Michelson Interferometer

Definition

A Michelson interferometer is an optical device that divides a beam of monochromatic light into two coherent beams using a beam splitter, sends them along two perpendicular arms reflected by mirrors, and then recombines them to form interference fringes. The pattern of fringes depends on the optical path difference between the two beams.

Main Content

1. Principle of Interference and Superposition

• The Michelson interferometer is based on the principle that when two coherent light waves meet, they superpose and produce interference.
• If the waves arrive in phase, constructive interference occurs and a bright fringe is formed; if they arrive out of phase by half a wavelength, destructive interference occurs and a dark fringe appears.

In this instrument, a beam splitter divides the incident light into two beams. These beams travel different optical paths, reflect from mirrors, and then recombine. The nature of the resulting fringe pattern reveals the difference in path taken by the two beams.

The condition for interference is determined by the path difference:

Constructive interference

• $\Delta = n\lambda$

Destructive interference

• $\Delta = (n + \tfrac{1}{2})\lambda$

where $\Delta$ is the path difference, $n$ is an integer, and $\lambda$ is the wavelength of light.

2. Construction and Optical Components

• The main parts include a beam splitter, two mirrors, and a compensating plate.
• The beam splitter is a partially silvered glass plate that reflects part of the incident light and transmits the rest.

The incident beam falls on the beam splitter at 45°. One part is reflected toward mirror $M_1$, and the other part is transmitted toward mirror $M_2$. After reflection from the mirrors, the beams return to the beam splitter and are directed to the eye or a screen, where they interfere.

The compensating plate is often used so that both beams pass through equal thicknesses of glass, which improves fringe visibility. This is important because different glass thicknesses can introduce additional phase shifts and reduce the sharpness of fringes.

The mirrors are highly polished and one of them is usually movable with a micrometer screw. This allows very small changes in path length to be introduced deliberately.

3. Fringe Formation and Measurement Applications

• The interference pattern may appear as circular fringes or straight fringes, depending on the alignment and path difference between the mirrors.
• By observing the shift in fringes, very small changes in distance, wavelength, or refractive index can be measured accurately.

When the mirrors are exactly perpendicular to each other and equally distant from the beam splitter, circular fringes are observed. If one mirror is slightly tilted, straight or curved fringes may appear. Each fringe corresponds to a change in path difference of one wavelength.

A key practical application is the measurement of wavelength. If a mirror is moved by a distance $d$, the optical path changes by $2d$ because the beam travels to the mirror and back. If $m$ fringes cross the field of view during this movement, then: $$\lambda = \frac{2d}{m}$$

This makes the Michelson interferometer a powerful precision measurement device in laboratories and optical experiments.

Working / Process

1. Splitting of the incident light

• A monochromatic light beam is directed onto the beam splitter.
• The beam splitter divides the beam into two coherent beams: one reflected toward mirror $M_1$, and the other transmitted toward mirror $M_2$.

2. Reflection and recombination

• The two beams travel along their respective arms, reflect from the mirrors, and return to the beam splitter.
• On recombination, the beams overlap and interfere with each other.

3. Formation and observation of fringes

• Depending on the difference in optical path lengths, bright and dark fringes are formed.
• By moving one mirror slightly, the fringe pattern changes. Counting the number of fringes displaced helps measure wavelength, displacement, or other quantities with high precision.

Advantages / Applications

• It provides extremely accurate measurement of wavelength, small distances, and refractive index changes.
• It is widely used in optical experiments to demonstrate and study the phenomenon of interference.
• It has important scientific and technological applications, including precision metrology, spectroscopy, testing optical components, and detecting tiny displacements.

Summary

• The Michelson interferometer is an optical instrument that produces interference by splitting and recombining a light beam.
• It is based on the principle of superposition of coherent waves and the formation of bright and dark fringes due to path difference.
• It is a highly sensitive device used for precise measurements in wave optics and laboratory optics.
• Important terms to remember: beam splitter, coherent beams, optical path difference, constructive interference, destructive interference, fringe pattern, compensating plate, mirror displacement