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## 06 August 2010

### Thickness of Gray vs. Brown Hair

In my AP physics institutes, I show the classic demonstration in which we measure the thickness of a hair via diffraction.  I hold the hair in front of a green laser, and project the resulting diffration pattern on the white board.  We measure the distance x between dark fringes.

The thickness of the hair d is given by the equation x = mλL/d, where m = 1 (because we measured between two fringes, not across several of them), λ is the wavelength of the laser, and L is the distance to the screen.

The thickness of every hair I've ever measured has been between 10 μm and 100 μm.  Though I've had students investigate, we've never found any significant and consistent difference in thickness between different colored hair, between boys' and girls' hair, or between "thick" and "thin" hair.  Perceived "thick" hair has the same diameter as anyone else's hair, it must just lie together differently so that the distance between hairs is larger.

At my Manhattan College institute, I asked for a volunteer hair for this demonstration.  I looked around the room and saw virtually everyone with either bald heads or extra-short, nearly shaved, haircuts.  Fortunately, Manhattan College alumna Regina Verdeschi shook out her hair clip to reveal a deep brown mane that hung halfway down her back.

Regina asked, "Do you want a brown hair, or a gray hair?"  I froze for a moment.  For one thing, no student of mine has EVER asked that question.  But more to the point, with my wife Burrito Girl that's a trick question to which I know the answer:  "Brown, of course, because you don't have any gray hair."  (This will be the correct answer even in 20 years when her hair is deepest silver.)

Even though Regina is emphatically NOT Burrito Girl, I still gave the appropriate answer: "Brown, please.  I didn't notice any gray hair."  I've been trained well, I guess.  We measured the thickness of Regina's brown hair to be about 50 μm.

When I described my history of 10-100 μm hair thicknesses in every color and gender, Regina spoke up again.  "What about gray hair?  It's noticably thicker.  That's why I asked."  She proceeded to pull one of her few gray hairs and hand it to me.  She was right that the hair felt noticeably thicker.

At this point, the entire class was clamoring for a second measurement.  We projected the diffraction pattern and saw immediately that the fringes were considerably closer together.  The calculation suggested that Regina's gray hair was about 75 μm thick, or 30% thicker than her brown hair.

While I will not be able to repeat this experiment in my class of 16-18 year old boys, some of whom are balding but none of whom is going gray, I would be interested in feedback from the audience.  Measure one of your colleagues' gray hairs.  Tell me your results.  *Is* gray hair generally thicker than not-gray hair?  I'd do the experiment myself, but neither I nor Burrito Girl has access to the necessary materials.

#### 4 comments:

1. Two thoughts:

1. When I was in middle school, I thought thick vs thin hair had to do with hairs on your head, not the thickness of each hair. Given that norm, how do you judge the perceived thickness of hair in your class?

2. That said, I wonder if there's a consistent pattern to thick vs thin hair colors when controlling for individual. My blond hairs certainly feel thinner than my brown ones, though I wouldn't make a guess about people who are blond generally being different from people who are brunette. Your guys might not have gray hairs, but surely there's still variation in the strands of hair each individual, including you and Burrito girl, has.

2. Thanks for showing the picture of the circuit board. It should work for my AP Physics B students labs. One without the coil and more resistors would be better. Do you know of any other similar products?

3. Check out PASCO; they have several different boards like that.

GCJ

4. Yes, grey hairs are visibly thicker to the naked eye but, the question is: Why? Why?