Miscellaneous
Hi! Here you'll find a fun/useful general science snippet and a physics note, followed by some brief information about the spelling of my name.
(Click here for past snippets & notes).
Science snippet #6: Caring for a new book
I recently encountered a trick to condition a new book to prevent the spine from cracking. This was sadly too late for one book (note the orange book below), but saved another (the blue book - the 1st printing of Pedrottis’ Introduction to Optics 4e). A cracked spine can cause pages to fall out, but if the spine bends instead of cracks then pages remain intact. In mathematical terms we want the slope of the spine to remain continuous.
The process takes about ten minutes (less than the time spent reading a book!), and adopts the following approach:
With the book at room temperature, and before opening the book fully...
-- The overall strategy is to place the book with its spine on a desk and gently push along the inside of the spine, with the spine kept concave as seen from below (check out the videos here and here).
-- I tend to start near the middle of a book, with half the pages lying flat on the desk and the other half held about 45° above the horizonal. I then lift around five pages each time up from the horizontal, pushing along the inside of the spine until all pages originally lying flat have been lifted.
-- I then repeat this for the other half of the book.
Then, enjoy!
Physics note #7: Some musing about “low-E windows” (at the upper-undergrad level)
While recently replacing the glass unit in a double-pane window, I was curious what was meant by a "low-E" coating on a window, and how to determine which of the four glass surfaces has this coating on it.
I explore here the first of these questions, and will examine the second at a later date.
The short answer is that a low-E ("low-emissivity") coating accomplishes two things. First, it makes the glass reflect, rather than absorb, incident mid-infrared "thermal" wavelengths. These wavelengths are predominately emitted from objects with temperatures between –30 and +40 °C, and are emitted more from hotter objects, so the coating reduces the heat flow from the warm side of a window to its cold side. Second, the coating is often also engineered to increase (or decrease) the reflectance of near-IR & UV "solar" wavelengths while leaving visible light transmission relatively unchanged. This can further reduce cooling (or heating) costs.
The relevant science is covered by the topic termed 'the optical properties of solids', and we are interested here in glass a few millimeters thick and metal a few tens of nanometers thick. Check out the first graph below, which shows the complex refractive index for silica (the values are typical for most clear, uncoated glass). We see the real part of the complex refractive index, nR, (simply called “the refractive index”, which we often encounter when exploring refraction), and the imaginary part, nI, (called the “extinction coefficient”, and which determines how rapidly light decreases in intensity as it passes through a medium). Both nR and nI affect the reflection of light at a surface, and thus how much light enters the medium, while nI and the thickness together determine how much of this light is subsequently absorbed. The horizontal axis shows wavelengths from 20 µm (a photon energy of 0.62 eV) to 125 nm (energy of 9.92 eV), and strong absorption is seen when crossing the silica band gap energy at ~9.2 eV (a wavelength of 135 nm).
For wavelengths between 5–20 µm (the "thermal" region) nR lies between 0.4 and about 3, and nI between 0.002 and 3. These give relatively low reflection at these wavelengths, so most incident thermal radiation would enter the glass. Then, even with an extinction coefficient of only 0.002 (at a wavelength of 5 µm), the absorption coefficient α > 5000 m-1, which for 3 mm-thick glass means strong absorption and very low transmittance (T ~10-7).
Heat flow through a window occurs through a combination of conduction, convection, and radiation. Compared to a single pane of glass, a double-pane window made from clear, uncoated, glass exhibits much-reduced conduction and convection. However, as we have just seen, much of the thermal radiation that strikes the pane from the warm side of the window is absorbed, which heats up the glass, which then radiates heat in all directions. Thus a double-pane window made from uncoated glass suffers significant heat transfer by radiation.
Data for uncoated and coated glasses used in windows in North America are found in the International Glazing Database (IGDB). From this we can learn that in the thermal region a single an uncoated 3-mm-thick clear glass pane has transmittance near 0%, reflectance around 16%, and absorption around 84%. (FYI this allows for multiple reflections, and assumes near-normal incidence of incoherent light). Thus ~84% of incident thermal radiation is absorbed by this glass pane and then re-emitted; the pane has high emissivity.
Meanwhile, for wavelengths between 300–2500 nm (in the "solar" region) nI is very small; it is smaller by a factor of ~1010 than its value in the thermal region. In the solar region the 3-mm-thick glass just considered has transmittance of 83%, reflectance of 8%, and absorption of 9% (in the narrower visible region, between 380–700 nm, these values are 90%, 9%, and 1%). High solar transmittance through a window heats a dwelling due to incoming sunlight, which is desirable on cold days and undesirable on hot days. The industry quantifies this heating, including secondary heating from absorption of sunlight followed by conduction or convection, by the solar heat gain coefficient (SHGC), which adopts a value between 0 and 1. A standard double-pane window made from uncoated glass panes has SHGC ~ 0.75.
Now let's examine the complex refractive index of a metal, for which we plot nR and nI based on a Drude model with a plasma frequency corresponding to incoming wavelength of 116 nm (a photon energy of 10.7 eV, just off the right side of the graph). In the thermal region nR and nI are so large that the reflectance is very high, and substantially higher than in the visible region. So glass coated with a very thin layer of, say, silver will exhibit the desired high-reflectance for this radiation.(2) An example of such a coated glass is #5142, with transmittance near 0%, reflectance around 90%, and absorption around 10%. The high thermal reflectance compared to uncoated glass means this glass strongly reduces heat flow due to radiation; it has low emissivity. Meanwhile, for very thin layers of the metal there is little absorption of the light that does enter the material.
We also see that the reflectance of the metal across the NIR region is greater than for visible light, and so glass with this coating has a reduced SHGC compared to uncoated glass (and little effect on visible light transmission). Indeed, various coatings can selectively tune the reflectance in the NIR and UV regions. For glass #5142 in the solar region the transmittance is 57%, reflectance is 26%, and absorption is 17%, while in the visible region these are 83%, 5%, and 12%. Thus, in addition to reducing heat flow through thermal radiation, such coated glass also reduces heat flow associated with solar radiation, which further reduces cooling costs on hot sunny days.
Low-E windows are one example of a real-world application of optics. Other examples can be found in our textbook, Pedrottis' Introduction to Optics, 4th ed.
(1) D. Franta et al, "Optical characterization of SiO2 thin films using universal dispersion model over wide spectral range", Proc. SPIE, 989014 (2016).
(2) Metal films retain their high reflectance even for thicknesses well below the skin depth, and only if they are a few nanometers thick or less do they then exhibit low reflectance. See A. E. Kaplan, "Metallic nanolayers: a sub-visible wonderland of optical properties", JOSAB, 35, 1328 (2018).
Finally, a note about 'Rayf'
I usually adopt the spelling Rayf, which is consistent with the pronunciation I prefer (/reɪf/), and used for many years by family and friends. The original (and still the formal, legal) spelling of my name is ‘Ralph’, yet this can be confusing in a way similar to the Stroop effect. Some background to the name, from Prof. Ralph Wedgewood at the University of Southern California, can be found here.