A Michelson interferometer is used to measure the wavelength of light put through it. When the movable mirror is moved by exactly \(0.100 \mathrm{mm}\), the number of fringes observed moving through is \(316 .\) What is the wavelength of the light?

Interferometry is an insightful technique used in science and engineering to measure extremely small distances with precision or to calculate wavelengths of light with high accuracy. It makes use of the principle of superposition to combine waves in a way that will cause the result of their addition to have a greater or lesser amplitude. In the case of light waves, when two waves meet, they can interfere constructively, creating a bright fringe, or destructively, which results in a dark fringe.

The Michelson interferometer is a classic example of this technology. It measures the change in interference patterns caused by a precise movement of a mirror, thus allowing the calculation of the wavelength of light. When a mirror in the apparatus is moved, it changes the path length for one of the beams of light that compose the interference pattern. The shift in the interference fringes can be counted and used to calculate the light's wavelength using specific equations, a critical aspect of optical physics.

Wavelength is a fundamental concept in the study of light and the entire electromagnetic spectrum. It is defined as the distance between consecutive points of corresponding phase of a wave, such as from crest to crest or from trough to trough. This distance is typically measured in meters, but because light wavelengths are so small, they are often expressed in nanometers (nm), where 1 nm is one billionth of a meter.

Light is a form of electromagnetic radiation and each color of visible light has a specific range of wavelengths. For instance, red light has a longer wavelength than blue light. The wavelength of light determines its color in the visible spectrum but we can also measure wavelengths outside the visible range using equipment tuned for those frequencies. Understanding how to measure wavelength is essential in numerous fields such as astronomy, fiber optics, and various forms of spectroscopy.

Optical physics is a branch of physics that studies the behavior of light, its interactions with matter, and the construction of instruments that use or detect it. Optics is divided into several sub-disciplines: geometric optics treats light as a collection of rays, wave optics deals with light as waves, and quantum optics treats light as discrete particles or photons.

A key application within optical physics is the creation and analysis of optical instruments like the Michelson interferometer, which merges geometric and wave optics principles to measure light's wavelength. By studying how light behaves under various conditions, scientists can design advanced technologies ranging from microscopes and telescopes to fiber optic communication systems. Moreover, the fundamentals of optical physics also permeate into more abstract studies such as the quantum characteristics of light, increasingly relevant in the fields of quantum computing and communications.