Problem 4: Consider a step index fiber with V = 8. a) Using the values of the zeros of Jn(x), find the positions of zeroes and infinities of the LHS of the eigenvalue equations (Equations 8.40 and 8.41, Ghatak and Thyagarajan )). Make qualitative plots of the LHS and RHS of the eigenvalue equations and determine the number of guided LP modes. b) Calculate the total number of modes and compare with the result of the formula V/2. c) Use the numerical approach to solve the eigenvalue equations to determine the normalized propagation constants of the guided modes. d) Consider the following two fibers. In each case determine the value of lo for which V = 8 and determine the corresponding values of neff and b. Fiber 1: n2 = 1.45, 4= 0.0064 and a = 3 um Fiber 2: n2 = 1.45, A= 0.010 and a = 2 um e) Using the values of the zeros of Jn(x), find the zeroes of the radial and angular intensity distributions and make qualitative plots. f) Use the graphical approach to find the guided modes and compare results with the numerical approach in part c).