Answer Happy

1. (Problem 4.4.2) The light from a sodium lamp is dominated by two closely spaced spectral lines at wavelengths of 589.0 nm and 589.6 nm. Assuming that each line has negligible width and they both have the same intensity, I, the sodium spectrum, I.(k), can be represented in terms of delta functions' by: 1(k) = 180k - kı) +18(k - km), where k is the wavenumber, with ki and k, corresponding to the wavenumbers of the 589.0 nm and 589.6 nm lines, respectively. The light from a sodium lamp is analyzed using a Michelson interferometer spectrograph (MIS). Show that the intensity, Im, detected at the output of the MIS as the path length difference between the arms, d, varies is given by: Akd Im(d) = 41 [1 + cos(kad) cos (144)] where kay is the average wavenumber of the two lines and Ak is the difference between them. Sketch Im as a function of d. If the arms of the MIS are initially of equal length, estimate how far d would have to be changed for Ak to be measured.