Experiment 11: Measuring a Human Hair

Purpose:
The purpose of this experiment is to measure a human hair by two method. The first method is using the concept of light interference when a light ray goes through two small (separated by a distance d) slits . The second method is using a micrometer. Two measurement will be collected and compared to see which method is better to measure a small object.

Procedure:

Using a laser
1. Obtain a hair and tape it across the hole in the 3x5 note card.
2. Clamp the card so that it is parallel to the white board a distance 1 m.
3. Pointing a laser toward the board through the hair.
4. The distance between the first 3 fringes is recorded.

The laser pointing through the hair

Diffraction pattern formed by the light interference

Data:

Trial	y (cm)	m
1	1.85 ± 0.05 cm	3
2	1.83 ± 0.05 cm	3

where: y = distance between 3 adjacent diffraction
λ = 633 nm  (wavelength of the laser beam)

L = 100 ± 1 cm (distance between the board and the note card)

d = diameter of the hair

d = mλL/y = 0.103 ± 0.038  mm

Using a micrometer
Place the note card under the micrometer and measure the diameter of the hair

The hair is seen through the micrometer

Data: 

Trial	d (mm)
1	0.18 ± 0.01
2	0.13 ± 0.01
Average	0.155 ± 0.02

Data Analysis:
% error = (0.103 - 0.155)/((0.103 +0.155)/2) = 4.03%

Summary:
           As the results, the diameter of the hair could be from a range 0.103 ± 0.038  mm  - 0.155 ± 0.02 mm, and the percent error is 4.03 %. The two methods give the results within their uncertainties. Therefore, the two methods are the appropriate ways to measure a small object such as a hair.
           Base on the observation of the experiment, light interfered constructively and destructively depends on the distance of the light source. At the middle, the light interfered brightest which the distance of the 2 light rays through the slits were equal. When the distance traveled was half a wavelength, there was no light. Therefore, the darkness was between the two bright fringes. Because the distance between the white board and the hair was a lot longer than the distance of 3 fringes, the equation d = mλL/y can be used. Otherwise, the equation cannot be used in this case. Moreover, the laser beam had to be perpendicular to the note card and pass through the hair to get the interference. The light interference method is more accurate than the micrometer method to measure the hair or the width of the slits. The micrometer had a big uncertainty in measurement. However, using the micrometer could be done faster because we don't need to worry about the distance between the hair and micrometer.