Question

part a
how far must the mirror m₁ in a michelson interferometer be moved if 620 fringes of 649-nm light are to pass by a reference line?
express your answer to three significant figures and include the appropriate units.
δx = value units
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Explanation:

Step1: Recall the formula for Michelson interferometer

In a Michelson interferometer, the relationship between the number of fringes \( N \), the wavelength \( \lambda \), and the distance moved by the mirror \( \Delta x \) is \( \Delta x = \frac{N\lambda}{2} \). This is because each fringe shift corresponds to a path difference of one wavelength, and the mirror movement causes a path difference of \( 2\Delta x \) (light travels to the mirror and back).

Step2: Identify the given values

We are given \( N = 620 \) fringes and \( \lambda = 649\space nm=649\times 10^{-9}\space m \).

Step3: Substitute the values into the formula

Substitute \( N = 620 \) and \( \lambda=649\times 10^{-9}\space m \) into \( \Delta x=\frac{N\lambda}{2} \).

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Answer:

\( \Delta x = \boldsymbol{2.01\times 10^{-4}\space m} \) (or \( \boldsymbol{201\space \mu m} \))