Measuring Hair Thickness

Objective

To measure the thickness of a human hair using both laser interferometry and  a micrometer.

Equipment:
Laser
Meter Stick
Note Card
Hair
Micrometer

Procedure

Laser and note card setup

Laser

Measurement of x

First a hole was punched into the note card and a strand of hair placed tightly across it. A flat surface (a white board) was set up parallel to the note cards surface. The distance L to the surface from the note card was then measured. A laser with wavelength 633 nm was used to shine at the hair, this created a diffraction pattern that was seen on the surface. The distance between the first maxima and the second in the diffraction patter, x, was recorded. the equation,

 d=λLm

     x

was used to determine the thickness of the hair using the known values of wavelength and m and the measured values x and L

The measurement obtained from this  was compared to the measurement obtained from measuring a hair with a micrometer.

The Length of separation was 1.00 ± 0.01m
     Sample 1: y= 3.1 ± 0.1cm
                    m=6
                      Diameter = 0.000123 ± 0.000005 m
     Sample 2: y= 3.3 ± 0.1cm
                    m=4
                      Diameter = 0.0000767 ± 0.0000032 m
     Sample 3: y= 1.2 ± 0.2cm
                    m=1
                      Diameter = 0.0000528 ± 0.00001.11 m

Micrometer Measurement

     The diameter measured was on the correct order of magnitude as expected(based on values found on a scientific website) of the diameter of hair. Using the micrometer was slightly difficult but it gave similar values. For sample 1 the micrometer gave a value of 0.0002 m. This is a %error of 48%. The  micrometer is less accurate because the minimum increment of measurement is a tenth of a millimeter  The laser method can better measure small lengths because it can more accurately measure the parameters needed and obtain much smaller values.