Question

An important experimental device that uses interference is the Michelson interferometer. Michelson interferometers are used to make precise measurements of wavelengths and of very small distances. A Michelson interferometer takes monochromatic light from a single source and divides it into two waves that follow different paths. Interference occurs when the two light waves are recombined. The figure below shows the principal components of a Michelson interferometer. A ray of light from a monochromatic source A strikes the beam splitter C, which is a glass plate with a thin coating of silver on its right side. Part of the light (ray 1) passes through the silvered surface and the compensator plate D and is reflected from mirror M1. It then returns through D and is reflected from the silvered surface of C to the observer. The remainder of the light (ray 2) is reflected from the silvered surface at point P to the mirror M2 and back through C to the observer's eye. The purpose of the compensator plate D is to ensure that rays 1 and 2 pass through the same thickness of glass; plate D is cut from the same piece of glass as plate C, so their thickness are identical to within a fraction of a wavelength. If the distance L1 and L2 are exactly equal and the mirrors M1 and M2 are exactly at right angles, the image of M1 and M2 coincide. If L1 and L2 are not exactly equal, the image of M1 is displaced slightly from M2; and if the mirrors are not exactly perpendicular, the image of M1 makes a slight angle with M2. Then the mirror M2 and the virtual image M1 play the same roles as the two surfaces of a wedge-shaped thin film, and light reflected from these surfaces forms interference fringes. Using a Michelson interferometer with He-Ne laser light (LaTeX: \lambdaλ=633 nm), you observe interference fringes. The mirror M2 of this Michelson interferometer is moved. As a consequence, the fringes move across a line in the field of view. How far must the mirror M2 be moved so that 1,919 fringes move across a line in the field of view?

Answer 1