Measuring a Human Hair

Objective: To measure the thickness of a human hair using a laser and micrometer.

Equipment:

• Laser
• Meter Stick
• Note Card 
• Hair
• Micrometer

Procedure: Punch a hole in the note card and secure the hair in between the hole as to split the hole into two. Make sure it is taut. Make the note card parallel to a vertical surface (like a wall or board) and measure the length between the surface and the note card, L. 

     Mount the laser so it shines over the hair and an interference pattern on the vertical surface. The wavelength of the laser is given to be 633nm. Measure the distance between maximum on the  diffraction pattern (y) and record the order of the maximum (m).

It was easier to mark the maximum and and measure the marks afterwards.

        The equation used to determine the diameter was:    

                                     d=λLm

                                           y

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

     The diameter measured was on the correct order of magnitude as expected 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.