Experiment 11: Measuring a Human Hair

Introduction: The purpose of this experiment is to use diffraction to accurately measure a human hair. The measurement will be confirmed with a micrometer.
Procedure: We hole punched a card and taped a hair taught over the hole. We then shined a laser through the hole, over the hair.

We then measured the distance from the card to the wall we would project the laser beam on with a 2 meter stick. This value is referred to as L.

We measured the spaces between the bright spots of the interference pattern, noting the uncertainty of the measurement. This value is referred to as y. The wavelength (represented as lambda) was stated on the laser.

Data and Analysis:

We used the formula in the picture and solved for d. In this formula, d is the measure of the gap between the light beam that causes the interference pattern. In this case, it is the diameter of the hair. We then calculated the maximum and minimum values of d, which came from the uncertainty in the measurement of y. We averaged them together and then subtracted the average from the maximum of d, and the minimum of d from the average. This gave the uncertainty of d. This yields the value of d  to be 5.4e -5 ± 0.25e -5. This measurement makes sense because the hair must be on the order of magnitude of the laser wavelength or smaller to cause interference. This answer is smaller than 650 nm. The d experimental is the measurement of hair obtained by the micrometer. It is not within uncertainty however, this is likely because the micrometer was not calibrated before measurement and was in a very used condition. It is on the same order of magnitude so we were in the right ballpark with a percentage error of 25.9%