Question

A Michelson interferometer using 800 nm light is adjusted to have a bright central spot. One mirror is then moved 200 nm forward, the other 200 nm back. Afterward, is the central spot bright, dark, or in between? Explain.

Answer 1

In a Michelson interferometer, when one mirror is moved forward while the other is moved backward, the central spot changes from bright to dark due to destructive interference.

Step-by-step explanation:

In a Michelson interferometer, when one mirror is moved forward while the other mirror is moved backward, the central spot will change from bright to dark.

This is because the interference fringes are created when the two beams of light recombine. When the paths of the two beams are perfectly matched, they interfere constructively, creating a bright central spot. However, when one mirror is moved forward and the other is moved backward, the paths of the two beams become mismatched, resulting in destructive interference and a dark central spot.

Answer 2

When the mirrors in a Michelson interferometer are moved to create a total path difference of half the wavelength of the light used, destructive interference occurs resulting in a dark central spot.

Step-by-step explanation:

The Michelson interferometer creates an interference pattern by reflecting light from two mirrors and recombining the beams. When the central spot is bright, it indicates constructive interference, which occurs when the path difference between the two beams is an integer multiple of the light's wavelength. If one mirror is moved 200 nm forward and the other 200 nm back, the total path difference will be 400 nm or 0.4 μm. Since the light used has a wavelength of 800 nm, the path difference is exactly half the wavelength. This results in a path change that equals half a wavelength for each beam, which will cause destructive interference and produce a dark central spot.