Inverted Shadows: a Polarization Frame

βλέπομεν γὰρ ἄρτι δι' ἐσόπτρου ἐν αἰνίγματι
(For now we see through a glass, darkly) 1 Corinthians 13:12

Usually, if you place an object between a light source and the observer, it will block the light and cast a dark shadow. Here the object, which has to be transparent to some degree, allows light, which otherwise would be blocked by the screen, to pass through it. So you get a bright "shadow" on a dark screen.

Some special effects, which I will try to explain in the scientific part of this instructable, can result in some colorfull "rainbow" patterns. For more information and images, please have a look on Step 2.

The device consists of five layers. The outer plates are made from clear acrylic, an inner frame from the same material holds the object(s) to be displayed. The object itself can be made from clear polystyrene, polycarbonate, polyethylene, PET, and various other plastics. You may also use acrylic objects that are covered with a thin layer of one of the materials mentioned above. The real interesting part are the two layers of polarization filters placed on the outer plates. These are set orthogonal to each other, so most of the light gets blocked. The object depolarizes the light polarized by the first filter, so parts of it can pass the second filter, thereby making the object visible.
It is quite simple, in a way.

On the second and third images above you have, in the top left corner, a piece of mylar (oven bag) membrane, on top right a piece of polystyrene (PS) and below a piece of polycarbonate (PC). When the round piece of PC turns a bit, it gets dark.

You can try this phenomenon by yourself without much effort. A cheap and widespread source for polarization filters are the "glasses" of 3D cinema glasses. They can be removed easily from the frame. Now place them against each other so a minimum of light passes through. Then place a small piece of plastic between the glasses. This actually is the situation on the last image. The plastic cover of a CD may work well, or just use some household foil. Depending on the material, you might find that the orientation of the plastic sheet may influence the amount and color of the light passing the membranes. Oven bags, which are basically made of Mylar, a stretched form of PET, are a good material to show this effect.

Here a large piece of polystyrene was placed into the frame and gave a nice and colorfull rainbow pattern.

So now we can use this as a "window" to paint the world. Or you could build a lamp to paint your room in rainbow colors. As any piece of pastic will give another pattern, so you can change your "rainbow" as often as you like.

In the top photo on the first page I used a similar piece of polystyrene as above, but placed a "H" cut from a piece of clear "cellophane" foil used to wrap around gifts. Only at a special angle this gave this "color inversion" effect as seen in the images. In other angless it was just erasing the colors.

What are the physics behind this?

As mentioned before, we are using the effect of depolarization of polarized light. So what is polarized light?

A beam, more precisely a quantum of light can be described by it's energy or frequency, direction and polarization. As light can be described as a wave, the up and downs of the wave also define a plane (think of waves on a water surface). Natural light has no predefined polarization direction, but reflections (e.g. on a water surface) can select light with a certain polarization. That is the reason why polarized sunglasses allow you to see better on a wet street or into water. A polarization filter allows only light with the correct polarization to pass, and blocks light with a polarization plane orthogonal to this. If we combine two such filters in a way that the first blocks horizontal polarized light and the second blocks vertical polarized light, most of the light will be blocked.

A number of substances are able to modify the polarization of passing light. Crystals like quarz, but also many organic substances, as sugar or several plastics do. As the later usually have the glas-type state of a frozen liquid with only tiny, undirected crystals in it, they will turn the polarization of passing light in a rather undefined way, hereby randomizing it.

The situation is a bit different if you have a look on streched plastic sheets, like Mylar or extruded PC, where the crystals in the plastic have a more defined, non-random orientation. These may turn the polarization in a more defined way, so here the relative orientation of the membrane to the polarization filters matters.

For more theory I would like to refer you to the Wikipedia articles on polarization filters and birefringence.

The "rainbow patterns" seen with many plastic pieces can result from "stress induced birefringence". Here the plastic pieces suffer from mechanical stress that had been "frozen" into the material during the rapid solidification of the plastic in the production process. As the degree of this berefringence is wavelength-dependent, it gives this nice color patterns (as seen on the images). The effect is used to analyse stress in mechanical systems by the method of photoelasticity.

In the case of mylar sheets the thickness and orientation of the membrane does influence the color.

The concept I tried to demonstrate and explain here is nothing new.
As a mater of fact I first came across it as a child in the early seventies. In the technical school my father was studying engineering they used this effect to demonstrate mechanical stress on plastic model of a screw wrench.

Please be aware that I have only very limited knowledge in optics, and English is not my native tongue.

So I hope could give you some insight without to much errors. If any corrections are required, please let me know.

The screen and frame:
As mentioned they consists of clear acrylic. For the prototype shown here I used 3 mm acrylic, laser-cut using the service of Formulor, Germany. The attached svg file ( ...-unfilled.svg) allows you to order them directly at Ponoko, USA, RazorLab, UK, or Formulor, Germany. You can modify the drawing, e.g. using Inkscape, and change the rectangle or the circle e.g. to a heart, hexagon or octagon. The limitation is that, using the P1 plate format, the maximum size of the frame is 90.5 x 90.5 mm.To simplify assembly, all parts contain four 3 mm holes, so you may use M3 screws or 3 mm acrylic rods to fix them in place. The costs are rather limited: about 12 €/US$ plus shipping for the plate.

In case you may have to adapt the SVG file according to the rules of your prefered laser cutting service.

Or you may use the classic jigsaw. In this case, I would recommend to build one with 10 x 10 cm, as it then fits perfect to the polarization filters.

The polarization filters:
That is the expensive part. You may order them online. I got mine from a German provider called Screen-Tech, where I ordered the self-adhesive ST-38-20S ones. One of this 10 x 10 cm filters is available at 14 €, but as you need two, calculate with 28€ plus shipping. Larger sizes of the filters are available as well.

Before you attach the filters to the plates, make sure you allign them correctly, turned by 90°, so the transmission of light is completely bocked. They have to look into the same direction, so finally one will face the outside and one the inner side of the frame. Sticking them to the plates without entrapping air bubbles and specs of dirt is not an easy task, so ensure that the surface of the plate is absolutely clean.

The object:
You probably find many pieces of clear plastic in you household. Just play and adjust as needed. In case you may glue several layers together, e.g. using acetone or dichloromethylene.

The object(s) may be given several forms and you may also place a logo or a message ( as "you light my darkness") on them.
Especially polystyrene pieces will give these nice rainbow-patterns, so check your materials first.

Polycarbonate (as CD covers) can give interesting color effects.

Happy playing.
H.