Brewster’s angle is the angle at which light of a certain polarisation won’t reflect off a surface. The resulting reflection will then be made up of only light from a single polarisation (p-polarised). This little optical quirk is how polarised lenses remove lots of scattered reflections in photographs and why polarised sunglasses are so much better when lounging by the seaside. However, rather than just being something that makes sunny days even better, it also provides a neat trick for visualising things that would otherwise be invisible to other analytical methods.

‘Simple’ Brewster’s angle schematic

Brewster’s angle for water is approximately 53.1°, which is calculated from knowing the refractive index of the water and the surrounding air. If either one of these values was to change, then the angle would also change. For example, if your measured the Brewster’s angle of a film of olive oil (refractive index of ~1.46) you’d get around 55.7° which is quite a big shift (relative to most things in optics).

Now, if you set up a light source and camera at exactly 53.1° over a tank of water and  block all the s-polarised light bouncing off the surface into the camera then all you will see is black. If you introduce to the water surface a contaminate, such as oil, this will change the Brewster’s angle and so the water will begin to reflect p-polarised light, which will pass straight through the s-polarised filter and into the camera. So, from the camera’s point of view, the water will appear black and the oil will appear bright. This will work no matter how thinly the material is spread, so if you have just a single molecule thick layer (~2 nm which is around the same thickness as a single strand of DNA) this will still show up nice and bright on the camera. (this is much clearer in the video but we’ll get to that in a moment).

Looking at materials like this provides a wealth of information to scientists on the way materials interact with each other or with the water beneath them. In the main this is used as a tool for examining materials for further use in applications such as benzene sensing or medical device coatings or examining a range of novel exotic materials. However it is not a commonly used technique, one reason for which is cost of a Brewster Angle Microscope (BAM). Recent developments in Micro-BAMs have brought the cost down but a BAM currently costs anything from £20,000 – £75,000, which is serious money. When I did this work I was a lowly PhD student with purchasing authority for the grand sum of £0, which is some way off £20,000, so I realised that if I wanted some nice pictures of my materials then I would need to get creative.

Lego BAM rig set up over a NIMA monolayer trough

The photograph above shows the second generation design of my home made BAM. The first design was made using laboratory retort stands which just about worked but the lack of gearing, motors or align-able parts meant it took a hour just to get a poor quality fuzzy image. The second generation has the major advantage of being made with Lego. A vital part of the BAM is getting the laser (1 mW green laser pen from SP3Plus Ltd) and the camera ( VMS-001 Veho, bought second hand) to align correctly.  This was big problem in the hand-adjusted  version because, not only were we trying to get the angle right, we were also trying to line up the the laser and the microscope. Lego neatly solved this problem by having such insanely high tolerances (~10 µm) on it’s parts, so I knew that if I build two identical frames and mounted the laser in the centre of one and the camera in the centre of the other they would aligned well enough to get a 0.5 mm beam into a 2.5 mm camera aperture. The frames shown also include motors and gearing to allow for simple changing of the angle of the camera or laser. These motors were re-calibrated at the start of every experiment so that specific changes could be made for an accurate measurement of the Brewster’s angle for the material being used. Attaching the laser and the camera to the frames was a little trickier as unfortunately neither Veoh or Sp3 make their respective kit with lego mounting or dimensions in mind. Conveniently, the Sp3 laser did come with a mounting rig which had mounting pins on the bottom plate, by chance these pins were within 0.5 mm of the required positions to simply drop them in to lego frame, this was quickly rectified with some sand paper. The camera however didn’t come with anything and was mounted using a V-shpaed holder this ensured that the centre of the camera lined up with the laser and it also allowed for an additional mount for a polarising lens to cover the camera aperture. More photographs of the finished system can be found here and here.

Finally once it was all set up the system was tested with some stearic acid (a common fatty acid) and it produced the video shown below.

As I mentioned before, the white shapes in this video are the stearic acid material floating on the black background. The shapes shown will naturally move around in the air currents in the lab and any residual currents in the water the material is spread on. The material spread in this video has been prepared in such a way that the film shown is only 1 molecule thick. In some regions it may be more than this and these show up brighter than the majority of the film.

The microscope is currently undergoing a re-design  and I hope that the 3rd generation will produce even clear images (auto focusing) over a wider area. I am also quietly optimistic that I can also motorise the polarising lenses, which would allow me to collect much more data on each material. Once improved I’ll publish a follow up set of results here. In the mean time you can always follow me on twitter (@MCeeP) to get some more detail on this and other work we do.

### Hi there!

#### David · 1 October 2012 at 20:24

“Now, if you set up a light source and camera at exactly 53.1° over a tank of water and *block all the s-polarised* light bouncing off the surface into the camera then all you will see is black”.

The Brewster angle is already doing this, don’t? Why do you put this s-filter?

Also, very good project. A good example for Brewster angle in class.

#### MCeeP · 1 October 2012 at 20:30

The filter is needed because only the central portion of the beam is at exactly the right angle, the edges are +/- of 53.1° so without the filter you get a very small area surrounded by haze. The polarising filter is really there just just help clean up this slight discrepancy.

When I build the next version I’ll document it a bit better so that others can copy the design of teaching. If your intreated we also have some of very simple experiments you can do with monolayers using food dye that are visually quite spectacular. I’ll try and do a blog post on the technique in the not to distant future.

#### HP Ink Coupons · 2 October 2012 at 00:54

Hi MCeeP,
excelent project!!! Lego is universal tools 🙂

Thanks for share.

