A Michelson interferometer is used to check the length of a “standard” platinum meterstick. The interferometer is operated with light from a specially constructed helium–neon laser, which gives red light with λ = 632.99139822 nm.
(a) The standard meterstick is placed next to one of the interferometer’s arms, and the mirror is moved from one end of the meterstick to the other. How many interference fringes  N are counted as the mirror is moved?
(b) Suppose the wavelength l is known with an accuracy of ±0.00000002 nm. Also, suppose the number of interference fringes N is known to an accuracy of ±1. What determines the uncertainty in the measured length of the meter stick, the uncertainty in the wavelength or the uncertainty in N?
(c) In a real experiment, you would not simply count the number of bright fringes but instead would measure “fractions of a fringe” by measuring the intensity and comparing it with the sinusoidal curve in Figure 25.5. If the number of fringes could be measured to ±0.0001, would the uncertainty in N still be a limiting factor?