2. Michelson Interferometer a. A research group at CSUSB is using a Michelson In

Question

2. Michelson Interferometer a. A research group at CSUSB is using a Michelson Interferometer to calibrate an affordable scanning the tunneling microscope that they are inventing. If the movable mirror in a Michelson Interferometer is moved through a distance of 0.233 mm, a shift of 792 bright fringes occurs. What is the wavelength of the light producing the fringe pattern?

b. If a thin film of index of refraction n = 1.40 is placed in one arm of a Michelson interferometer, perpendicular to the optical path. This produces of shift of 7 bright fringes. The wavelength of the light used in the interferometer is 589 nm. How thick is the film?

Explanation / Answer

Given that
Number of bright fringes N = 792
Deal(x) = 0.233 mm
= 0.233*10^-3 m

We know that
(a)
wavelength of the light is given by

Lambda = 2*Deal(x) / N

= 2*(0.233*10^-3) / 792

= 5.88*10^-7  

= 589 mu*m

(b)
The number of fringes shifted when we insert a film of refractive index n and thickness Lin michelson interferometer is

Deal(N) = (2*L / Lambda)*(n - 1)

Here
Lambda = wavelength of the light used

Rearrange for L

L = (Lambda*Deal(N)) / 2*(n -1)

= (589*10^-9)*(7) / 2*(1.40 - 1)

= 5.15*10^-6 m

L = 5.14 mum

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