Hello, and welcome back to MPC! Last week, we discussed some of the theory behind matter waves. This week, we will start discussing the experimental proof for the existence of matter waves.

Before we resume our discussion on matter waves, we have to obtain a better understanding of the double-slit experiment. In a previous post, we discussed how waves emanating from two nearby sources will interfere to create an interesting pattern.

Figure 1: An interesting interference pattern

(image source: https://i.ytimg.com/vi/fjaPGkOX-wo/maxresdefault.jpg)

In that post, we discovered that light is able to interfere in this way, allowing scientists to confirm that light has wave-like properties.

It is easy to see the pattern in Figure 1 because it was created with ocean (water) waves. However, how were scientists able to see this pattern with light? There are many answers that may come to mind. For instance, the double-slit experiment example that we originally discussed involved dropping two rocks into a pond.

Figure 2: Creating water waves using rocks

It is easy to think that, just how two sources of water waves (two rocks) are able to create the interference pattern we are interested in, simply having two sources of light will also create the interference pattern. For instance, you could try shining two adjacent flashlights on a wall:

Figure 3: Shining two flashlights on a wall

As you will soon see, though, this does not produce the desired result. Instead, it results in two blobs of light on the wall.

Figure 4: Result of shining two flashlights on a wall

That’s not very interesting! It does not seem like the two lights are interfering at all!

However, just because the lights do not seem to be interfering with each other in Figure 4 does not mean that light lacks wave-like properties. The light that comes out of a flashlight is rather “disordered” (specifically, in Figure 3 / Figure 4 the two light sources are incoherent; to find out more about what this means, be sure to check out the links at the bottom of this post). Perhaps we would obtain better results if our experiment were more “controlled.”

Amazingly enough, physicists managed to create a more controlled experiment: the double-slit experiment. To understand their approach, we need to understand an(other) important property of waves: diffraction!

Diffraction is a phenomenon in which waves bend around corners. For our purposes, we are particularly interested in what happens when a wave approaches a small opening (slit) in an object, such as a wall:

Figure 5: A wave approaching a slit in a wall

**Note: The orange arrow indicates the direction that the wave is propagating in.**

When the wave in Figure 5 reaches the small slit, it will actually bend, or diffract, around the two corners of the slit:

Figure 6: When the wave reaches the slit, it will bend around the two corners of the slit

This results in the wave spreading out (radially) from the slit in the wall:

Figure 7: The wave appears to emanate radially from the wall

Now, this is where things get interesting! Imagine shining a monochromatic (i.e. only one color; red in this case) light on a wall that has two adjacent slits in it:

Figure 8: A wall with two adjacent slits in it

**Note: The red arrow indicates the direction that the wave is propagating in.**

When the light wave reaches the wall, it will actually “bend” around the corners of both slits!

Figure 9: The light wave diffracts around the corners of both slits

**Note: For those of you with a little more physics knowledge, the waves emanating from the two slits are coherent.**

Generally speaking, this experimental set-up (waves approaching a wall with two slits in it), is known as the double-slit experiment.

The interference between the waves emanating from the two slits in Figure 9 may look familiar — it looks just like the interference of the waves in Figure 2! The only difference between these two figures is that the waves in Figure 2 are water waves whereas the waves in Figure 9 are light waves! Of course, just as the water waves did, the light waves will interfere constructively and destructively to create an intriguing pattern!

What is this “intriguing pattern”? When conducting the double-slit experiment, what did physicists see that confirmed that the light waves were interfering with each other? Well, when you shine a flashlight on a wall, the light simply creates a giant blob on the wall. We must now ask, what does the light passing through the double-slit set-up (specifically the double-slit set-up — not just two flashlights shining on a wall) look like when it hits a wall? Does it also just look like a blob?

Believe it or not, the light actually creates this strange pattern:

Figure 10: The interference pattern generated on a wall by the double-slit experiment with light

(image source: http://www.sciencephoto.com/image/157198/530wm/C0094585-Double-slit_Experiment-SPL.jpg)

Although this pattern seems odd at first, it makes perfect sense when we consider what we know about the interference of waves. The brightest spots on the wall are simply where the waves are interfering constructively (“helping each other”) and the darkest spots on the wall are where the waves are interfering destructively (“canceling each other out”):

Figure 11: Locations of constructive interference and destructive interference

**Note: Blue arrows are locations of constructive interference, green arrows are locations of destructive interference.**

(image source: http://www.sciencephoto.com/image/157198/530wm/C0094585-Double-slit_Experiment-SPL.jpg)

It is extremely important to note that the diffraction, interference patterns, etc. we have been discussing for light only occur because light has wave-like properties. When the double-slit experiment for light was originally conducted in the 19th century, physicists had no clue what the true nature of light was. In fact, before the double-slit experiment was conducted, all of the results we have discussed (including the interference pattern in Figure 10) had only been predicted using theory— physicists predicted that, if light did have wave-like properties, the double-slit experiment would produce the results seen in Figure 10. When the double-slit experiment yielded these results, physicists took it as confirmation that light has wave-like properties.

That is all for this week! Next week, we will start looking at another double-slit experiment: a double-slit experiment with electrons. If you do not think the concepts we have been discussing are strange enough, just wait until next week! See you then!

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For more information, be sure to check out these resources: http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/opt/mch/diff.rxml, http://www.phys.lsu.edu/~jzhang/Chap27.pdf, http://www.hep.fsu.edu/~wahl/phy1020/spr97/homework/hwk08/hwk08.html, http://www.physicsclassroom.com/class/light/Lesson-3/Young-s-Experiment, http://www.s-cool.co.uk/gifs/a-phy-osdiff-dia49.gif

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