Construction of Michelson Interferometer:
The Michelson interferometer consists of a beam splitter, two mirrors, and a detector. The beam splitter divides a beam of light into two separate beams, one known as the reference beam and the other as the sample beam. The mirrors are placed in such a way that the reference beam is reflected back towards the beam splitter, while the sample beam is directed towards the sample being tested. The two beams then recombine at the detector, and interference patterns are observed.

Working of Michelson Interferometer:
1. The beam splitter splits the incoming light into two beams. One beam travels towards the reference mirror, and the other beam travels towards the sample.
2. The reference beam is reflected back towards the beam splitter, while the sample beam is reflected back after interacting with the sample.
3. The two beams recombine at the detector, where interference occurs between the two beams.
4. The interference pattern is observed, usually in the form of bright and dark fringes.
5. By adjusting the path length of one of the beams, the fringes can be made to shift, allowing for precise measurements.

Measuring Wavelength of Light:
The Michelson interferometer can be used to measure the wavelength of light by measuring the fringe shift when the path length of one of the arms is changed. The formula for calculating the wavelength is given by:

λ = 2 * (Δd) / n

where:
- λ is the wavelength of light
- Δd is the change in path length between the two arms of the interferometer
- n is the number of fringes shifted

To measure the wavelength, the path length of one of the arms is adjusted, causing a shift in the fringes observed at the detector. The change in path length (Δd) is measured, and the number of fringes shifted (n) is counted. By substituting these values into the formula, the wavelength of light can be calculated.

The Michelson interferometer is a versatile instrument used in various applications such as measuring small displacements, testing optical components, and studying the properties of light. Its ability to produce interference patterns makes it a valuable tool in physics and optics research.