Final answer:
The thickness of the aluminum foil measured with a Michelson interferometer and a He-Ne laser with a 632.8 nm wavelength is calculated using interference fringes observed when the foil is clamped. The formula t = (m * λ) / 2 is used, where m is the fringe difference and λ is the wavelength.
Step-by-step explanation:
To calculate the thickness of the aluminum foil using a Michelson interferometer, the concept of interference fringes is employed. When the micrometer clamps down on the foil, a difference of 27 fringes is observed. Given that the light source is a He-Ne laser with a wavelength of 632.8nm, the thickness (t) of the foil can be calculated using the formula t = (m * λ) / 2, where m is the number of fringes (27 in this case) and λ is the wavelength of light used (632.8 nm).
Inserting the given values into the formula gives t = (27 * 632.8 nm) / 2, which results in the thickness of the aluminum foil. Note that the shift of 27 fringes corresponds to the path difference of 27 λ/2 because each fringe corresponds to a path difference of one half-wavelength.