A Michelson interferometer is adjusted so that a bright...

A Michelson interferometer is adjusted so that a bright fringe appears on the screen. As one of the mirrors is moved $25.8 \mu \mathrm{m}, 92$ bright fringes are counted on the screen. What is the wavelength of the light used in the interferometer?

Key Concepts

Wavelength Determination

Wavelength determination in interferometry is based on the relationship between the optical path difference and the number of observed interference fringes. As the mirror moves, every time the optical path difference changes by one wavelength (or half a wavelength in terms of mirror displacement in a Michelson interferometer), a fringe shift occurs. By relating the total mirror displacement to the fringe count, the wavelength of the light can be calculated accurately.

Interference Fringe Patterns

Interference fringe patterns occur when the recombined light beams overlap and interfere constructively or destructively, forming alternate bright and dark bands. The position and number of these fringes are highly sensitive to variations in the optical path difference. Counting the number of bright (or dark) fringes as a mirror is moved allows for accurate measurement of wavelength or displacement.

Michelson Interferometer

The Michelson interferometer is a precision optical instrument that splits a beam of light into two paths, reflects them back using mirrors, and then recombines them to produce an interference pattern. This pattern results from differences in the optical path lengths the beams travel, providing a highly sensitive method to measure small distances, changes in refractive index, or wavelengths of light.

Optical Path Difference

The optical path difference is the effective difference in distance traveled by two light beams, taking into account the refractive index of the medium. In a Michelson interferometer, moving one mirror changes the optical path length by twice the actual displacement, which directly affects the interference pattern observed. Precise calculation of this difference is essential for interpreting changes in fringe positions.

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