A Michelson interferometer with a He-Ne laser light source \((\lambda=632.8 \mathrm{nm})\) projects its interference pattern on a screen. If the movable mirror is caused to move by \(8.54 \mu \mathrm{m},\) how many fringes will be observed shifting through a reference point on a screen?

Interference patterns are fascinating physical phenomena that occur when waves superimpose, creating regions of constructive interference (where the waves add up) and destructive interference (where they cancel each other out). In the context of the Michelson interferometer, this pattern is created by the overlap of two coherent light beams reflected from mirrors.

When these light beams come back together, they can constructively interfere, creating bright fringes on the screen, or destructively interfere, resulting in dark fringes. The pattern consists of a series of light and dark bands and can provide valuable information about the light's wavelength, the path difference between the beams, and any changes in these parameters.

A Helium-Neon (He-Ne) laser is a popular type of gas laser where the gain medium is a mixture of helium and neon gases. The He-Ne laser emits coherent, monochromatic red light, typically at a wavelength of 632.8 nanometers (nm). Its stable output and well-defined wavelength make it an ideal light source for precision instruments like the Michelson interferometer. The laser's properties, including its phase and frequency stability, ensure that it produces a clear and stable interference pattern, which is critical for accurate measurements in optical experiments and applications.

Path difference is a fundamental concept in interferometry, referring to the difference in distance traveled by two beams of light before they combine to form an interference pattern. In the Michelson interferometer exercise, this path difference is created when one of the mirrors is moved, altering the travel distance of one of the beams.

The path difference is directly related to the displacement of the mirror and the resulting shift in the interference fringes. Since one mirror moves and the light travels two ways to and from the mirror, the path difference is twice the distance the mirror moves. It's crucial for determining the number of fringes that shift on the screen, making it a key component in calculating measurements with an interferometer.

The wavelength of light is the distance between two consecutive peaks (or troughs) in a wave, which determines its color in the visible spectrum. In many optical experiments and calculations, such as those involving a Michelson interferometer, it is vital to know the wavelength precisely, because it influences the interference pattern created.

In the given exercise, the wavelength of the He-Ne laser light is 632.8 nm, which is used to calculate the number of shifting fringes on the screen when the mirror moves. The wavelength is inversely proportional to the frequency of the light, meaning that light with a longer wavelength has a lower frequency. In practical applications, knowing the wavelength of light allows for the determination of optical path differences and assists in the analysis of various materials and components.