Tag Archives: Light

Transparent Metals

Can metals be transparent at certain wavelengths? My first reaction is No Way! It’s a myth, sort of like the transparent aluminum which is mentioned in the Star Trek whale movie. But then … reading the book Solid State Physics by J. S. Blakemore (2nd revised edition of 1985, published by Cambridge), I noticed in the table on page 24, under the list of properties of solids with various bonding types, the entry for metallic bonding type, this: “opaque and highly reflective in infrared and visible light; transparent in U.V.”. The three example materials listed for that row of the table are Sodium, Silver, and Nickel. So I have to suppose there must be some frequencies at least, at which at least one of those metals is transparent.

Now I’m really curious. A preliminary search for “transparent silver ultraviolet” turns up an article, at the URL http://www.telfor.rs/telfor2004/radovi/PEL-9-9.PDF which describes silver-dielectric crystals which allow some wavelengths through. An example application of such frequency-dependent transparency or opacity is a material which might be used as a microwave oven window, which would be transparent to visible light but opaque to microwaves. OK. My horizons have just expanded. A new concept, and some application possibilities.

Consider, for instance, what might be done with solar cells. Capture long wavelength radiation (greenhouse effect in micro) in an enclosure, achieve high temperature, and black body distribution provides shorter wavelength photons to kick photoelectrons off a material. Thermoelectric applications too. This is really neat! Got to do some reading.

I still don’t know about transparent pure metals, whether silver or aluminum or whatever. But at least it’s not an automatic dismissal of the concept anymore.

Best wishes,
Ken Roberts
20-Apr-2014

Addition of Speed

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Suppose C is a positive real number and we have a binary operation on the closed interval [0,C], denote the operation by *, which is associative, and satisfies the following other conditions: u*0 = u and 0*u for all reals u; u*C = C and C*u = C for all reals u; the differentials d(u*v)/du and d(u*v)/dv exist and are continuous in u and v; and, provided u and v are in the open interval (0,C) (that is, are neither 0 nor C), the differentials d(u*v)/du and d(u*v)/dv are strictly positive. Then, says the book I’m reading, there is a function f(u) defined on [0,C] such that f(u*v) = f(u) + f(v), for all u and v in [0,C], and f(u) is differentiable and strictly monotonic increasing.

That’s really nice. The prototype for that result is the rapidity of motion in special relativity. In that situation C of course denotes the universal maximum speed (of light). The point of the result is that there is a function f(u), where u denotes ordinary speed, let’s call f(u) the rapidity of that speed, which allows us to determine the speed of a combined motion by adding rapidities. That is, given object P moving with speed u with respect to object Q, and object Q is moving with speed v with respect to object R, in the same direction, then the speed of object P with respect to object R is given by the f-inverse of f(u)+f(v).

This is from page 6, and thereabouts, of the little book “Spacetime and Electromagnetism” by J. R. Lucas and P. E. Hodgson, Oxford, 1990. There’s much more in their book but I haven’t got there yet. It’s a delight to read. I hadn’t thought about the addition of velocities in special relativity in such general mathematical terms before.

There is an interesting possibility of a cross-over from those ideas (rapidity, ordinary trig and hyperbolic trig functions, and of course imaginary and real exponentials), and some problems I’ve been fiddling with in quantum mechanics. So often what we see in one context, a structure of ideas, has utility elsewhere in clarifying other topics which are seemingly unrelated.

I haven’t delved into the details of the Lucas and Hodgson material. It seems as if one should also have to assume that the operation * is commutative, as u*v = f-inverse of (f(u) + f(v)) is certainly commutative. So then the conditions on the * operation as stated above, imply commutativity? Which of the assumptions would break down, then, if the operator * were not commutative? Something to think about… Maybe play with functions on a sphere?

Best wishes,
Ken Roberts
30-Mar-2014

Teach Yourself Physics — Bryant

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Teach Yourself Physics, by David Bryant, is a very good introductory book. If you are a scientific tinkerer, Bryant’s book will suggest several interesting projects.

The book has been around a while; the first edition was published in 1971. The 2nd edition, of 1985, is the one which I borrowed from the library. I think it’s out of print, but is available from the used booksellers.

Bryant explains the physical ideas clearly, and I really enjoy his descriptions of experiments. There are plenty of project ideas for demonstrating to the young, and also many opportunities to learn oneself — allowing for serendipity from observation. Perhaps my favourite experiments are his shallow water wave demonstrations. But another, light going in a “straight line”, is the one which I’ll describe here because it is reasonably concise, and provocative.

page 132: “Saying light travels in straight lines does not really achieve much. More to the point is that when viewing along a light beam we interpret it as having taken a straight path — even if it has not! This can be shown by carefully filling a long transparent tank half full of strong salt solution and half full of water with a little fluorescein to make the path visible [he refers to his figure 6.2]. The water is best put in first and the brine added slowly down a tube through the water to the bottom of the tank. Inevitably some mixing occurs where the liquids meet and a turbulent region is formed. A narrow beam of light aimed at this meeting layer can clearly be seen to wiggle about when viewed from the side of the tank. When it is viewed from the end of the tank though it appears to be a perfectly straight line!”

Ken Roberts
04-Feb-2014