### Heat Mirror

February 11, 2016

Like fire, the mirror is one of those simple physical objects existing in nature that have caused wonderment and probably advanced our need for scientific explanation. Without the example of fire and the changes it causes, chemistry would have advanced much more slowly. The mirror likewise sparked some primitive theory-building in early man, giving a jump-start to physics. As in the example from Aristotle's On Dreams, shown below, demonstrates, some of these theories were quite imaginative.

 "If a woman chances during her menstrual period to look into a highly polished mirror, the surface of it will grow cloudy with a blood-coloured haze." - From Aristotle's On Dreams (Περι ενυπνιου). Greek text via mikrosapoplous.gr. English translation by J. I. Beare via MIT Classics.

Children notice their reflection in a mirror at about six months of age, but they don't recognize that reflection as an image of themselves. They're just interested in another face, or the appearance of another child near them. They only recognize the reflection as themselves at about 15-16 months. A simple experiment to determine when this happens is to put a smudge or sticker on a child's face, and see whether he or she will grab for it on themselves when looking at a mirror.

Another curious thing about mirrors is that we see our image in a mirror as a "mirror reflection" in which left and right are interchanged, but why doesn't the mirror also swap our feet and head? The reason for this is that the symmetry we see is an "inside-out" symmetry called parity that's analogous to having a copy of ourselves walk around to the back of a transparent mirror and face us. Richard Feynman explains this in a YouTube video.[1] I wrote about parity and other symmetries in a recent article (CPT Symmetry, October 29, 2015).

 Diagram of a mirror reflection.The mantra of geometrical optics is "virtual image." Understanding virtual images helps to explain many optical principles.(Created using Inkscape.)

Mirrors can be fabricated to be selective in which wavelengths of light they reflect, and which they allow to pass through. Dichroic reflectors are thin-film optical devices designed to allow visible light to pass through while reflecting infrared radiation. Since infrared light carries most of the heat, such a mirror can be used in front of an intense light source, such as a halogen lamp, to produce a cooler beam. There must be provision, however, to remove the reflected heat from a lamp.

The principle behind such mirrors is the interference of light waves as they pass through an interface of one refractive index to another. At such an interface, a portion of the light will be reflected, and the rest will be transmitted. By selecting the thickness of multiple refractive layers, the reflected rays can be selected to interfere constructively or destructively at certain wavelengths. This is an optical manifestation of Bragg's law, and modern material deposition techniques make it easy to produce such multilayer optical films.

 One example of thin-film optical interference - A rainbow pattern produced by diesel oil on water.The thickness of the oil layer defines the color.(Photo by "John," via Wikimedia Commons.)

Scientists and engineers from the Massachusetts Institute of Technology (Cambridge, Massachusetts) and Purdue University (West Lafayette, Indiana) have put the heat mirror concept to good use in improving the much maligned incandescent light bulb by trapping the infrared energy to enhance its efficiency.[2-5] The luminous flux of this nanophotonic-enhanced lamp is a factor of three greater than a plain emitter for the same input power.[2]

 MIT nanophotonic incandescent light bulb.Nanophotonics has enhanced the efficiency of this bulb by a factor of three.(MIT photo by Ognjen Ilic.)

Incandescent lights operate by heating a tungsten filament to about 3,000 kelvin, where it emits blackbody radiation in which only a small portion of the spectrum is visible light. For that reason, the luminous efficiency of conventional incandescent lights is just 2-3 percent, while the efficiency of fluorescent lamps is from 5-15 percent, with LED lamps coming in at 4-15 percent.[3,5] The MIT nanophotonic lamp used their "heat recycling" structure to put the normally wasted heat back into the filament so it needs less power to heat to its temperature.[3]

To do this, the research team first reformed the tungsten filament into a planar structure with a large area. The large area made it more efficient in absorbing the reflected heat.[4] The heat-reflecting photonic crystal was composed of up of 90 layers of silica (SiO2) and tantalum oxide (Ta2O5) on a silica substrate.[5] This combination yielded an efficiency of about 6.6%, and it's believed that a heat mirror of 300 layers with a more complex oxide mix might give 40% efficiency.[2-3,5] An important design aspect was creating a photonic crystal that works over a wide range of viewing angles while still maintaining the required visible wavelength window.[3]

 Spectral performance of the MIT nanophotonic incandescent light. The photonic crystal had ninety layers of silica (SiO2) and tantalum oxide (Ta2O5) on a silica substrate. (Rendered in Inkscape using data from fig. 4 of ref. 2.)[2]

Although inefficient, incandescent lights have the advantage that they are better at rendering colors, and that's why these lights have been preferred to fluorescent lighting for decades.[4] There may be other applications for the MIT photonic mirror, such as in increasing the efficiency of thermo-photovoltaics in which the light from heated materials is converted into electricity.[3-4] This research was funded by the U.S. Army Research Office and the U.S. Department of Energy.[3]

### References:

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