# Observing Two-Beam Interference at Home

I want to know how difficult it would be for me to observe two-beam interference at home.

I have:

• A laser pointer.
• A non-polarizing beam-splitter.
• A mirror.
• Two concave lenses.
• An uneven shaky floor, some chairs, and tape.
• Patience that spans an entire day.

This is the sketch of the setup that I have in my mind: where the laser, lenses, and so on are taped to the chairs.

How close do the two paths lengths have to be to each other? In my case, the two path lengths will differ by dozens of centimeters.

The laser spot from the laser pointer is not even uniform. Will that be an issue?

Are there any other ways this could go wrong? Is there any advice on how I could observe two-beam interference?

• You need, at least, the path lengths to remain stable to well under a wavelength (they don't need to be accurate to that, just stable). For a red laser pointer that means well under 650nm: this may be hard to achieve. – tfb Aug 10 '17 at 6:06

One problem I can see with your setup is that, unless your beams are VERY long, they intersect at a steep angle. So the fringe spacing is $k\,\sin\theta$, where $\theta$ is the angle which the beams intersect at and $k$ the wavenumber. $k$ is about 12 million radians per meter or 2 million waves per meter, so even a one degree crossing angle (0.017 radians) gives you about 35 000 fringes per meter, or about a 30 micron fringe spacing. So you're going to need a microscope to see your fringes, which really is not a good idea when you are using a laser pointer - you could get quite a harmful eyeful of light. This is why one uses arrangements like the Mach-Zehnder or Michelson interferometers, so that the beams can be arranged to meet with a very small angle.

I would recommend you have a look at these instructions for a home made Michelson interferometer from the outreach people at LIGO:

LIGO Scientific Collaboration, "Build Your Own Michelson Interferometer", LIGO Document # LIGO-T1400762-v1

and there is a slightly more sophisticated version here:

LIGO Scientific Collaboration, "The Magnetic Michelson Interferometer", LIGO Document #LIGO-T0900393

It's slightly more complicated than your setup, but it will be much more controllable and there's a great many different experiments you can do with it. Be sure to post any results that show a fringe shift when you rotate the interferometer!

Another, simple setup which is easy to demonstrate is the Fizeau fringe pattern from the two surfaces of a microscope coverslip. You can get long, several centimeter by 1 centimeter coverslips of the standard thickness of about $170{\rm \mu m}$. Then, you shine the laser onto the surface of the coverslip and observe the reflexion on a screen. You get inteference between the reflexions from the two surfaces of the coverslip. See my sketch below:

The great thing about this arrangement is that the amplitudes of the two reflexions are almost identical, which means you get highly visible fringes (the nulls go almost completely dark). Here's an image from a 3cm x 1cm #1 coverslip taken with a 532nm semiconductor laser. My screen was the far wall of the room, and the image you see is about a half a meter across. So the fringes are very well observable in this case. The bending you see actually comes from the distortion of the coverslip's surface: it's showing you that there is a curvature on one surface that is not present on the other.

• Thank you! This was the most direct answer to my question. I'm very grateful for those pdf resources that were linked. You also saved me A LOT of trouble by mentioning the fact that the beams would have to be extremely long in my scenario. (I haven't done anything yet, but I might do something pertaining to this in the future.) – SpiralRain Sep 10 '17 at 4:29
• @SpiralRain Be sure to build an interferometer at some stage: if you google "alignment Michelson interferometer" there are quite a few helpful YouTube videos on the procedure. I'm not much of an experimenter, but I have taught myself interferometry pretty well and, although you need patience, it's a really fun once you get the knack. A sound theoretical understanding of what the light is doing does help a great deal in alignment. – WetSavannaAnimal Sep 10 '17 at 9:07

Have a go at setting up Lloyd's mirror which I have just done.

You produce two coherent sources by have a source and its image in a mirror.
Where the direct beam (red) and the reflected beam overlap (grey) you get interference fringes.
Note that the zero order fringe (equal path differences) is dark because there is a $\pi$ phase change on reflection from an optically more dense material (glass) and so the two coherent sources are $\pi$ out of phase.

Here is my set up with adjustments done using blutac and my hand as I have to press a switch to turn on the laser.

I used a microscope slide as microscope slides are reasonably flat. On front surfaced optical flat might well have improved the contrast.
The magnifier just spreads the light from the laser to increase the region over which interference occurs.
Without it it the fringes can be seen as a row of points of light.

You should use glancing incidence and you will see two circular beams on the screen (wall?).

As you move the laser beam get the two circles to overlap and you should see some fringes.

I held an iPhone in one hand and pressed the laser button with another hand so the quality of the fringes can be improved on.

• +1 Awesome! BluTak, microscope slide, a loupe and a laser pointer. – WetSavannaAnimal Aug 10 '17 at 12:20

The setup you describe is similar to the one used in creating holograms. All you would need to add would be the beam spreaders.

Unfortunately, this demands a level of stillness which is hard to achieve without a properly isolated optical bench. Red lasers are roughly 650nm, and if you want to see effects, you're going to want the path length to be stable down to 1/10th of that or better (1/10th being a reasonable heuristic). That kind of precision is not found with a few chairs. To do this, holographers set up an optical bench that is properly isolated. A DIY solution which has been recommended to novice holographers is to get an innertube and put a heavy piece of granite on top (sometimes the places which cut granite counters will have leftovers that you can get!). The heavier the better! Anchor everything to that piece of granite. Then, turn off your air conditioner and wait a bit -- the differences in air densities will affect holograms, so it will affect your measurements as well.

• Without the beam splitter, which is a way of forcing the beams from two coherent sources to overlap, this is just a Lloyd's mirror arrangement and the fringes can be observed using a laser with the minimum of effort. – Farcher Aug 10 '17 at 10:41

I think you need less than that, though my setup may result in a very narrow viewing region.

A concave lens form a virtual image behind it, reflect the image with a mirror and you get two point sources.

• The reflected beam cannot interferer with itself. You have missed out the direct beam from the real source to the viewing region. – Farcher Aug 10 '17 at 10:42
• @Farcher well technically you are right; I omitted the beams from the original image. I simply assumed it could cover the whole wall, but its mirror image could cover only that region as restricted by the mirror size. – Carl Lei Aug 10 '17 at 11:45