Chapter 35, Problem 82P

The element sodium can emit light at two wavelengths, λ₁ = 588.9950 nm and λ₂ = 589.5924 nm. Light from sodium is being used in a Michelson interferometer (Fig. 35-21). Through what distance must mirror M₂ be moved if the shift in the fringe pattern for one wavelength is to be 1.00 fringe more than the shift in the fringe pattern for the other wavelength?

Figure 35-21 Michelson’s interferometer, showing the path of light originating at point P of an extended source S. Mirror M splits the light into two beams, which reflect from mirrors M₁ and M₂ back to M and then to telescope T. In the telescope an observer sees a pattern of interference fringes.