Experiment 3: Interference

The wave-particle duality of light is one of nature’s most baffling realities – and the confusion is rightly so. The true nature of light had, in fact, perplexed scientists for decades before the strange concept of wave-particle duality came to light. The likes of Isaac Newton vehemently backed the idea that light was a particle, yet on the other corner, existing and forthcoming theory from prominent names such as Christopher Huygens, seemed to indicate that light was wave. It wasn’t until the year 1803, that English physicist Thomas Young finally confirmed the apparent behaviour of light as a wave, in his famous yet surprisingly elegant demonstration, the double slit experiment. Yet the solidification of the wave aspect of light did not mean the end of its understanding as a particle. As Albert Einstein eloquently put it, "It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do". It then became apparent that these two seemingly irreconcilable ideas, when put together, revealed the true nature of light.

Here’s a thought experiment. Imagine aiming a loaded shotgun at two adjacent walls, standing a few feet apart from each other. Aiming straight at a slit in the first wall, fire a stream of bullets using a shotgun (these guns spread their bullets out). Looking at the other side of the wall, what kind of impact mark would these bullets leave on the second wall? Well, the answer is quite intuitive. The bullets that made it through would obviously leave a line of tiny craters on the wall’s surface. Next, cut a second slit into the wall, just beside the first one. Firing the shotgun once again, what would you expect to happen? Well, a duplicate of the first turnout should happen. Now you have two lines of bullet marks on the second wall. Now let’s look at how waves would interact with this setup. This time, imagine the two walls half submerged in a pool of water. Let’s take it a step further and say the back wall lights up where it is hit with the most intensity. A single ball bobbing up and down in the water will serve as a wave source. As these waves travel through the single slit and hit the back wall, the area of brightness left on the wall would be at a maximum directly in front of the slit, and decrease as it goes further to the sides. Repeating the process with the double slit setup, what pattern would you expect to emerge on the back wall? Intuitively, it should be once again a duplicate of the single slit setup, which would be two bands of light side-by-side with decreasing intensity from the center. However, intuition can only get us so far. What actually happens is this. 

Figure 1: Double slit diffraction

Suddenly, it is not just two bands that appear. As you can see, the ratio of slit to band is not one-to-one. So if that’s not what’s going on, then what is? In order to get a grasp of what is happening, we must first understand the concept of interference.

Interference is one of the things that make waves and particles fundamentally different in behaviour. When two particles collide, you could get a change in direction, a transfer of momentum, or even obliteration. However, when two wave pulses with the same amplitude meet, depending on their amplitude’s signs (this can be interpreted as facing up or down), two possible things could happen. In the case that the two wave pulses exhibit the same sign in amplitude, what would happen is the two waves would add to each other to form a single wave of with an amplitude equal to the sum of the two waves’ initial amplitudes. This is called constructive interference. On the other hand, if two wave pulses with opposite signs in amplitude meet, they would simply cancel each other out, leaving their location of collision flat and undisturbed. This is called destructive interference. It is these two concepts that explain the behaviour of a wave when passed through two adjacent slits. As the initial wave hits the slits, it splits into two separate source points, generating two different waves beyond the first wall. These two waves then interact with one another as they radiate forward. The alternating light and dark bands on the wall are representative of the parts of the wave where instructive or destructive interference occurred respectively.  The resulting array is called a diffraction pattern.

Now let’s take that shotgun we were talking about a while back, and shrink it down to a quantum level, where instead of having bullets for ammunition, we fire photons. Starting with the single slit setup, we fire photons into the wall. What results is a splay of photon marks plastered on the second wall in the shape of a slit. Typical particle behaviour. Moving on to the double slit setup, we fire the photon gun once more. But this time, instead of seeing two slit-like patterns on the second wall, we observe a diffraction pattern splayed across the wall. Could it be the photons colliding with each other to cause more than two bands to appear on the wall? We then fire photons one at a time to remove the possibility of the photons colliding with each other. Surely a particle can’t collide with itself. Upon firing, however, we see the same result – another diffraction pattern. This is in fact, very similar in essence to Thomas Young’s double-slit experiment. And it was this experiment that led to the inescapable conclusion that light is indeed simultaneously both a particle and a wave.

The experiment we conducted (we’re talking about the experiment done in this very study), however, takes the slit diffraction concept to a bit of a more complex level. All the previous examples worked on the assumption that the slits were just wide enough to fit a single particle. In reality, mechanical constraints obviously prevent us from creating slits of such infinitesimal widths; so what we end up working with are slits of considerably small widths, but at the same time are very large when compared to the photons we shoot through the slits. According to Huygen’s principle, each point on a wave front can be thought of as point source of an individual wave. So in essence, what it means is that a single wave front is in fact an infinite number of wave fronts that, when combined, result in a single and coherent wave. It may be hard to grasp, but it can be understood better when we recognize that all of these individual waves interfere with one another. The reason why we see only a single wave front is that everything else has destructively interfered, and what remains is the only result of constructive interference. When a laser beam is fired through an actual and realistic slit, the light that makes it through the slit diffracts into its individual source-points, causing an enormous number of waves to occur and interfere simultaneously, in turn causing a diffraction pattern to appear on the second wall. And in fact, this is how the first part of the experiment went.
A monochromatic red laser was fired through a single slit, producing a diffraction pattern on the wall. Although pictures were not able to be taken, here is a graphical representation of what turned out.

