Before we all left for break, I introduced the equation dsinθ = mλ. With a "take good notes" warning, I diagramed the typical double-slit situation, defining each variable, and explaining how the relationship comes about. I told the class how dsinθ was the path difference between light from the top and bottom slits. I told them that m represented the number of wavelengths in the path difference. But I am confident that none of this information sunk in. (That's okay -- it's in their notes, and they'll need to see the idea of "path difference" a bazillion times before they get it. Gotta start somewhere.)
Importantly, when I introduced the equation, I did several simple qualitative demonstrations. I used both red and green lasers through a couple of diffraction gratings, each time asking which variable I was changing, and what the pattern on the screen should look like. For example, I showed the red laser through the 600 lines / cm slit. I asked, "What will happen to the dots on the screen if I use the green laser through the same slits?" They had to figure out that d and m stay the same, while λ decreases... therefore, sinθ also decreases, and the dots will get closer together. Sure enough, that was what happened.
(Why did I use a diffraction grating rather than a true double slit? It's easier for the class to see, and the mathematics are identical. Once the students know what they're doing, I'll explain and demonstrate the differences between diffraction gratings, double slits, and single slits. As an introduction, though, screw subtlties: show the diffraction grating patterns, calculate for double slits.)
As I promised, the class's assignment for our first post-vacation meeting will be a couple of very simple problems with double slits. I keep the problems barely above the plug-and-chug level to start with, because I just want them to be able to identify the correct variables, and to plug properly into the calculator. When I graded a double slit problem on the 2004 AP Physics B exam, it broke my heart to see folks who wrote down the correct equation, then seemed to plug in values randomly for each variable. Half the battle is to know what the letters mean. The other half is recognizing that 500 nm is NOT equal to 5 x 10-9 m.
For tomorrow's quiz, I'm going to be sure that everyone gets the basics. I'll give the class a problem, but not ask them to solve for anything. Rather, they must simply identify variables and write the equation. Take a look:
You may use a calculator for today’s quiz.
A red laser with wavelength 620 nm in air shines through two slits which are separated by 0.50 mm. On a screen 2.0 m away from the slits, the laser makes an interference pattern. The brightest spot is located directly in front of the two slits. The next bright spot is located 0.25 cm from the brightest spot on the screen.
1. Assign a value to the following variables for the location of the next bright spot. USE UNITS OF METERS FOR ALL DISTANCE QUANTITIES!!! (You may want to make a sketch to help you with the trigonometry.)
d = (in units of meters)
λ = (in units of meters)
2. What equation relates the variables above?
That's it! Tomorrow we'll go over subtleties, including the small angle approximation that allows for the equation x = mλL/d.
Oh, by the way... did anyone notice any problems with the picture at the top of the post?