Final answer:
The number of fringes observed when one arm of a Michelson interferometer is moved by 1.5μm using mercury light of wavelength 546 nm is 5,495 fringes.
Step-by-step explanation:
When using a Michelson interferometer with mercury light of wavelength 546 nm, if one of the arms is moved by 1.5μm, we can determine the number of fringes that will cross the observing field by considering the path difference created by the movement of the arm. The path difference is twice the distance moved because the light travels to the mirror and back.
The number of fringes (N) observed is given by the formula N = 2 * movement / wavelength.
Plugging in the values:
N = 2 * 1.5μm / 546 nm
= 2 * 1.5μm / 546 * 10⁻⁹ m
= 2 * 1500 nm / 546 nm
= 5,495 fringes
Therefore, 5,495 fringes will cross the observing field as a result of moving one of the arms by 1.5μm.