A 5.08-cm-long rectangular glass chamber is inserted into one arm of a Michelson interferometer using a 633 -nm light source. This chamber is initially filled with air \((n=1.000293)\) at standard atmospheric pressure but the air is gradually pumped out using a vacuum pump until a near perfect vacuum is achieved. How many fringes are observed moving by during the transition?

Optical Path Length (OPL) is a fundamental concept in understanding the workings of the Michelson interferometer. It's calculated by taking the physical distance light travels and multiplying it by the medium's refractive index through which it's traveling. Simply put, you could think of OPL as the 'effective' distance light has traveled in a medium, which might differ from its actual path due to the medium's optical properties.

In the context of the interferometer, when we have a chamber filled with air, the OPL is slightly longer due to air's refractive index being slightly greater than 1. But, when the chamber is emptied to a near-perfect vacuum, the refractive index effectively becomes 1, as a vacuum doesn't alter the path of light. Calculating the change in OPL between these conditions helps us understand the shift in interference fringes observed, a concept that's intimately connected with how interferometers function.

The refractive index, denoted as 'n', is a dimensionless number that describes how light propagates through a medium. It represents the ratio of the speed of light in a vacuum to the speed of light in the specified medium. For example, the refractive index of air at standard atmospheric pressure is around 1.000293, which is very close to the refractive index of a vacuum, which is exactly 1.

Understanding the refractive index is crucial for precision instruments like the Michelson interferometer because it determines how much the light bends when entering a different medium, and thus affects the OPL. In the exercise, the refractive index is central to calculating how many fringes pass by during the transition from air to vacuum, as it directly affects the changes in the optical path.

Interference fringes are a visual manifestation of the wave nature of light. When two coherent light waves meet, they can interfere constructively or destructively, producing bright and dark bands known as interference fringes. In an experiment like the Michelson interferometer, these fringes are essentially patterns of light and dark lines or bands resulting from the interference.

By observing the movement of these fringes, one can determine changes in the optical path. As the refractive index changes from air to vacuum, the path difference between the beams in the interferometer arms changes, resulting in a shift of the interference pattern. The number of fringes moving can provide insight into many physical properties, including changes in the refractive index or confirming the wavelength of light used.