Question

In Michelson Interferometer, the distance traversed by the mirror between two successive disappearances is $0.289 \, \text{mm}$. The difference between the wavelengths of two lines is (Assume the wavelength of one line is $5890 \, \text{\AA}$):

• A. $6 \, \text{\AA}$
• B. $12 \, \text{\AA}$
• C. $120 \, \text{\AA}$
• D. $60 \, \text{\AA}$

Hint:

In interferometry, the fringe shift is proportional to the change in the optical path length, which can be used to measure minute differences in wavelength.

Answer 1

The Correct Option is B

The Michelson interferometer produces interference fringes based on the optical path difference. The change in the interference pattern is related to the change in the optical path length, which corresponds to a difference in the wavelength of the two lines. The formula for the change in wavelength is:
\[\Delta\lambda = \frac{2 \Delta x}{m}\]
where \(\Delta x = 0.289 \, \text{mm}\) is the distance traveled by the mirror and \(m\) is the fringe order. Based on the given values, we find \(\Delta\lambda = 12 \, \text{\AA}\).