Measuring a human hair

Purpose: We are going to measure the thickness of human hair by using a laser and micrometer, and we compare the accuracy of measuring the hair.

The expected range of thickness of human hair is (1.7 x 10^-5, 1.8 x 10^-4) m

Measure with a laser:


We obtain a human hair of one of the group mate and tape the hair across the hole in a 3x5 card.

We point the laser that is perpendicularly to the hole to the whiteboard. The interference pattern is shown on the whiteboard. We measure the distance between the card and whiteboard, and we mark the first three orders maximum measure the distance between orders.

Distance between card and whiteboard L= 604.9 cm= 6.049 m.

m	y (Left) (m)	y (Right) (m)	λ (m)	L (m)	d (Left) (m)	d (Right) (m)
0	0 ± 0.0005	0 ± 0.0005	6.2*10^-7 ± 2*10^-8	6.049± 0.0005
1	0.066 ± 0.0005	0.062 ± 0.0005	6.2*10^-7 ± 2*10^-8	6.049± 0.0005	5.68E-05 + 2.310E-06 - 2.227E-06	6.049E-05 + 2.464E-06 - 2.424E-06
2	0.109 ± 0.0005	0.105 ± 0.0005	6.2*10^-7 ± 2*10^-8	6.049± 0.0005	6.88E-05 + 2.567E-06 - 2.515E-06	7.144E-05 + 2.659E-06 - 1.984E-06
3	0.152 ± 0.0005	0.153 ± 0.0005	6.2*10^-7 ± 2*10^-8	6.049± 0.0005	7.40E-05 + 2.667E-06 - 2.137E-06	7.354E-05 + 2.624E-06 – 2.148E-06

Then we take the average value of d for each order m.

m	d (Left) (m)	d (Right) (m)	D (avg) (m)
0
1	5.68E-05 + 2.310E-06 - 2.227E-06	6.049E-05 + 2.464E-06 - 2.424E-06	5.865E-05 + 4.304E-06 – 4.077E-06
2	6.88E-05 + 2.567E-06 - 2.515E-06	7.144E-05 + 2.659E-06 - 1.984E-06	7.012E-05 + 3.979E-06 - 3.835E-06
3	7.40E-05 + 2.667E-06 - 2.137E-06	7.354E-05 + 2.624E-06 – 2.148E-06	7.377E-05 + 2.897E-06 – 2.378E-06

Finally, we take the average of the order 1, 2 and 3 to find the final average thickness d. We have the final average thickness d = 6.75 x 10^-5 + 9.154 x 10^-6 - 1.294 x10^-5 m, which is in the range of expected value.



Measure with a micrometer:

Our group mate Chris use micrometer to measure the thickness of hair. He finds the thickness of the hair using microscope is 0.1mm, which is 1 x 10^-4 m, which is in the range of the expected range of thickness of a human hair.

The advantage of using laser is easier to look at and mark the reading by eyes for the value of measurement. The disadvantage of using laser is it has lower accuracy of measurement as there are such more measuring errors such as measuring the distances between board and card, and measuring the distance between maximum points of board.
The advantage of using microscope is it has higher accuracy of measurement. The disadvantage of using microscope is harder to look at the reading by eyes for very smaller value of measurement.

We successfully find the thickness of hair by using laser, and we successfully find the thickness of hair by using a microscope as the thicknesses of measure in both method are in the expected range. We find the method of the thickness of hair by using microscope is more closed to the expected value as the uncertain range is smaller.