Final answer:
By moving the mirror in a Michelson interferometer at a distance of x/4, one creates a path difference of x/2.
Step-by-step explanation:
When moving the mirror through a distance of x/4 in a Michelson interferometer, the path difference created is x/2. This is because the Michelson interferometer creates two paths for the light beam, and moving one mirror by a distance x changes the path length for the beam reflecting off of that mirror by x.
However, since the light has to travel to the mirror and back, the path difference ends up being twice the distance the mirror was moved, i.e., 2x. When the mirror is moved by x/4, the path difference is therefore 2(x/4) = x/2. Thus, the correct response to the question is option B) x/2.