(20%) The output of an argon ion laser can consist of a number of modes of frequency that match the cavity resonance condition and are within the gain bandwidth of the lasing transition. Assume the gain bandwidth is 2.0 GHz, and the laser cavity is defined by a Fabry-Perot cavity with the mirrors separated by ~ 0.5 m. (a) If the center laser wavelength is 488 nm, which is also at the center of the gain medium spectral range, find the shortest and longest lasing wavelengths in the gain spectrum. (b) Find the maximum length d and minimum mirror reflectivity R of an etalon that could be used to limit this laser to single-mode operation.