Figure 8 – Layout of ferrofluid cell experiment.
In my experiments white light is projected onto the ferrofluid cell with 45 degree incident angle and a magnetic pole of a permanent magnet is placed under the mirror. The field of a permanent magnet produces hysteresis shaped patterns when viewed from directly above the ferrofluid cell.
Surely the 45 degree incident angle between the light source and camera is a strong argument to characterize the ferrofluid cells as a metamirror. A argument for displacement current is that ferrofluid cells are made up of glass, oil, and rust. There are not many conduction band electrons in the system YET we know from first principals that it takes electrons to scatter photons. How does this device scatter light without conduction band electrons? Of course the aluminum surface mirror scatters light at 90 degrees but I'm referring to the non-90 degree scatter. One can build a ferrofluid cell with two glass windows and obtain very similar results to the data in this document.
Figure 9 – Applying classical optics to the ferrofluid cell.
Starting with Figure #9, a light ray from the left hand side approaches the center of the ferrofluid cell at 45 degrees. Of course other light rays from the same source with be a bit less than 45 degrees on the left hand side of the cell and a bit more than 45 degrees on the right hand side of the cell. The average index of refraction of BK7 is around 1.515 .
I did some checking and light machine oil which seems to have similar viscosity as the ferrofluid medium and can be measured at 15 drops per cubic centimeter. Doing the math, it works out to 8.4 micrometers per drop of height for the 100mm diameter ferrofluid layer. Assuming I used 5 drops of ferrofluid, that gives 42 microns of thickness for the layer.
The average index for refection for light machine oil is around 1.45 which is pretty close to the index of refraction of the BK7 glass. The light ray comes in at 45 degrees and hits the first glass interface which changes it to 27.82 degrees and it travels thru the 6mm thick BK7 glass. Then the light ray hits the second glass interface and changes the incident angle to 29.23 degrees.
After it travels through the 42 micron thick ferrofluid layer then the light ray hits the aluminum surface and using the law of reflection, the incident angle becomes -29.23 degrees. I ran the numbers, but course the system is symmetric and light ray follows the same angles that brought it into the system and exits the top glass interface 6.33mm downstream at -45 degrees.
Figure 10 – Zoomed in on the ferrofluid layer.
The Brewster's angle of Bk7 glass 56.56 degrees which leads to an interesting observation. Notice that in the experiment the incident angle inside the glass was 27.82 degrees. If you run the numbers, you will find that it is impossible to trap light inside the cell using the Brewster’s angle for either the BK7 glass layer and/or the ferrofluid layer.
If you inject light from the top the cell; you can not trap it inside the cell!
Another observation is that the ferrofluid layer is over 140 times thinner than the glass window about it. This means that the light is spending 140 times more time in the glass layer, versus the time that it spends in the ferrofluid. The maximum path length of the light passing though ferrofluid is less than 120 microns.
Figure 11 – Testing a new ferrofluid cell, note the color change of the wire.