The gas mixture in a helium-neon laser (end mirrors removed) emits light at \(633 \mathrm{~nm}\) with a Doppler-broadened spectral width of about \(1.5 \times 10^{9} \mathrm{~Hz}\). Calculate the coherence time \(\tau_{c}\) and the coherence length \(l_{c}=c \tau_{c}(c=\) the speed of light) for this light. Repeat for the 488-nm line of an argon ion laser, which has a Doppler-broadened line width of about \(7.5 \times 10^{9} \mathrm{~Hz}\).