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 (see the blue book). A cracked spine can cause pages to fall out, but if the spine bends instead of cracks then all is well. 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:
-- Start with the book at room temperature or warmer, and before opening the book fully.
-- The general 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 usually start near the middle of the 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 the pages originally lying flat have been lifted.
-- I then repeat this for the other half of the book.
Now, 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 about what was meant by a "low-E" coating on a window, and how to determine which of the four surfaces of the window 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 this coating reduces the heat flow from the warm side of a window to the 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 shown are typical for most clear, uncoated glass). We can 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 and which affects how rapidly light decreases in intensity as it passes through a medium). Both nR and nI determine 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 encompasses 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 located at ~9.2 eV (at wavelength 135 nm).
For wavelengths between 5–20 µm (in 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. Note that even with an extinction coefficient of only 0.002 (at a wavelength of 5 µm), the absorption coefficient α is more than 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 seen from the last paragraph, much of the thermal radiation that strikes the pane on the warm side of the window is absorbed, which heats up the glass, which then radiates heat towards the other pane. Therefore a double-pane window made from uncoated glass suffers significant heat transfer by radiation.
Data for uncoated and coated glasses used in windows across North America are given in the International Glazing Database (IGDB). From this we learn that a single 3-mm-thick uncoated clear glass pane has transmittance, reflectance, and absorption values in the thermal region of about 0%, 16%, and 84% respectively. (These account for multiple reflections, and assume near-normal incidence of incoherent light). Thus ~84% of incident thermal radiation is absorbed by this glass pane and subsequently re-emitted; the pane has high emissivity.
Meanwhile, for wavelengths between 300–2500 nm (in the solar region) nI is very small; in fact 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, reflectance, and absorption of 83%, 8%, and 9%, respectively (in the narrower visible region, between 380–700 nm, these are 90%, 9%, and 1%). High solar transmittance through a window heats a dwelling due to incoming sunlight, which is desirable on cold days but 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 has SHGC ~ 0.75.
Now 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 a wavelength of 116 nm (at 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 thermal radiation.(2) An example of such a coated glass is #5142, with transmittance, reflectance, and absorption in the thermal region of 0%, 90%, and 10% respectively. The large thermal reflectance compared to uncoated glass means that this glass strongly reduces heat flow due to radiation. 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 metal coating would have a reduced SHGC compared to uncoated glass (and not much effect on visible light transmission). Indeed, with various coatings it is possible to selectively tune the reflectance in the NIR and UV regions. For glass #5142 the solar-region transmittance, reflectance, and absorption values are 57%, 26%, and 17%, while in the visible region they are 83%, 5%, and 12%. Thus in addition to reducing heat flow through thermal radiation, this coated glass also reduces heat flow associated with solar radiation, which further reduces cooling costs on hot sunny days.
We see how low-E windows illustrate a real-world application of optics. More examples can be found in our recent 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 when they are a few nanometers thick or less do they then exhibit how reflectance. For more information 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 to all in a similar way to the Stroop effect. Some information about the origin of the name, from Prof. Ralph Wedgewood at the University of Southern California, can be found here.