Coherence

A continuous-wave, semiconductor laser has a transform-limited bandwidth of 7.14x10¹⁰ Hz at a center wavelength of =1 micro millimeter.

(a) What is the shortest pulse that could be obtained in principle if this laser was operated in pulse mode?

(b) What is the longitudinal coherence length of light from the laser?

(c) The collimated laser beam enters a Michelson interferometer which has one perfect and one defective mirror. The defective mirror has a high spot at its center, so the cross-sectional image of the output beam shows three dark fringes between its center and its edge. What is the height of the defect (in microns)?

(d) Next, the Michelson interferometer is adjusted so that its two arms have very different lengths and the defective mirror is replaced with a perfect one. The total path difference between the two arms is made large (=30cm). Under these conditions, will fringes be observed by scanning one mirror of the Michelson a few millimeters about its position? Why, or why not?