A hair was used to form one end of an air wedge with two glass plates. The glass plates were in contact at the other end. When light of wavelength (4.6x10^-7m) was reflected from the air wedge, the 320th dark
fringe coincided with the position of the hair. What was the thickness of the hair?
http://www.schoolphysics.co.uk/age16-19/Wave%20properties/Interference/text/Wedge_fringes/index.html
So let thickness be e, and the distance from the wedge be x. With the small angle assumption
e =Theta=m*wavelength/2 . In this case, m=320
so e= 320*4.6e-7 /2
To find the thickness of the hair, we need to use the formula for the path difference in an air wedge interferometer:
Δx = λN / 2
Where:
Δx is the path difference between the interfering rays
λ is the wavelength of the light used
N is the number of dark fringes
In this case, we are given the wavelength (λ = 4.6x10^-7 m) and the number of dark fringes (N = 320). We want to find the path difference Δx, which will give us the thickness of the hair.
First, we can rearrange the formula to solve for Δx:
Δx = λN / 2
Substituting the given values:
Δx = (4.6x10^-7 m) * (320) / 2
Δx = 1.472x10^-4 m
Therefore, the path difference between the interfering rays is 1.472x10^-4 m, which is equal to the thickness of the hair.