Question

a micrometer is connected to the movable mirror of an interferometer. when the micrometer is tightened down on a thin metal foil, the net number of bright fringes that move, compared to the empty micrometer, is 272. what is the thickness of the foil? the wavelength of light used is 611 nm.

Answer 1

The thickness of the metal foil measured using a Michelson interferometer with a wavelength of 611 nm and observing 272 bright fringes is 36.832 micrometers.

Step-by-step explanation:

To determine the thickness of the metal foil using a Michelson interferometer, we can use the fact that each fringe shift corresponds to a change in the optical path length that is equal to half the wavelength of the light used in the interferometer. In this case, the net number of bright fringes observed is 272, and the wavelength of the light used is 611 nm (which is 611 x 10-9 meters).

Since each bright fringe corresponds to a change in path length of one-half of a wavelength, we can express the total change in path length as the number of fringes times the half-wavelength:

Total change in path length = Number of fringes x (½ x wavelength)

As the path length change due to the presence of the foil is twice its thickness, we can write:

Foil thickness = ½ x Total change in path length

Now substituting the known values:

Foil thickness = ½ x (272 x ½ x 611 x 10-9 meters)

Foil thickness = ½ x 272 x 305.5 x 10-9 meters

Foil thickness = 36.832 x 10-6 meters

Therefore, the thickness of the foil is 36.832 micrometers (or μm).