Light Interference: Measuring a Human Hair

     The purpose of this lab is to measure the thickness of a human hair in two different ways then compare the values. The first method of measuring the human hair will involve treating the human hair like a double slit screen that produces light interference. The second method will involve a traveling microscope: this method will be used to compare the thickness from method one.


     The setup involved using a red laser that was incident directly on a taut human hair. A screen was placed several meters away from the hair. The result was a pattern of light and dark fringes. By using the equation

it will be possible to obtain a reliable value for the thickness of the hair.

The bright and dark fringes projected onto the screen.

Fringe pattern denoted by dots followed with measurements

     The distance from the hair to the screen was 6.049 meters. The wavelength of the laser is estimated to be between 620-670 nanometers. Theta for m = 1 can be calculated through trigonometry. Theta is equal to the inverse tangent of 6.6 cm over 604.9 cm. This calculation results in theta being 0.625 degrees. Using 645 nm for wavelength, 0.625 degrees for theta and m = 1, the calculated value for d is 59130 nm which is equal to .059130 mm.


     The second method, the use of a traveling microscope to measure the hair thickness, resulted in a thickness of 0.1 mm +/- 0.05 mm.


     The two values fall within a reasonable range for hair thickness (provided by the professor: 1.8x10^-1 to 1.7x10^-2). The calculated value from the first method falls within the range of uncertainty of the second method. However, both of these methods have redeeming qualities and pit falls; consequently, this leads to both measurements being unreliable.  The first method uses exaggerated distances such as the screen being 6.049 meters away to overcome some uncertainties and errors in the experiment. The draw back to method one that makes it unreliable is the clarity of the interference pattern and the laser being directly incident on the strand of hair. Since those two factors are difficult to overcome without more of a time investment and a more secure apparatus for the laser/hair, it can be concluded the resulting value for hair thickness is unreliable. The advantage of method two is the ability to resolve the hair in a microscope and a sliding scale that can be moved with the microscope. The only disadvantage to the sliding microscope is the size of the sliding scale. Since the hair used in this lab was relatively fine, the traveling microscope had too large of a scale to measure the hair thickness without a large uncertainty. So while the two values fall within excepted range of hair thickness, this lab was unable to resolve absolute thickness of the studied hair sample.