Final answer:
The mirror in a Michelson interferometer must be moved by 215.085 m for 730 fringes of 589 nm light to pass by a reference line.
Step-by-step explanation:
To calculate how far the mirror in a Michelson interferometer must be moved for 730 fringes of 589-nm light to pass by a reference line, we can use the principle that for each fringe observed to shift, the path difference changes by one wavelength of the light used. Since each fringe corresponds to a round-trip path difference of one wavelength, the actual mirror movement is half of a wavelength. The formula for the distance the mirror is moved (D) is given by D = (m lambda 2, where m is the number of fringes and lambda is the wavelength of the light.
Using the given parameters:
m = 730 fringes
lambda = 589 nm (which is 589 x 10-9 m)
We get D = (730 x 589 x 10-9 m) 2.
Calculating the product yields:
D = (430,170 x 10-9 m) 2
D = 215,085 x 10-9 m
D = 215.085 x 10-6 m
D = 215.085 m
Therefore, the mirror must be moved by 215.085 m for 730 fringes of 589 nm light to pass by a reference line in a Michelson interferometer.