You are asked to find the index of refraction for an unknown fluid, using only a laser and a michelson interferometer. a michelson interferometer consists of two arms--paths that light travels down, which end in mirrors--attached around a beam splitter. (figure 1)the beam splitter separates the incoming light into two separate beams and then recombines them once they return from the ends of the arms. the recombined beams are sent to a telescope, where their interference pattern may be observed in detail.

part a

part complete

first, you must find the wavelength of the laser. you shine the laser into the interferometer and then move one of the mirrors until you have counted 100.0 fringes passing the crosshairs of the telescope. the extremely accurate micrometer shows that you have moved the mirror by 0.03164 millimeters. what is the wavelength λ of the laser?

express your answer in nanometers, to four significant figures.

part b

you now immerse the interferometer in a tank filled with some unknown liquid and carefully align the laser into the interferometer. you move the mirror until you count 100.0 fringes passing the crosshairs of the telescope. the micrometer indicates that the mirror has moved 0.02381 millimeters. what is the index of refraction for this mystery fluid?