Monochromatic light is beamed into a Michelson...

Monochromatic light is beamed into a Michelson interferometer. The movable mirror is displaced 0.382 mm, causing the central spot in the interferometer pattern to change from bright to dark and back to bright N = 5 1 700 times. (a) Determine the wavelength of the light. What color is it? (b) If monochromatic red light is used instead and the mirror is moved the same distance, would N be larger or smaller? Explain.

Key Concepts

Michelson Interferometer

A Michelson interferometer is an optical instrument that splits a beam of light into two paths using a beam splitter, reflects the beams off separate mirrors, and then recombines them to produce an interference pattern. The device is highly sensitive to differences in optical path lengths, making it useful for precision measurements of wavelengths, refractive indices, and small displacements.

Interference and Fringe Formation

Interference occurs when two coherent light waves overlap and superpose, leading to regions of constructive interference (bright fringes) and destructive interference (dark fringes). The resulting fringe pattern is directly related to the phase difference between the paths, which is affected by the optical path difference introduced by the interferometer's mirrors.

Optical Path Difference

The optical path difference in an interferometer is the extra distance one light beam travels relative to the other. In a Michelson interferometer, when one mirror is moved, the change in optical path length is twice the physical displacement. This doubling effect is crucial for accurately relating mirror movements to changes in the interference pattern.

Wavelength Calculation

The wavelength of light can be determined by relating the number of fringe shifts to the distance the mirror is moved. Since a single fringe shift corresponds to a change of one wavelength in the optical path difference (which is twice the mirror displacement), the relationship ? = 2d/N can be used, where d is the mirror displacement and N is the number of fringes observed.

Visible Light Spectrum

The visible light spectrum ranges from about 400 nm to 700 nm, with different regions corresponding to different perceived colors. By calculating the wavelength of light, one can determine its color. For instance, shorter wavelengths within this range are associated with violet or blue light, while longer wavelengths correspond to red light. This concept is used to deduce the color of the light based on its wavelength.

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