hair’s width

The width of a human hair is pretty small, so you probably don’t have a good way of measuring it directly. However, you can use other methods, and these are the same as how you might study materials and the arrangement of molecules that you can’t see directly. We use the diffraction of light around these small structures, and we end up measuring how the light interferes as it goes through our object. 

In my case, I had to pluck one of my hairs from my head. I don’t normally pull out my own hair, but this is for physics and for my students. I affixed the hair at the opening of the laser:

hair taped to laser aperture

When I turn the laser on, you can see that it goes through and around the hair:

hair taped to laser, illuminated

Here are some details about my laser for those who may be doing this calculation along with me.

label on my green laser pointer

Normally, this green laser would make a very precise dot, as Gus the cat is observing here:

Gus observes a dot of laser light

However, with the hair in the path of the coherent green light, a diffraction pattern was formed. I lined things up so that the hair was running horizontally across the aperture of the laser, making the diffraction pattern align vertically. The staircase made a good place to set this all up, and one of my favorite books was a good prop for lining up the laser so that the pattern could be displayed on the wall above the stairs.

laser propped by Steinbeck

setup for projection of diffraction pattern

Gus observing physics

The diffraction pattern on the wall was in a good place for me to look at and measure it closely:

diffraction pattern without scale

diffraction pattern with scale

The central maximum is at the 50cm mark on this meter stick, with minima extending on either side. The projection of this pattern is 360 cm away from the aperture of the laser where the hair is taped. Here’s my schematic:

Schematic of hair width calculation

 

Based on all of this, how can you calculate the width of my hair?