# The rule breaker, emissivity + reflectivity = 1

If emissivity and reflectivity are inversely proportionate, why does glass have a high emissivity of around 0.95-0.97 as well as being very reflective for IR Radiation?

normally it works but not with glass!

Can anyone explain this?

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Can you quote your source for the high reflectivity of IR by glass. As far as I know the emissivity remains around 90-95% and the reflectance 5 - 10% out to at least 2,500nm. – John Rennie Apr 3 '13 at 11:16
I do not have a exact number, but i use thermal cameras often and often see reflections incredibly easily showing very high or low temperatures. for example when looking up at a house the top windows may show -20 Degrees C from the reflection of the sky. – Chris Deakin Apr 3 '13 at 11:49
Dear Chris, this isn't necessarily an argument that the reflectivity is high. It may just mean that your digital camera becomes more sensitive at smaller light intensity, the dependence of the response on energy flux is nonlinear. – Luboš Motl Apr 3 '13 at 12:06
Could it be that the reflectivity is angle dependent, and you're looking at the windows from a shallow angle? – jkej Apr 3 '13 at 12:06
Dear @ChrisDeakin, fine, so replace the digital camera by "thermal camera" in my comment. Nothing else is changed, the problem is still the same. You're not really measuring the quantities you're claiming to measure (reflectivity), you're just using your (misleading) intuition to estimate it. The law you don't like always holds. – Luboš Motl Apr 3 '13 at 12:47

According to this article the lenses on thermal cameras are not made from glass, but rether from Germanium, CZinc Selenide or Zinc Sulfide. These materials are not transparent to light so it's quite reasonable for them to have a high reflectivity.

Response to comment:

The emissivity and reflectivity only have to add up to one at the same wavelength. So if the emissivity is high for infra-red that doesn't clash with the reflectivity being high for visible light. This (or rather it's converse) is exactly why greenhouses heat up in visible light. They have a high emissivity and low reflectivity at visible wavelengths but a low emissivity and high reflectivity at IR wavelengths.

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yes that they do, very reflective (make great mirrors)! and yes i understand the germanium lenses by my problem is when looking at glass i.e windows ect – Chris Deakin Apr 3 '13 at 14:24
@ChrisDeakin: I've amended my answer to respond to your comment – John Rennie Apr 3 '13 at 14:30
both emissivity and reflection are in IR, through temperatures between -20 to 70 they all seem to have high emissivity and high levels reflections when viewed with a thermal camera – Chris Deakin Apr 3 '13 at 14:39
How can you judge the reflectivity of the IR light? Are you photographing the reflections with a second IR camera? – John Rennie Apr 3 '13 at 15:12
i am sorry i am confused. the IR light? the IR energy is that emitted from either me, a hot cup or the cold sky as explained in my experiments in the comments above. i am looking at the glass and measuring the reflection in the glass using the IR camera, i will then point the camera at the object that is being reflected in the glass (such as my skin, the cup or the sky. i only use one IR camera to take both measurements – Chris Deakin Apr 3 '13 at 15:18

I experienced the same problem: too often, the emission value of glass is misquoted in different sources on the internet, as I found to my own dismay. My own calculations found about an average reflectivity R of 0.2, transmittance T of 0.4 and absorption of 0.4 for glass of about 2mm thick. (I calculated those values using absorption spectrum graphs of wikipedia for soda lime glass, http://en.wikipedia.org/wiki/Soda-lime_glass, using black body radiation curve to get a weighed average, and hemispherical averaging to account for the different reflectivity, transmittance and absorbance for different angles at the same wavelength). The emission value for glass quoted is often 0.82, however: this cannot be right. The error is in the fact that only the 0.2 reflectivity of glass is deducted from 1, instead of both transmittance and reflectivity. The glass absorption coefficient for glass is (kirchhoff law) equal to the emissivity of glass, and thus equal to approximately 0.4, or 40 percent. When I used this emission value in the heat transport model that I created, the outcome was a calculated U value of about 6 W/m2*Kelvin for the glass plate, in good agreement with the value to be expected for a glass plate.

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In an isothermal steady state condition, meaning when the temperature is uniform and not changing with time,

%Reflected + %Transmitted + % Absorbed = 100%

For opaque system,

%Reflected + % Absorbed = 100% .........(1)

Now, if the object absorbs infrared radiation, its energy (and thus temperature) will increase, but as the object is in steady state, to offset that increase in temperature, the rate of emission must be equal to the rate of absorption. So,

% Absorbed = % Emitted.

Substituting in equation (1),

%Reflected + % Emitted = 100% .........(2).

So reflectivity is reciprocal to emissivity.

For translucent system,

%Reflected + %Transmitted + % Emitted = 100%.........(3).

This is the associated physics.

normally it works but not with glass!

It is true for glass also, only transmissivity comes into picture, but still, reflectivity is reciprocal to emissivity.

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Glass Is not thermally transmissive, i understand what the text books say and the equations, but still this doesn't explain why glass has such a high emissivity and reflectivity? the glass has a high emissivity, and thus a high rate of absorption, it also is highly reflective in all my experience, you can clearly see reflections with a thermal camera. – Chris Deakin Apr 3 '13 at 12:43

Based on the experiments you describe in the comments, it seems like you might very well have a reflectivity of 20-30% in your window, for the spectral region where your camera measure. The question is where you got the high emissivity numebers from. It seems likely that the problem is that you're assuming the emissivity and reflectivity is the same throughout the infrared region. The high emissivity might be for another part of the spectrum than where your camera measure.

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the emissivity is around 0.9 to 0.97 (90%-97%) on multiple emissivity tables from multiple places. – Chris Deakin Apr 3 '13 at 15:07
Ok, but do you know what wavelength region that is for? – jkej Apr 3 '13 at 15:13
i don't, no. so is it possible the reflections i am picking up from temperatures between -30 to 70 are going to be different to those at higher temperatures (different wave lengths) – Chris Deakin Apr 3 '13 at 15:21

To me the problem is not linked to the reflectance, but to the surface finish.

Picking up an image of a reflection in the visible part of the spectrum is possible even on a black carbon surface if that surface is polished well enough. To convince yourself of this, simply pick a dark material with a well polished surface (or a not so well polished surface but placed at an highly inclined angle). Then place the surface to reflect the sky day light. And you will see the surface reflecting the color of the sky even if the surface color is blue, red or any other dark color/tint.

Thus, since the glass window is a well polished surface, it will reflect any image of the surrounding in the thermal infrared. This is also true for the sky in the visible part of the spectrum as would tell you any bird that survives hitting a cleaned glass window at spring time... ;-)

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