Final answer:
The index of refraction of a plastic sheet can be calculated using the interference pattern shift observed in a Michelson interferometer after inserting the sheet. The formula involving the number of fringes shifted, the wavelength, and the thickness of the plastic is used to find the index.
Step-by-step explanation:
The question involves calculating the index of refraction of a plastic sheet, using data obtained from a shift in the interference pattern seen in a Michelson interferometer. The shift is due to the insertion of the plastic sheet into the path of one arm of the interferometer.
Fringe shifts in an interferometer are related to changes in optical path length, and when a medium with a different index of refraction is introduced, it changes the optical path such that the effect can be observed as a number of fringes shifting. To find the index of refraction of the plastic, we use the formula:
n = ⅓ + (mλ) / (2d)
where n is the index of refraction, m is the number of fringes shifted, λ is the wavelength of the light in vacuum/air, and d is the thickness of the sheet.
Given that the wavelength is 610 nm and the thickness of the plastic is 75μm with a fringe shift of 86, we calculate:
n = ⅓ + (86 * 610e-9 m) / (2 * 75e-6 m)
Upon performing the calculation, we find the index of refraction of the plastic sheet.