# Frostbite Theater

Measure the Width of a Hair - With a Laser!

Exactly how small is a hair's breadth? Measure it for yourself with nothing more than a laser pointer and a tape measure!

Announcer: Frostbite Theater presents... Cold Cuts! No baloney!

Joanna and Steve: Just science!

Joanna: Hi! I'm Joanna!

Steve: And I'm Steve!

Joanna: If you have a laser pointer, and you know how to use it safely, try this.

Take a hair, perhaps from a coworker, and tape it in a cardboard frame.

Place it a few meters away from the wall and shine the laser through it, making sure that the laser hits the hair.

You should see a pattern of light that looks like this.

Steve: The pattern is caused by the diffraction and interference of the laser light. Diffraction and interference are things that waves do, so seeing this pattern tells us that light behaves like a wave.

Joanna: We can also use the pattern to see how wide the hair is by making a few simple measurements.

We need to know the distance from the center of the pattern to the center of the first dark area and we need to know the distance from the hair to the wall. Do yourself a favor and measure both of these distances in centimeters.

The final bit of information that we're going to need is the wavelength of the laser. This should be marked somewhere on the laser itself. If it isn't, you can use 650 nanometers if you're using a red laser pointer or 532 nanometers if you're using a green one.

Steve: We can now use this equation to calculate the diameter of the hair.

The variable 'm' is a counter that keeps track of which minimum we used. And, since we used the first one, 'm' is equal to 1.

Lambda is the wavelength of the laser light that was used. Which, for us, is 532 nanometers.

As far as the sine of theta is concerned... Theta is the angle measured off the main beam that lands you on a minimum. And, theta is small. Since it's small, we can use the small angle approximation, so the sine of theta simply becomes the distance we measured to the minimum, which, in our case, was 8.8 centimeters, divided by the distance to the wall, which, in our case, was about 880 centimeters.

Doing little math, we find that the diameter of the hair is about 53,000 nanometers, or about 53 microns.

Joanna: Since we have a micrometer handy, we can measure the diameter of the hair directly. It's about 0.002 inches which is about... 51 microns!

Thanks for watching! I hope you'll join us again soon for another experiment!

Steve: So, did you at least pull out a gray hair?

Joanna: Ummm.... How could I not?!

Steve: Ouch! That hurt more than the pulling of the hair did...

Joanna: [Evil Laugh]

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