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A thin film with index of refraction n=1.40 is placed in one arm of a Michelson interferometer, perpendicular to the optical path. If this causes a shift of 7.0 bright fringes of the pattern produced by light of wavelength 589nm, what is the film thickness?

Short Answer

Expert verified

The film thickness is 5.2μm.

Step by step solution

01

Given data

Wavelength of light λ=589nm

Index of refraction n=1.4

02

Concept of Michelson interferometer

Fiber optic Michelson interferometer employs the same principle of splitting a laser beam and inserting the optical path difference between the arms.

03

Determine a film thickness

The number of fringes shifted when we insert a film of thickness L and an index of refraction n in Michelson interferometer.

ΔN=2Lλn-1

Here is the thickness of the film,

ΔN=7L=λΔN2n-1=589nm721.4-1=5153.75nm=5.15375μm≈5.2μm

Hence, the film thickness is 5.2μm.

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