Quantum Basics 1 of 3

Quantum Basics 2 of 3

Quantum Basics 3 of 3

You might think that experiments involving Quantum Mechanics require a giant laboratory and a team of researchers but there several experiments you can do yourself with easily available materials. Quantum interference, quantized energy levels, and that non-orthogonal states that are not mutually exclusive; are testable claims that *individuals* can check. But I’m getting ahead of myself – this post is just about the first of these claims, that the paths of particles interfere with each other as though they are waves.

Now technically this experience just proves that light has a wave character and could be described classically as though light is a simple wave – but we can handle why that’s an incomplete explanation i the next blog post. For now let’s get down to the details of this experiment.

**Materials: **You’ll need a small hand-held laser, some “LEAD” (graphite) mechanical pencil refills, a card (you can use the packaging backing or note cards), opaque tape, a ruler and a tape measure.

**Experimental steps:**

- Begin by making a rectangular hole in the card. This is the area that the slits will be built over.
- Next cut 4 strips off the card and tape the pencil refills to the one edge of each strip. Try to minimize any gaps between the card and the graphite stick, then place a piece of tape over top and bottom of the refill being sure to leave the central portion clear of tape. If you can’t get a good alignment try trimming the strip of card so it’s straighter or use your tape to half cover the graphite stick, being sure not to overlap the pencil refill.
- Next place two of the strips side by side over the hole you made earlier. Push them right up next to each other with the graphite sticks facing. The tape should make a small gap between the graphite. If not you can manually spread the strips slightly apart. Once satisfied tape in place, insuring you leave the gap you created.
- Do almost the same for the second pair of graphite sticks except this time place one more pencil refill between the two that are attached to cards. This should result in a clean double slit separated by the single pencil refill in the middle. Tape in place.
- Tape over any gaps in the cards or tape other than the single and double slit that you just made.
- Test your slits. Play around with shining a light from the toy laser through the single slit and then the double slit. You may place the laser directly against the slits in the card. If the slits were correctly built you should see no light and dark patches for the single slit and clear light and dark spots for the double slit. It may be helpful to have a partner check what the light pattern looks like when projected from over 1 meter away. If no partner is available you can use overturned cups (as shown in the video) to make sure you have clear light and dark patterns.
- Now set up a ruler on the wall or screen you are aiming the laser towards.
- Next measure the distance between the card and the wall/screen. This had to be greater than 1 meter. You will have more accurate results the larger you can make this distance.
- Shine the laser through the double slit. You may use a partner or position the laser so that it stays on while you make measurements.
- Take the necessary measurements for the math below. This includes, length on the wall between some number of fringes (light and dark spots), the number of fringes, distance to the wall and the distance between the two slits of the double slit (this will be the mm size of the pencil refill).

**Data:**

For my setup the specific values were as follows:

Number of fringes (N) =6

Distance to wall (X)=1.3m (130cm)

Distance between fringes (Y) = 0.00925m (9mm)

Distance between slits (D)=0.0005m (0.5mm)

**Math:**

The math used in this set up is what is called a small angle approximation. The math can be much more complex than this but since the distance to the wall or screen is much greater (4 orders of magnitude in fact) what would normally be trigonometric functions and variables simplify greatly (loosely the small angle approximation just takes the first term of the power series of a trig function and assumes it’s the entire value so sin(x)=x, tan(x)=x and cos(x)=1). So instead of having to deal with an equation like this:

(eq1)

Where X is the distance to the wall, θ (theta) is the angle between the face of the slits and the angle to the maximum on the wall, N is the number of fringes and λ (lambda) is the wavelength – and having to figure out the exact angle between your card and a screen/wall that is over a meter away you can simplify the equation to this:

(eq2)

Where Y is the length between the counted fringes on the wall/screen, D is the distance between the slits, N is still the number of fringes, X is the distance between the card and the wall/screen and λ (lambda) is still the wavelength. While the equation technically needs more inputs the elimination of the trigonometric element simplifies the math, plus all these values can be measured more easily. Taking from equation 2 and plugging the values (see data section) I got:

(eq3)

This is just at the edge of wavelengths that could be considered red. While my values wernt perfect I’m still pretty pleased with this value. Allowing for a 0.5mm variability in the length on the wall and a 1cm variability in the distance to the wall/screen and rounding to two significant figures I get the following value for the wavelength:

590 ± 20 nm

Max Wavelength

Min Wavelength

This is slightly different from what I said in the recording (I calculated wrong at the time). This is relatively close to the value printed on the toy laser I used.

**Error analysis:**

According to the label the wavelength of the laser was between 630nm and 650nm. If I assume that the peak of the light was at the mean value (640nm) I can calculate the percent error between my experimental value and the printed value.

Giving a value of 7.8% error in my calculation. However considering that I have a range of possible values for my measurement and a range of possible values for the printed value the error itself has an uncertainty. If I take the minimum and maximum values for the percent error and average them the percent error moves down slightly to 7.7% with an uncertainty of ±4.5%. I’d say that’s pretty loose but this could easily be improved upon. If you try this see if you can do better. If you can take the distance to the screen to be very large (several meters) the value you can get will improve greatly.

**Linkography:**

https://en.wikipedia.org/wiki/Double-slit_experiment

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/slits.html

http://hyperphysics.phy-astr.gsu.edu/hbase/trgser.html#c2

http://www.studyphysics.ca/newnotes/20/unit04_light/chp1719_light/lesson58.htm

http://www.wolframalpha.com/input/?i=red+light

http://astro.physics.uiowa.edu/ITU/glossary/percent-error-formula/

https://www.youtube.com/watch?v=dEaecUuEqfc

https://www.youtube.com/watch?v=a8FTr2qMutA

## 2 Comments