When discussing the history of invisibility physics, I typically cite Ehrenfest’s 1910 paper on radiationless motions as the first publication dedicated to the subject.  Ehrenfest’s paper, which attempts to explain how electrons could oscillate in a classical atom without radiating, is a direct precursor to the long history of nonradiating sources and nonscattering scatterers that I’ve been chronicling on this blog.

However, it turns out that Ehrenfest was not the first author to discuss some form of invisibility!  I recently stumbled across an article in an early issue of the Physical Review: “The invisibility of transparent objects,” by R.W. Wood, 1902.  It is not an earth-shattering paper, but it presents some intriguing ideas and suggests that visions of invisibility may go even further back in the sciences…

In 1902, I think it would be fair to say that the Physical Review was still in its infancy.  First published out of Cornell University in 1893, it would not be taken over by the American Physical Society until 1913; the APS itself was not founded until 1899.  Reading the papers from that early period, my impression is that the journal was still untested, and most important results were still gravitating to Philosophical Magazine and the Philosophical Transactions of the Royal Society.  Physical Review was a place for scientists to publish more technical research, brief musings on specialized topics, and pedagogical strategies.

Nevertheless, some very interesting papers were published in that era, and a number of important researchers contributed to the journal in its early days.  One of the most notable is Robert W. Wood (1868-1955), a physicist and optical scientist who made important contributions to the study of infrared and ultraviolet radiation and diffraction theory.  Wood contributed regularly to the journal in its early years, mostly with suggestions for novel classroom demonstrations, for instance: “Lecture-room demonstration of orbits of bodies under the action of a central attraction” (1897), “Demonstration of the Doppler effect” (1897), “Apparatus for illustrating potential gradient” (1898).

In 1902, though, Wood published, “The invisibility of transparent objects.”  This article is best summarized as the musings of Wood on invisibility, and it culminates in a rather intriguing hypothesis, with an experiment to back it up!

Wood starts with a familiar and well-known observation:

A transparent body, no matter what its shape, disappears when immersed in a medium of the same refractive index and dispersion.  Could a transparent solid substance be found, whose refractive index and dispersion were the same as those of air, it would be absolutely invisible.

By “transparent body”, Wood means an object which does not significantly absorb light in the visible spectrum, such as glass.   Though such an object does not absorb light, it is still visible because its index of refraction is different than the surrounding air, and light therefore is partially reflected and partially refracted as it meets the object: some of the light is “bounced back” (reflection), while the light that enters the object has its direction of propagation altered (reflection).   At a planar surface, for instance, an incident and refracted light ray satisfy Snell’s law,

,

where and are the refractive indices of air and the medium, respectively, and and $\theta_2$ are the angles which the rays make in each region with respect to the normal.  This is illustrated below:

If a transparent object is put into a medium with exactly the same refractive index, i.e. , the direction of the ray is unchanged.  There is also no reflection, though one must use the more complicated Fresnel equations to demonstrate this.  An imperfect example of this can be done by putting a glass rod (index ) into a glass of water (index ):

(Note: vegetable oil works even better!)

It is interesting to note that the type of invisibility described here may have been the inspiration for what is considered to be the very first “scientific” story of invisibility, What Was It? by Fitz-James O’Brien (1828-1862), written in 1859.  In the story, an invisible monster unexpectedly invades a home one evening.  Later, one of the characters attempts to explain the idea rationally:

“Here is a solid body which we touch, but which we cannot see.  The fact is so unusual that it strikes us with terror.  Is there no parallel, though, for such a phenomenon? … It is not theoretically impossible, mind you, to make a glass which shall not reflect a single ray of light — a glass so pure and homogeneous in its atoms that the rays from the sun will pass through it as they do through the air, refracted but not reflected…”

“That’s all very well, Hammond, but these are inanimate substances.  Glass does not breathe, air does not breathe.  This thing has a heart that palpitates — a will that moves it — lungs that play, and inspire and respire.”

The physics here is garbled — it is not possible, even theoretically, to make an object which refracts but never reflects — but the material O-Brien writes about sounds very much like the “transparent solid substance” that Wood mentions.

Liquids exist which can hide a glass rod much better than water, but the effect is still not necessarily perfect, as Wood notes:

The disappearance of a transparent substance when immersed in a medium of identical optical properties is usually illustrated by dipping a glass rod into Canada balsam, but the disappearance is not complete, for the dispersion of the glass and the liquid are not the same.  A better fluid is a solution of chloral hydrate in glycerine which is quite colorless… A glass rod disappears completely when dipped into it and when withdrawn presents a curious aspect, for the end appears to melt and run freely in drops.

