A Michelson interferometer is set up using white light. The...

A Michelson interferometer is set up using white light. The arms are adjusted so that a bright white spot appears on the screen (constructive interference for all wavelengths). A slab of glass $(n=1.46)$ is inserted into one of the arms. To return to the white spot, the mirror in the other arm is moved $6.73 \mathrm{~cm}$. (a) Is the mirror moved in or out? Explain. (b) What is the thickness of the slab of glass?

Key Concepts

Michelson Interferometer

A Michelson interferometer splits a beam of light into two paths, reflects them back, and then recombines them to produce an interference pattern. The pattern results from differences in the optical path lengths of the two arms. It is a fundamental instrument in physics for measuring wavelengths, coherence, and small displacements and index variations.

Optical Path Length

Optical path length represents the product of the physical distance a light beam travels and the refractive index of the medium it travels through. It determines the phase of the light at any point along the path, and variations in optical path length between beams lead to interference, whether constructive or destructive.

Constructive Interference in White Light

Constructive interference happens when the optical path difference between two beams is an integer multiple of their wavelengths, resulting in bright fringes. With white light, which comprises various wavelengths, achieving simultaneous constructive interference across the spectrum requires careful balancing of the optical paths in the interferometer.

Refractive Index and Glass Slab Insertion

When a glass slab is inserted into one arm of an interferometer, its refractive index increases the optical path length relative to the same physical distance in air. This change necessitates adjustments in the other arm (e.g., moving the mirror) to restore the condition for constructive interference across all wavelengths, emphasizing the role of refractive index in modifying light's phase.

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