Question

Moving mirror $M2$of a Michelson interferometer a distance of $100\mu \mathrm{m}$causes$500$bright-dark-bright fringe shifts. What is the wavelength of the light?

Short answer

Wavelength of the light is$400nm$

Step-by-step solution

Wavelength

The wavelength of a waveform signal conveyed in space or down a wire is the distance between identical points (consecutive crests) in adjacent cycles.

This length is commonly stated in meters (m), centimeters (cm), or millimeters (mm) in wireless systems (mm).

Find Wavelength

The wavelength utilized in the Michelson interferometer experiment can be expressed as

$\Delta m=\frac{2\Delta L}{\lambda }$

$\Rightarrow \lambda =\frac{2\Delta L}{\Delta m}$

In our numerical example, we have

$\lambda =\frac{2\times 1\times {10}^{-4}m}{500}$

$=4\times {10}^{-7}\mathrm{m}$