Consider an infinitely long continuous string with linear mass density p1 for x < 0 and for x > L, but density p2 > p1 for 0 < x < L. If a wave train oscillating with an angular frequency w is incident from the left on the high-density section of the string, find the reflected and transmitted intensities for the various portions of the string. Find a value of L that allows a maximum transmission through the high-density section. Discuss briefly the relationship of this problem to the application of non-reflective coatings to optical lenses.