The thickness of hair from a diffraction pattern, science of a different passion

Sometimes in 2007 or early 2008, this picture was taken (with a camera fitted on a mobile phone.) It captured a unique diffraction pattern by accident (serendipity!!). I did a preliminary analysis to determine the thickness of the hair of the person in picture [Me!]

A diffraction pattern is produced as a result of the dual nature of objects at a very small scale. When a wave such as light “rays” has a wavelength comparable to the size of an object, hair in this case, the wave bends and spreads upon hitting the object. If light were to be very tiny particle only, it would undergo scattering like small balls scatter off each other. But since they bend and spread unique patterns are created.

We see such a spreading in the pattern. The bands that are created are much thicker than the hair itself as can be easily seen. But to make things simpler the color of the bands are clear. Upon a close look I see that it has almost all the colors in the basic set of color, namely, VIBGYOR except for Red. Red has the longest wavelength ~800 nm, that’ is 800 nano meters or 800 divisions out of a billion divisions of a meter. This means, since red is missing, that the hair is definitely thinner than 800 nm. In-fact the wavelength of this spectrum goes from 600 nm to 400 nm. That means the hair has to be thinner than 600 nm. But considering the fact that the hair is densely packed some groups of hair are going to be much thicker for the light so the higher wavelength. So the individual hair thickness has to be less than 400 nm. Now it might still be thinner but the optical spectrum of light is off. Considering a rough difference of 100 nm between the wavelength of light and the hair thickness, for diffraction to happen, the hair of the person in picture is at most 300-400 nm in thickness.

In comparison, an atomic force microscope [resolution ~1 nm, it can view objects the size of an atom] can make 400 lines of marks appear on a single hair. For comparison, some molecules are a few nano meters in size.