To determine the number of interference paths in Michelson's experiment, we can use the formula for the path length difference:
ΔL = 2d
where ΔL is the path length difference and d is the distance one of the mirrors is moved away from the coincidence position.
Given that the distance moved is 25 cm (or 0.25 m), we can substitute this value into the formula:
ΔL = 2(0.25 m) = 0.5 m
The path length difference determines the number of interference fringes observed. Each fringe corresponds to a path length difference of half the wavelength (λ/2).
Therefore, the number of interference paths counted can be calculated by dividing the path length difference by half the wavelength:
Number of interference paths = ΔL / (λ/2)
Number of interference paths = (0.5 m) / (643.8 nm / 2)
First, we need to convert the wavelength from nanometers to meters:
λ = 643.8 nm = 643.8 × 10^(-9) m
Substituting the values, we have:
Number of interference paths = (0.5 m) / (643.8 × 10^(-9) m / 2)
Number of interference paths ≈ 1551957.95
Since the number of interference paths must be a whole number, we round the result to the nearest whole number:
Number of interference paths ≈ 1551958
Therefore, Mitchelson would count approximately 1,551,958 interference paths in his original experiment.