Measuring a human hair

we are to accurately measure the thickness of a human hair, not by a ruler but by the idea of double slit.  We can use the distance between the hair and the board, the interference y_m of the slit as well as overtones.

we first make a hole in a 3x5 card and taped a human hair on to it, than we pointed a laser through the hole, we used the image to be projected oh to the white board, we now can measure the distance between the board, and the distance between the middle of the zero overtone and third.  

from what we learned in class about double slit, we can derive an equation 

 

y_m=L(lambda)(m)/d

but we are looking for d

d=L(lambda)(m)/y_m

where y_m is the distance between the zero overtone and the m we picked

L is the distance between the hair and the white board

d is the thickness of the hair

y_m we got to be about 6.5 cm _+ .023cm

L = 2m

we used the third overtone m=3

and the wavelength of the laser is 660nm

applying the data to the equation above we get d to be about 6.09 *10^-5 and 6.27*10^-5

from this picture we can clearly see the interference of the double slit experiment, we are getting a bright slit then a dark slit, bright  meaning the waves are converging, while the dark slits are diverging, we can also see that the bright slits are going to be brighter on the inside and as it gets closer to the out side it gets darker.

analysis

by taking looking at this experiment we can assume that there is a lot of mistakes that can be made during the processes of the experiment.  measuring the distance of y_m might be the biggest, but compare that number to that of L, the mistakes is minimum.  the focus of this experiments is to show that light can be shown as a wave rather then particles.