I spend a lot of time talking about invisibility on this blog, and it really has become a fascinating and vibrant area of optics, with lots of remarkable results.  However, most of those results are theoretical, and the experimental results which do exist are very limited, and not typically done for visible light (with a few notable exceptions).

While we wait for our own personal invisibility cloaks, however, we can do some cute invisibility tricks at home to demonstrate some nice optics!  In the video below, I show versions of the same disappearing act, each of which is quite inexpensive and can be done with very simple ingredients.

The first demonstration is the simplest: all you need are a glass of water and a set of clear water gems, the latter of which can be bought at craft stores.

Drop the gems into the glass of water and — presto! — they seem to disappear once they vanish below the surface.  If you look very hard, you can spot the faint outlines of the gems in the water, but the illusion is very effective.

The second demonstration involves only a little more effort, requiring a glass of mineral oil, which can be found at a drug store, and one or more Pyrex (borosilicate) glass stirring rods.    The rods will appear to disappear below the surface of the mineral oil, though again a faint outline of the rods can be seen if you look hard.

Why do these beads and rods seem to disappear in their respective liquids?  The trick in both cases is that the objects are index-matched: they have a refractive index that is almost the same as the liquid they are immersed in.

The refractive index is one of the oldest quantities introduced and measured in optical science: it is a simple number that indicates, through Snell’s law, how strongly a ray of light gets bent when it passes a surface from one medium to another.  Snell’s law is a trigonometric relationship between the angles of the incident and transmitted rays and the refractive indices of the media, given as

.

This is illustrated below.

The refractive index of absolute vacuum is n=1.  For visible light, the refractive index of water is roughly n = 1.33, and the refractive index of common glass is usually between n =1.5 and n=2.0.

There’s a lot we can say about refraction, and I have said a lot in an earlier post.  It turns out that, when we consider the phenomenon of refraction from the perspective of the wave properties of light, the refractive index also indicates the degree by which the speed of light is slowed in the medium.  Labeling the speed of light in vacuum as c, the speed of light in matter is therefore c/n.  In common glass, then, the speed of light is c/1.5, or 2/3rds the vacuum speed of light.

When light passes through a material with a different refractive index, it therefore gets deflected from its original trajectory.  Furthermore, some amount of light is always reflected at the interface between two different index media.  Therefore, even though an object might be transparent, it is still visible due to distortions of light and reflections.  It is for these reason that we can make glass doors and building facades without people constantly crashing into them (well, most of the time).

However, if we submerge one transparent object into a medium which has the same refractive index, or almost the same index, there will be no refraction or reflection!  The object becomes almost completely invisible.

In the case of the water gems, this index matching works because the gems themselves are  almost entirely made out of water.  They are fashioned from a carbon-based polymer that can soak up 300 times their own weight.  Therefore, even though they are solid, they have almost the same optical properties as water.  If you’re interested in seeing how much water they can soak up, you can purchase dry “phantom crystals” at some science supply stores.  These can be soaked overnight and swell to remarkable sizes.

The mineral oil-Pyrex invisibility relies on the remarkable coincidence that the oil and the glass have almost the same refractive index over the entire visible light spectrum.  As noted in the video, the only challenge in this demo is buying a huge amount of mineral oil laxative at your local drug store without getting embarrassed.

Index matching forms the basis of one of the classic works of science fiction, H.G. Wells’ 1897 The Invisible Man!

The titular man describes the process to a colleague late in the book:

“If a sheet of glass is smashed, Kemp and beaten into a powder, it becomes much more visible while it is in the air; it becomes at last an opaque white powder. This is because the powdering multiplies the surfaces of the glass at which refraction and reflection occur. In the sheet of glass there are only two surfaces; in the powder the light is reflected or refracted by each grain it passes through, and very little gets right through the powder. But if the white powdered glass is put into water, it forthwith vanishes. The powdered glass and water have much the same refractive index; that is, the light undergoes very little refraction or reflection in passing from one to the other.

“You make the glass invisible by putting it into a liquid of nearly the same refractive index; a transparent thing becomes invisible if it is put in any medium of almost the same refractive index. And if you will consider only a second, you will see also that the powder of glass might be made to vanish in air, if its refractive index could be made the same as that of air; for then there would be no refraction or reflection as the light passed from glass to air.”

“Yes, yes,” said Kemp. “But a man’s not powdered glass!” “No,” said Griffin. “He’s more transparent!”

Both of the demonstrations suggested require the submersion of the object to be hidden in an appropriate liquid.  In fact, many undersea creatures have evolved a remarkable degree of transparency as a defense against predators, as this article from Scientific American demonstrates (pdf). You might wonder: is it possible to find materials which are index matched to air and therefore can be hidden in plain sight, such as on one’s desktop?  The problem is that air is a very tenuous medium, and the refractive index of our atmosphere is very, very close to that of vacuum.  We would need a material that does not inhibit light at all, and in fact allows it to travel unimpeded at “Einstein’s speed limit,” a criterion that seems unlikely to ever be achieved.

The absolute speed limit of light in a vacuum turns out to be a limitation for more sophisticated cloaking devices, as well.  Looking at the diagram of one of the original 2006 spherical cloaking designs shown below, we can see that rays passing close to the central hidden region must take a longer path than rays that would travel in straight lines outside the cloak.

However, if our cloak is trying to hide things in air, this means that light traveling near the center must travel faster than the speed of light in air in order to keep up with those rays traveling outside; otherwise, the total light field would be distorted and in principle detectable.  I only note at this time that it is possible to “break” the vacuum speed of light at a single frequency, but it is not possible to break it for a large range of frequencies.  Therefore the cloak pictured above will only work for a small number of colors.  It might appear invisible to red, but not blue, for instance!

The theory of optical cloaking is still in its infancy, however, and it is possible that someone in the future come up with a clever and surprising new way to hide objects for all frequencies.  Until that day arrives, however, at least we have a few simple clever tricks to demonstrate what such invisibility might look like if we lived underwater!