You're using a monochromatic beam of light with wavelength 500 nm in an interferometer. What is the miminum distance you would need to move one of the interferometer's mirrors to change a spot of constructuve interference to a spot of destructive interference?

Minimum distance needed to move one of the mirrors = 125 nm

Explanation:

Constructive interference occurs when the maxima (trough or crest) of two waves that are in phase add together so that the amplitude of the resulting wave is equal to the sum of the individual amplitudes.

Destructive interference occurs when the maxima (trough or crest) of two waves that are out of phase by 180⁰ or half a wavelength combine to produce a smaller amplitude than the individual amplitudes that combine. It can even produce a wave of zero amplitude.

Since the spot of constructive interference has been changed to destructive interference, Path difference = Wavelength/2

Path difference = 500nm/2 = 250 nm

Path difference = 250 * 10⁻⁹ m

Since there are two interferometer's mirrors and only one is moved, the minimum distance will be a half of the path difference.

That is, minimum distance = (path difference) / 2

Minimum distance = (250 * 10⁻⁹) / 2

Minimum distance = 125 * 10⁻⁹ m

Minimum distance = 125 nm