#### Gus · 2 October 2012 at 04:19

In your figure, did you swap the labeling of the s and p polarizations? p polarization (transverse magnetic polarization, really) is defined as the polarization with the electric field in the plane defined by the incident ray and the normal to the the interface layer (see http://en.wikipedia.org/wiki/Brewster%27s_angle). I learned a trick (credit to the Univ. or Rochester) to tell between the two: Imagine that you throw a flat pebble (aligned with the electric field) at a grazing angle to the sea (assumed flat); the pebble will Skip; if you turn it 90°(corresponding to transverse electric polarization) and then throw it, it will Plunge.

This skip-plunge analogy helps me remember the formulas of some of the equations describing reflection. If θ is the angle of incidence and φ the angle of refraction (as measured from the surface normal), and n1 and n2 the indices of refraction, n1 being the refractive index in the incidence medium, then the reflection coefficients are

(n1*cosθ-n2*cosφ)÷(n1*cosθ+n2*cosφ) for the s-polarization, and
(n1/cosθ-n2/cosφ)÷(n1/cosθ+n2/cosφ) for the p-polarization (pairing the refractive index of each medium with the angle measured in the same medium), so in this form the cosines “skip” and “plunge,” just like the actual rays.

Superb article. Maybe you should consider selling this microscope? If the price is right, I think many would prefer buying than bother building one. The Arduino boards are an example. They are open, they are inexpensive, but the guys who started the Arduino as a hobby cannot make those boards fast enough.

#### MCeeP · 2 October 2012 at 07:16

Yes I had swapped p and s in the image, it has been corrected thanks for catching it! I liked you analogy for explaining the difference between the two types of waves, in future I may steal it (if you don’t mind?) to explain some of this when we do demos or talks in schools.

I’m not sure we could sell it to people, at least not in it’s current state, it’s too easy to break. I suppose with further development (and some 3D printed parts) we could produce a version that was lab/school friendly, something we may think about in the future.

I’m glad you liked the article, we hope to put up more interesting articles from the rest of the team every week. I can’t promise that future posts will contain lego but we do end up playing with some odd hacked together stuff.

#### Gus · 3 October 2012 at 06:26

No problem, use the skip and plunge analogy as you wish. After all, I was not the one who came up with it; I gave credit for it to the Univ. of Rochester, Rochester, NY, USA.

I will be monitoring this site religiously from now on. I came to it from the hackaday.com site.

#### Patrick · 2 October 2012 at 17:48

I really liked how you explained things (you made some points clearer, thanks!)

BTW, you’re very right about that Arduino thing. Arduino became very successful not because of the board itself, but the convenience and user-friendliness it provides (makes programming uC’s easier even for children, which is also what the Raspberry Pi Org. is trying to achieve). Commercial BAM’s cost money for their accuracy, precision, and quality. It’s like comparing legit devices vs China made (quality and quantity vs. price).

#### Gus · 3 October 2012 at 06:44

🙂

The arduino has taken the embedded world by storm. I think that ALL μcontroller manufacturers have taken notice. For example, Microchip, in coöperation with another company, extended the arduino IDE to include (at least some of) its powerful 32-bit μcontrollers! For more details, you may take a look here:

http://www.eetimes.com/electronics-blogs/other/4216245/Microchip-s-32-bit-Arduino-clones-are-mega-cool

On the OMAP (Texas Instruments) side, there has been a lot of effort to make development on the OMAP painless. You may start watching the videos at the beagleboard site:

http://beagleboard.org/

I know I read somewhere on the hackaday.com web site that they are trying to duplicate all this progress on the beagleboard on the raspy.

#### Gus · 3 October 2012 at 07:02

LOL, I just realized I have to correct myself in one spot (that’s what happens when you try to discuss stuff late at night…). Towards the end of the first paragraph, it should be “if you turn it 90°(corresponding to transverse MAGNETIC polarization)…”, bringing it to agreement with the beginning of the same paragraph. In s-polarization (pebble Skipping), the electric field is really parallel to the interface (assumed flat); hence it is normal to the plane of incidence (as defined by the ray and the normal to the interface); that’s transverse ELECTRIC polarization. In p-polarization (pebble Plunging), the electric field lies on the plane of the ray and the normal to the interface, hence the magnetic field vector is normal to that plane; that’s transverse MAGNETIC polarization. (The cross product of the electric field vector by the magnetic field vector, in that order, points to the direction of power flow. This has the fancy name “Poynting vector.”) It gets convoluted, I know. My apologies for blabbing, but I felt I had to correct myself to prevent further confusion. And yes, I think your figure is correct now.

#### Mark Rijckenberg · 6 October 2012 at 23:35

Very interesting project! Thanks for posting.

Small suggestion: can you please open-source the documentation (bill of materials, build steps, all electronics schematics) using the following websites as a template for the documentation approach? The bill of materials will give us an excellent insight into the actual cost of the project .

#### MCeeP · 7 October 2012 at 08:01

Open source – Yes! 🙂
Documentation – Err probably not 🙁

I realise that it’s a little hard to open source something when all you have done is provide blurry photographs and a vague description. Obviously I would love to provide more documentation to help with this but, me wishing it is one thing, me spending hours meticulously detailing it well enough for someone else to build is quite another. The design process was very organic and involved very little planning so there are no existing notes on the design other than “make BAM….for cheap” and my retroactive BOM just reads;

Microscope – Kids USB microscope – Amazon
Laser – Green pen thingy from Sp3
LEGO – Mindstorms kit (v.1) – eBay
Total cost ~£200-ish

However, given the interest in version 2 I will rectify this for version 3 and do my best to document every stage of the build so that I can publish proper documentation!.

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