A Michelson interferometer is used in a class of commercially available optical instruments called wavelength meters. In a wavelength meter, the interferometer is illuminated simultaneously with parallel beams from a reference laser of known wavelength and an unknown laser. The movable mirror of the interferometer is then displaced by a distance Ad, and the number of fringes produced by each laser and shifting past a reference point (a photo detector) is counted. In a given wavelength meter, a red He-Ne laser (λRed = 632.8 nm) is used as a reference laser. When the movable mirror of the interferometer is displaced by a distance Ad, the shifting of λNRed = 6.000- IO4 red fringes and λNunknown = 7.780-104 fringes is observed by the photo detector.
a) Calculate the wavelength of the unknown laser.
b) Calculate the displacement, Δd, of the movable mirror.