8. A particular Gaussian beam is characterized by w 0 =3.6 mm and λ 0 =405 nm. a) What is the Rayleigh length of the beam in meters? b) What is the far-field divergence angle of the beam? Be sure to specify whether you are finding the half-angle or full-angle (making a sketch removes the ambiguity). c) By how much has the intensity reduced after the beam propagates 10 km ? d) Suppose your experiment needed the intensity after 10 km to be 10,000 times higher than this. By how much should you turn up the optical power? By how much would the electric field amplitude need to increase? e) But, alas, you cannot turn up the power that much. Instead, what should you do to the laser near its source to realize the 10,000 -fold higher intensity at the 10 km-distant location?