Figure 2: Intensity plot of diffraction pattern as a result of monochromatic light passing through a slit

A series of fringes were splayed across the wall, with the brightest and widest of them all, called the central maxima, at the center. The goal of this experiment was to determine the width of the slit, using the other measureable factors of the experiment. Namely, these other measureable factors were, the distance L of the pattern from the slit, the wavelength of the light source λ, and the angle θ indicated on the figure. By setting y=0 to be the center of the central maximum (the brightest intensity maximum), the locations of the intensity minimums (dark fringes) could also be measured. To solve for the width of the slit a, a simple and elegant equation was used

Before calculating for the slit width, the wavelength of the light source was first calculated for. After manually measuring all variables (using rulers and meter sticks) except and using the given specs of the stup, the measured quantities were tabulated and the wavelength was calculated for in two different situations. The first using a slit with a known width of 0.02 mm, and the second using a slit with a given width of 0.04 mm.

Table 1: Wavelength of the Laser diode

	m = 1, slit width = 0.02mm	m = 1, slit width = 0.04mm
distance between side orders	10.3 cm	2.7 cm
center to side	5.15 cm	1.35 cm
Calculated wavelength	624 nm	327 nm
% difference	4%	49.7%
slit to screen distance	1.65 m	1.65m
Average wavelength	475.5 nm

The first calculated wavelength turned out pretty well, with just a 4% deviation from its known value. The second setup, however, deviated by 49.7%. Next, the slit width was calculated for using the given wavelength of 650 nm.

Table 2: Data and results for the 0.04 mm single slit

	m=1	m=2
Distance between side orders	2.7 cm	5 cm
Distance from center to side	1.35 cm	2.5 cm
Calculated slit width	0.08 mm	0.08 mm
Percent difference	114.5%	114.5%

The calculated slit difference turned out to be consistent for both values of m. On a side note, the precision of the results makes me doubt the integrity of our measurements, and this is furthered by the fact that if we use the distance between side orders instead of the distance from center to side in our calculations, we end up with a calculated slit width if 0.04 mm. Curious. However, with what we have right now, 114.5% is the percent devation of our results.
The following portion of the experiment, this time, dealt with a double-slit setup. The result was akin to a combination of what went on during the single slit setup. However, with two sources of light, one from each slit, a second source of diffraction occurred. Just like the pattern produced in the single slit setup, what is called a diffraction envelope was displayed on the wall. Here are some borrowed pictures of the two setups (Figure 3).

Figure 3. Difference between single slit and double slit diffraction patterns.

Figure 4. Diffraction envelope and interference fringes of double slit setup

however, a noticeable difference between the two setups is the presence of many small, equally spaced, and alternating light and dark fringes occurring inside each diffraction envelope. These are called interference fringes. This is, as mentioned above, the result of the two light sources (coming from each slit) interfering with each other. It is also worth mentioning that like the single slit diffraction pattern, the diffraction envelope loses brightness as you move to its sides. Thus, the tiny fringes inside the envelope follow suit (Figure 4).

Since the diffraction envelope is highly similar to the diffraction pattern produced by the single-slit setup, the same equation (1) was used to calculate the slit width using data gathered from the double slit setup.

Table 3: Data and results for the a = 0.04 mm, d = 0.25 mm double slit

	m=1	m=2
distance between side orders	5.1 cm	6.85 cm
center to side	2.55 cm	3.425 cm
Calculated slit width	.0421 mm	.063 mm
% difference	5.30%	57.50%

Once again, the first order’s results turned out relatively fine at 5.3% deviation, but the second order’s calculations yielded a 57.5% error.
Finally, the last part of the experiment involved the simple counting and measuring of the interference fringes in the diffraction envelopes.

Table 4: Data and results for double-slit interfence

	Slit width: 0.04 mm Slit separation: .25 mm	Slit width: 0.04 mm Slit separation: .50 mm	Slit width: 0.08 mm Slit separation: .25 mm	Slit width: 0.08 mm Slit separation: .50 mm
number of fringes	12	25	14	12
width of central maximum	5.1 cm	5.35 cm	5 cm	2.1 cm
Fringe Width	.425 cm	.214 cm	.357 cm	.175 cm

At the end of the experiment, here were some notable observations. As the slit width decreases, the diffraction envelopes increase sin length. Also, the fringe width increases as the wavelength increases, and likewise, as the distance of slit to surface increases, so does the fringe width. These are all in line with the experimental observations, yet can also be inferred from equation (1). Similarly, since the patterns in the double slit setup go by the equation 

The mentioned relationships above are practically the same. It was also predicted that when the slit width was changed, the diffraction envelope and the interference patterns would remain the same in width; only changing in focus and clarity. However, due to faulty data (most likely due to error in the measuring process), the data was not in line with these predictions (refer to Table 4). Lastly, it was seen that as the slit separation was increased, the number of interference fringes within the diffraction envelope increase. At the same time, the width of the fringes decreased. These were consistent with observations (refer to Table 4).

In totality, the experiment demonstrated some key characteristics of light's nature as a wave, while also showing us that not everything can be derived from intuition alone.

Sources:

[1] Dr Quantum: Wave Particle Duality and the Observer! Youtube. 12 Mar. 2011. Television.

[2] "Experiment 8 Interference and Diffraction." Physics 103.1 Experiment Manual. Quezon City:               National Institute of Physics, 2011. N. pag. Print.
[3] Double slit diffraction. Digital image. Youtube. N.p., n.d. Web. 24 Feb. 2016.                                       <https://i.ytimg.com/vi/yaEym48DGkw/maxresdefault.jpg>.