Applications of Michelson's Interferometer: Measurement of wavelength

Application of Michelson's Interferometer

Measurement of Wavelength

One of the important applications of a Michelson interferometer is the accurate measurement of the wavelength of monochromatic light.

For a dark finge One of the important applications of a Michelson interferometer is the accurate measurement of the wavelength of monochromatic light.

\[ 2d = n\lambda \\.............(1)\]

When the movable mirror \(M_1\) is displaced through a distance \(x\), the optical path difference changes by \(2d\), because the light travels to the mirror and returns. As a result, the interference fringes shift.

If \(N\) fringes cross the reference point during the displacement of the mirror, then the change in optical path is:

\[ 2(d+x) = (n+N)\lambda ................(2)\]

by eq.(2) - eq.(1)

\[ 2x = N\lambda \]

Therefore, the wavelength of the monochromatic light is:

\[ \boxed{\lambda = \frac{2x}{N}} \]