Final answer:
To determine the number of fringes observed in a Michelson interferometer during the evacuation of an air-filled chamber, the optical path difference is calculated, and the result is divided by the wavelength of the light source.
Step-by-step explanation:
Calculating Fringes in Michelson Interferometer
The student's question pertains to the number of fringes observed during the transition from air at standard atmospheric pressure to a near-perfect vacuum in a Michelson interferometer. To find this, we use the concept of optical path difference (OPD) which gives rise to interference fringes. As the refractive index changes, the OPD changes, causing the fringes to move.
Given the initial refractive index of air (nair) to be 1.000293 and the final refractive index for a vacuum (nvacuum) being 1.0, we can calculate the total change in OPD when the air is removed. The physical length of the air chamber L is 5.08 cm, and the wavelength of the light source (λ) is 633 nm.
The total OPD change is calculated as ΔOPD = L * (nair - nvacuum). The number of fringes (N) passing by is the OPD change divided by the wavelength: N = ΔOPD / λ. First, we need to ensure consistent units by converting L to meters and λ to the same unit, hence L = 0.0508 m and λ = 633 * 10-9 m. Plugging the values in, the calculation becomes N = 0.0508 * (1.000293 - 1) / (633 * 10-9). Multiplying by 2 since a single journey in the chamber corresponds to two optical paths in the interferometer, we obtain the total number of fringes observed.
Therefore, the number of fringes observed moving by during the transition from an air-filled chamber to a vacuum is the result of the above calculation.