By adding waves inside the Fabry-Perot cavity and then applying techniques like those of last prob- lem in previous homework set (Problem 4, Fabry-Perot Transmittance and Reflectance), develop expressions for the intensities of the internal right- and left-traveling waves inside the Fabry-Perot cavity. (a) Consider the behavior of these intensities at a transmission peak and between transmission peaks. Give expressions involving R (R = r2) relating the incident intensity to the internal intensity at a transmission maximum. (b) Some of the best commercially available Fabry-Perot interferometers have a finesse of 40,000. Suppose that a wave is incident on such a device and is resonant with one of the transmission maximum. The wave's intensity is 1 mW. What is the internal intensity of either of the traveling waves? Note that with such a large finesse, the right- and left-traveling wave intensities can be taken as approximately equal.For a Fabry-Perot interferometer, supply the derivation of the transmittance, T, and reflectance, R, that was skipped in class. Begin with the following expressions for the transmitted and reflected fields, Et = Ei 1-120-16 (3) it'e is E, = Ert Eir' (4) and show that the following expressions result: TFP = 1 + F sin-(6/2)' (5) F sin (6/2) RFP (6) 1 + F sin-(6/2) where F = 4r2/(1 -72)2