.)
At point P (Fig 8-9B), one section travels half a wavelength farther than the other, so the 2 sections cancel, producing a dark spot by destructive (ie, subtractive) interference. At point Q (Fig 8-9C), the sections differ by a full wavelength and again produce a bright spot by constructive interference. Alternating intervals of constructive and destructive interference produce a fringe pattern. However, as the distance from point O increases, the wave train sections overlap less and less, decreasing the degree of fringe contrast (ie, the difference in intensity between the brightest and darkest points). At point R (Fig 8-9D), one section lags the other by more than its coherence length, so the sections do not overlap at all. Because the superposition of nonidentical sections does not produce stable interference, fringes are no longer visible.
Sunlight (composed of numerous frequencies) has a coherence length of 1–2 µm, whereas laser light (composed of few frequencies) typically has a coherence length of several centimeters. If the point source in Figure 8-9 were to be replaced by a laser light source, many more fringes of much higher contrast would be generated.
Another aspect of coherence concerns a light source’s physical size (ie, length or area). Consider a second point source illuminating 2 pinholes (Fig 8-10). Fringes produced by the second source are shifted slightly relative to the first. When the 2 fringe patterns are combined, the result is lowercontrast fringes. If the light source consists of many point sources distributed over a broad area, the net result will be a total loss of contrast and no fringes will be evident. Spatial coherence refers to the size of the light source, which must be small to produce visible fringes.