- figure 3.1 - represents the circular crests - the maximum height - of the supposed waves. Where these wave crests, expanding from slits A and B, intersect, they reinforce each other and create a higher wave crest, a maximum. Where the wave troughs - the minimum heights - extending from A meet the wave crests from B - and vice versa for B and A - they will annihilate each other.
In Young's sketch you can clearly see that the maxima will be found along the lines fanning out from between the slits. These lines are formed by connecting the intersecting wave crests. Where those lines of maximum wave crests reach the screen (C-D-E-F), the light will show maximal intensity. Halfway in between these maximum wave crests the light waves will annihilate each other so you will observe darkness where they reach the screen. This reinforcing and annihilating phenomenon is called interference.
Wikipedia: In physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive interference result from the interaction of waves that are correlated or coherent [1] with each other, either because they come from the same source or because they have the same or nearly the same frequency [2]. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves [3]. The resulting images or graphs are called interferograms.
The moiré effect [4] - see figure 3.2 - is also an interference phenomenon. When you slide two sets of concentric circles, drawn on transparent material, over each other the visual result is utterly similar to Young's drawing in figure 3.1. Watch this in the moiré animation film by Amanita [5]. Where the circles overlap the interference is constructive. Observe how the curves of constructive interference move depending on the varying distance of the two central circles that can be equated to the two wave sources in the slits.
Figure 3.2: Moiré effect of two overlapping sets of concentric circles. Compare this with Young's sketch of wave interference.
Source: Wikimedia Commons.
Frequency - usually denoted by the Latin letter f or the Greek letter ν (pronounced 'nu') - tells us the number of complete vibrations per second. The international standard unit for frequency is the Hertz (Hz), which is the number of oscillations per second. The most elementary wave type used in physics is the sine wave. The phase of a sine wave is expressed in degrees of a circle and represents the state of the wave within the timespan of a full oscillation period. So:
0o is the moment when the wave height is zero and rising,
90o is the moment when the wave height is maximal (a crest),
180o is the moment when the wave height is zero and falling,
270o is the situation when the wave height is minimal (a trough).
When two waves are in opposite phase, their phase difference is 180o.The value of the deflection from the middle where the maximal height is reached (90o) is called: the peak amplitude [6].
Figure 3.3: Constructive and destructive interference.
Source: Wikimedia Commons.
The bold wave (upper left) or line (upper right) in figure 3.3 shows the oscillation of a single point in time. Think of a fishing float going up and down with waves coming from two different sources. The horizontal axis is the time line of up and down movement of the float. Both bold graphs are the summation of the two thinner drawn waves below. These are the waves meeting each other at that fishing float. The two thinly drawn waves on the lower left arrive in-phase at the float. Adding these two waves together will produce constructive interference, resulting in a greater peak amplitude of the float at their meeting point. The two waves on the right meet each other at the float with opposite phases. They extinguish each other completely, which is called destructive interference. The float will be at rest.
This summing of waves is called superposition. Interference and superposition are concepts that will become important in understanding the double-slit experiments we will encounter repeatedly in this book.
Figure 3.4: Interference as a result from differences in traveled distance . P is the location of the first maximum. The wavelength will then be equal to δ.
Figure 3.4, with a monochromatic light source on the left, two slits and a screen, shows the geometric approach taken for explaining the interference effect by considering path length differences.
Please note: the distance O-Q of the double-slit to the screen, as compared with the distance between the slits S1-S2, is depicted here considerably smaller than it is in a real experimental set-up.
Circular wave fronts originating from the source on the left arrive simultaneously in the slits S1 and S2. As a result, synchronous oscillating elementary wave sources originate in S1 and S2. Synchronous elementary Huygens waves will depart then from S1 and S2. When O-Q is considerably longer than the mutual slit distance S1-S2, the path-length difference between S1-P and S2-P can be determined, in very good approximation, by drawing a line from S1 perpendicular to S2-P. This creates two similar triangles S2-R-S1 and Q-O-P. From this follows the geometrical relationship:
δ : S1-S2 = O-P : P-Q.
When δ is exactly equal to an integer number of wavelengths, the arriving waves will constructively reinforce each other, and a maximum of light intensity will appear at P. But when δ is exactly equal to an odd number of half-wave lengths, the waves will arrive at the screen with opposite phases. This causes destructive interference and therefore a minimum, which will be observed as a dark band. When P is the first observed maximum, counting from the central maximum in O in figure 3.4, δ has to be equal to the wavelength: λ. This can be used to measure λ very accurately.
From this moment in history, interference is among physicists the undisputed signature of a wave phenomenon. However, less than a century later, a major and paradoxical problem arose with this wave concept of light.
Do you see perhaps the logical error that is made here? The logical reasoning here is "If light is a wave, then we will see interference, so if we see interference, light is a wave." Which is the same logic as "If B follows from A then A follows from B". I hope you agree with me that this is not strictly correct conform the rules of logic. As you will understand later, this rather loose logic will become the source of the wave particle paradox of light emerging in the start of the 20th century.
Please note here: Thomas Young's (1805) double-slit interference test has become a very basic experiment in the research and understanding of quantum
