I’ve spent a lot of time on this blog talking about the optics of invisibility, both hypothetical and actual. Though a number of forms of invisibility have been considered in both science and fiction for over a hundred years, the study of the subject really exploded in 2006 with the publication of two theoretical papers introducing designs for “invisibility cloaks.”
The principle behind one of these cloaks is illustrated below, taken from the original paper by Pendry, Schurig and Smith. The cloak guides light around the central region and sending it along its original path, like water flowing around a boulder in a stream. The lines in the illustration represent rays of light being deflected and returned to their original trajectories.
The device is passive; it “works its magic” by virtue of the materials it is built out of, and guides light around the hidden region by what amounts to refraction.
It is fun to talk about the unusual implications of optical invisibility, but it is hard to show it! Cloaks are complicated, and there are relatively few experimental realizations to date — and those that do exist are not easily reproducible without a lot of resources.
Fortunately, there exists a simple trick, suggested by my colleagues*, that can be used to demonstrate the principle of cloaking in a striking way! I assembled a version of this trick myself for use in a recent popular talk on invisibility physics that I gave; a short video of it is shown below.
A finger placed behind the device is readily visible, but a finger placed within the cloak vanishes!
For about $50, you too can make your own “cloaking device”, albeit an oversimplified and crude one! Let’s take a look at how it is done.
The device is constructed out of eight glass right-angle prisms arranged as shown in the top-down photograph below.
The operation of the cloak is really simple to explain. Suppose we look through the device from the bottom up; light coming from above bounces through the system as shown in the following image. (Rays have been color-coded to clearly show path of travel.)
The illusion is obviously not perfect — looking at the “cloak” from any direction other than directly in front of one of the flat faces will not provide any effect, other than a highly distorted image. This is not exactly a flaw, as more recent cloaking investigations have focused on such “directional” cloaks as a way to simplify the design requirements.
But an interesting question arises: the prisms are made of clear glass: why doesn’t some of the light passing through the system just go right through the side of the prism and into the diamond-shaped cloaked region? For that matter, why doesn’t some of the light escape out through the sides of the cloak as it bounces around? The answer is that the light is totally internally reflected at the glass interfaces, and none escapes until it hits the exit surface head on.
What is total internal reflection? As discussed in my “basics” post on refraction, when light crosses a flat interface between two media, it changes direction: this is the phenomenon of refraction. When light goes from a rarer medium (like air) to a denser medium (like glass), the ray gets bent towards the line perpendicular to the surface. When it goes the other way, from a denser medium to a rarer medium, it gets bent away from the perpendicular; this is illustrated below.
Refraction satisfies Snell’s law, which says that the angles of the rays and the refractive indices (labelled by n) satisfy the relation:
We won’t worry about Snell’s law in detail right now, but the important thing to note is that light coming from glass to air exits the interface at a bigger angle than it hit the interface. But this means that there is some critical angle at which the light is refracted parallel to the surface!
This means that any light hitting the interface at greater than the critical angle will not be refracted at all: in fact, it will be completely reflected inside the glass, and no light will escape. This is total internal reflection, and it is also, loosely speaking, how fiber optic cables can transmit light over long distances with little loss. The light is trapped inside the glass cable and cannot escape except at the ends.
A glass with a refractive index of n = 1.5 will have a critical angle of 41.8°, meaning that any light hitting the interface with an angle larger than this will be totally reflected. In our prism cloak, light is hitting the boundary at 45°, so all the light is funneled from one side of the cloak to the other without escaping.
Though this device is not even close to a perfect cloak and is certainly not invisible, it does demonstrate two important aspects of the original invisibility cloak design. First, it guides light around a hidden region, as a perfect cloak would be expected to do. Second, it hides the interior region by total internal reflection, and this is essentially what happens in a perfect cloak as well. In fact, a perfect cloak in principle would have a refractive index of zero on the interior edge, meaning that all rays of light, regardless of angle, must be trapped within.
The effect is also good enough to impress people and convey that invisibility is scientifically feasible, if not possible — yet!
* A special thanks to Mike Fiddy and Robert Ingel of UNC Charlotte for suggesting this idea.