Experiment 9: Measuring a Human Hair

In this experiment we were measuring the thickness of a human hair. This task is tough to do by hand so we found out the thickness by using a laser. We were using HeNe lasers during this experiment.To begin this experiment we used one strand of hair and taped it to a 3x5 card with an opening in it.

We shined the laser through the hole in the card and hit the strand of hair to produce different interference patterns. The light will be the strongest in the middle and dissipate as the number of minima increase. We can measure the distances of the gaps in the interference patterns to help us determine the thickness of the hair. We initially measured the distance of interference patterns while using a marker.

We measured the distance between the different minima with a much finer tool than a marker. We changed the tool of measurement to a pen and measured the distance between multiple minima and divided it by the total number of minima we measured across. 

                                                     

We tested this with two different people's hair. We first tested this with a male student's strand of hair. We can analyze the data with this formula.  λ = dy/L. In this equation λ is equal to the wavelength of the laser. d is the thickness of the hair. y is the distance between the minima and L is the distance of the laser to the whiteboard. We rearrange this equation for d because it is the value that we are looking for and the result is d = λL/y. λ = 632.8 nm This laser is calibrated under extreme conditions so we assume that there is no uncertainty. L is 1.00m + 0.05m. y for the first strand of hair is 0.00516 m + 0.0002m. The value of d for the first trial is 122.6 μm + 30.8 μm The uncertainty for this result was determined by using partial derivatives. 

Δd = + sqrt((∂d/∂λ)^2*(Δλ)^2 + (∂d/∂L)^2*(ΔL)^2 + (∂d/∂y)^2*(Δy)^2) 

= + sqrt((L/y)^2*(Δλ)^2 + (λ/y)^2*(ΔL)^2 + (-λL/y^2)^2*(Δy)^2) 

This formula reduces to + sqrt((λ/y)^2*(ΔL)^2 + (-λL/y^2)^2*(Δy)^2)) because Δλ = 0. 

Δd = 30.8 μm 

In the second trial of the experiment we used a female students hair instead. 

Only the value of y changed. y = 0.0025 m + 0.0002m.

d was determined to be 253.1 μm + 63.6 μm. 

Conclusion

The hypothesis for the strand of hair being much thicker in this is case is because the female student used more hair care products than the male student. When measuring objects with a really small thickness, it is best to measure them with a laser. When a laser is shined on the object it will produce interference patterns on a screen and the distance of the maxima or minima can be measured. This is more accurate than measuring the object by hand.