Dispersion refers to the fact that the refractive index of a material depends upon the frequency of the illuminating light, i.e. .  Red light, then, will refract at a different angle than green light.  A prism separates white light into multiple colors due to the dispersive properties of the glass, as illustrated in a classic Pink Floyd album cover:

To make an object invisible to all colors, then, requires that the object’s refractive index match that of air for all frequencies of visible light.  Wood was unknowingly quite prescient in pointing out the challenge in making such objects; modern invisibility cloaks are subject to a similar limitation, in that they are typically only invisible for a single frequency.

In 1902, it was simply impossible to design and fabricate a material with tailored optical properties; even today, such capabilities fall under the heading of, “plausible, but not yet possible.”  Wood, however, knew of another idea for producing an invisibility of sorts:

Lord Rayleigh in his article on optics in the Encyclopædia Britanica [sic] points out that perfectly transparent objects are only visible in virtue of non-uniform illumination, and that in uniform illumination they would become absolutely invisible.  A condition approaching uniform illumination might, he says, be attained on a top of a monument in a dense fog.

The hypothesis of Lord Rayleigh is a rather surprising one which I had never heard of before.  “Uniform illumination” refers to a situation in which an object is illuminated by natural light of equal intensity from all directions, i.e.

“Non-uniform illumination” refers to a situation where light falls on an object more in some directions than others:

Even if an object is perfectly transparent, it still reflects light and refracts light; if you look in the direction of such an object, you will typically see it because less light is transmitted through it due to reflection and the light which is transmitted is deflected by refraction.

Lord Rayleigh, however, suggests what may be considered a conservation law of sorts: if an object is uniformly illuminated, the sum total of all  reflections and refractions from the object is uniformly radiated.  This would in principle look not different than a situation in which no object was present at all, making the object invisible!

To see how this works, we consider a crude model of uniform illumination which involves only four directions: up, down, left, right.  In the absence of an object, we would see the same amount of light if we observe the system from any direction:

An observer on the left will see the same amount of light coming from the right that the observer on the right sees coming from the left.   Now let us suppose we put a transparent object in the middle of this system.  Rayleigh’s hypothesis suggests that any right-going light which is deflected from reaching the right observer is perfectly balanced by light which is deflected from another direction.  An example of such an effect is shown below, where it is assumed that the object makes each ray of light make a right turn:

As far as an observer is concerned, the object is completely invisible!   From each of the four directions, the same amount of light is measured as was measured in the case of no object.  There is no way for the observer to distinguish between a ray which came straight across the domain and one which was bent onto that path:

Is Rayleigh’s hypothesis true?  I’m not sure, though I have my doubts that it is true in general.  However, as long as geometrical optics (light travels along well-defined rays) is valid, and the illuminating light is natural (i.e. incoherent),  it seems like the hypothesis works very well.  I’m actually going to try and prove it as a little research project, though the proof is certainly rather difficult.

Wood actually made a simple experimental test of this invisibility effect:

I have recently devised a method by which uniform illumination can be very easily obtained and the disappearance of transparent objects when illuminated by it illustrated.  The method in brief is to place the object within a hollow globe, the interior surface of which is painted with Balmain’s luminous paint and view the interior through a small hole.

…

If the inner surfaces be exposed to bright daylight, sun or electric light, and the apparatus taken into a dark room, a crystal ball or the cut glass stopper of a decanter placed inside, it will be found to be quite invisible when viewed through the small aperture.  A uniform blue glow fills the interior of the ball and only the most careful scrutiny reveals the presence of a solid object within it.  One or two of the side facets of the stopper may appear if they happen to refect or show by refraction any portion of the line of junction of the two hemispheres.

In short, Wood applied luminous paint to the interior of a hollow sphere, which provides uniform illumination inside the sphere.  With a small hole for viewing, he found that glass objects became quite invisible while inside the device:

This is a quite fascinating experiment, and one that could be done by pretty much anyone, thanks to the ease of acquiring luminous paint these days!  I’m sorely tempted to try the experiment myself; if I do, and am successful, I’ll blog about the results.  (Let me know if any of you readers try it, too!)

There’s one problem with Rayleigh’s hypothesis: I can’t actually find the original reference!  Wood does not give a specific citation, though he is clearly referring to Lord Rayleigh’s articles in the 9th edition of the Encyclopædia Britannica, the so-called Scholar’s Edition.  I’ve found Rayleigh’s articles in that edition, but can find no mention of invisibility in them.  The lack of citation suggests that Wood was citing Lord Rayleigh from memory, and he may have misremembered the actual location of the discussion.  (It is also possible that Lord Rayleigh’s comments appeared in the revised 10th edition of the Encyclopædia, but I find that unlikely.)

Lord Rayleigh’s articles in the Britannica are also fascinating from a historical point of view, and I’ll come back to them in a future post.  Wood’s comments, however, suggest that the history of invisibility physics may go back significantly further than I originally imagined.