## 1.4 The infrared radiation of the human body

Using late 19 century laboratory physics, and recent biophysics we may find out why the human body radiates most at a wavelength of about 10µm. The specific intensity of the human skin can be approximated with that of a modified black body.

 (1.6)

The ε(λ) emissivity of human skin in the wavelength range of 1µm< λ <14µm is nearly unity, ε(λ)=0.98±0.01 (Hobbie and Roth 2007). We may actually say it radiates like a black body. The Wien’s displacement law may be used to find out in which wavelength range it radiates most. Assuming a skin temperature of 300 K < T < 310 K we arrive to 9.3µm < λmax (T ) <  9.7µm. The total surface area of the human body can be approximated by the depth-weight formula as

 (1.7)

where w is the weight in kg and H is the depth in cm (Du Bois and Du Bois 1916). The total surface area for a typical adult male is Area ~ 1.73m2 . The total radiated power at a skin temperature of T = 306 K may be calculated from Stefan’s law as:

 (1.8)

Although only a 5/7 fraction of the total skin surface is considered as effective radiator, the uncovered skin is a bright infrared source. We shine bright in the infrared while the human eye detects only 1% of the light at 0.69 µm, and 0.01% at 0.75 µm, and so we eﬀectively cannot see wavelengths longer than about 0.75 µm.

It is not only the radiation of the human body that we can not see by our eyes. In space, there are many regions which are hidden from optical telescopes because they are embedded in dense regions of gas and dust. However, infrared radiation, having wavelengths which are much longer than visible light, can pass through dusty regions of space without being scattered. This means that we can study objects hidden by gas and dust in the infrared, which we cannot see in visible light, such as the center of our galaxy and regions of newly forming stars.