# Single-, double- and n-slit with visible light

A few days ago I had the idea to write a program which can render the result of n-slit experiments (I learned about the experiment at school). I was able to find a formula for the intensity:$I_G(N,\gamma,x)=\frac{1}{N^2}*(\frac{sin(\gamma*\pi*x)}{\gamma*pi*x})^2*(\frac{sin(N*\pi*x)}{sin(\pi*x)})^2$ with $x=\frac{d*sin(\alpha)}{\lambda}$ and $\gamma=\frac{a}{d}$ ($N$ being the slit count, $d$ the grating spacing, $a$ the slit width, $\lambda$ the wavelength and $\alpha$ the angle; found in the german paper "Beugung am Spalt" by Institut für Angewandte Physik, Technische Universität Hamburg).

Unfortunately I could not find any photos of the interference pattern of n-slit experiments with visible light using its full spectrum besides this one:

(source: "The Original Double Slit Experiment" by Veritasium on YouTube)

My question is the following: How do the interference patterns of n-slits (primarily 1-3 slits) with visible light actually look? My renderings look like the following but I have no idea whether they are correct in any way: The interference patterns for 1 and 2 slits looks like a lot of the photos of interference pattern with monochromatic light sources and the one with 2 slits looks similar to the one by Veritasium but I have no idea whether the renderings with 1, 3 and 4 slits even closely resemble the reality (I know that the color addition in the rendering is not perfect at the moment):

(Own rendering of 1 to 4-slit interference patterns, from top to bottom)

• There are doubtless many assumption that went into your calculation. You might make some progress by asking yourself which ones are violated in the experiment from which the actual picture is taken. I'd suggest as one possibility that the photon setup may have used an slightly extended light source (a bulb, say). Rather than either an idealized plane wave or a point source (which ever you assumed in your computational solution). – dmckee --- ex-moderator kitten Sep 25 '16 at 3:28
• @dmckee I assumed a perfect point light source in which the light is perfectly "in phase" (I hope that that is the correct term in english) and an ideal plane. And I am fairly certain that all of those assumptions are violated in the experiment of which the first picture was taken: The light source was the sun and the plane was a cardboard box. My Problem is, that I just developed a method for rendering everything like I think it should look and be like but that I, as a 12th grade high school student, have no way of verifying anything. Any my physics teacher can not help me either. – Stefan Baumann Sep 25 '16 at 8:34
• To the eye your results look reasonable. The only obvious reality violation going on is that you used an idealized light source. – dmckee --- ex-moderator kitten Sep 25 '16 at 17:04
• @dmckee Thank you for the clarification - that was the kind of answer I hoped to get (an opinion whether the renderings look good to someone with some experience with that topic - maybe that was not completely clear due to my wording). I will try to improve its "realityness" a bit but if it generally seems quite reasonable that already is something. – Stefan Baumann Sep 26 '16 at 5:05
• If anyone is interested in the program which I used to create these rendering (which I would say is mostly verified to be correct except for the assumption of perfect conditions), I published everything as an open-source project on GitHub: github.com/stefan-baumann/MultislitSimulator – Stefan Baumann Oct 1 '16 at 12:33