... continued from previous post.
My Reproduction, Part II: Results and Conclusions
Results and Conclusions in a nutshell:
Now that we have nice crops, all we need to do is add up or average the pixels values in each scenario. PixInsight has an easy way to do this using the Statistics process, where it gives you the arithmetic mean of the pixel values in a given image. So that is what I used.
Arithmetic mean pixel value, Left Slit Covered: 190.468
Arithmetic mean pixel value, Right Slit Covered: 189.908
Arithmetic mean pixel value, Both Slits Open: 371.243
Figure 7: Results
According to ideal theory, the average pixel value with both slits open should be quite close to twice the average value of a single slit. Or if the slits are of slightly different size, the value with both slits open should be about the same as the single slit values added together.
Sum of single slit values:
190.468 + 189.908 = 380.376
So, my results differ from theory by about
\frac{380.376 - 371.243}{380.376} = 2.4 \%
I'd say 2.4% ain't bad, and is within my own margin of experimental error. I expect I could have even done better with more careful cropping.
So I'm going to be so bold as to claim that my results pretty much agree with theory (more-or-less).
Additional analysis:
I also wrote a C# program that sums all the pixel values together in each column to be used for plotting the 1-dimensional spacial results. Here are the resulting plots:
Figure 8: Both slits open plot.
Figure 9: Left slit covered plot.
Figure 10: Right slit covered plot.
The shapes of the diffraction/interference patterns also agree with theory.
Notice the central peak of the
both slits open plot is interestingly 4 times as high as either single slit plot. Yes, this agrees with theory and can be explained using classical theory or by quantum theory.
In the classical approach, the intensity of an electromagnetic wave is proportional to the square the amplitude of the electric field. So if you have two waves constructively interfering (doubling the electric field amplitude), the intensity increases by 2^2 = 4.
As others have pointed out, quantum theory is not necessary to explain the shapes. But you
could use quantum theory if you really wanted to. If you did you'd find the probability density of a photon landing exactly on the central peak is approximately twice that for the double slit configuration than it is for the single slit configuration. So that's a factor of 2 right there from the probability. The other factor of 2 comes from the fact that there's two slits open in the double slit scenario, so twice as many photons arrive at the detector compared to only 1 slit open. And that's the other factor of 2. So 2 \times 2 = 4.
In any case, even though the central peak is 4 times as large in the
both slits open scenario, the area under the curve is only twice as large, in part due to more frequent regions of destructive interference.
And that's about all I have on this.