Exercise 1 Bisection method [15 points] Planck's radiation law tells us that the intensity of radiation per unit area and per unit wavelength from a black body at temperature T is I() = 2hc2 5 e hc/kBT 1 , where h is Planck's constant, c is the speed of light, and kB is Boltzmann's constant. a) Show by setting the derivative of I() to zero that the wavelength at which the emitted radiation is strongest is the solution of the equation 5e hc/kBT hc kBT 5 = 0. b) Make the substitution x = hc/kBT and hence show that the wavelength of maximum radiation obeys the Wien displacement law: = b T , where the so-called Wien displacement constant is b = hc/kBx, and x is the solution to the nonlinear equation 5e x x 5 = 0. c) Plot the left hand side of this equation. You will see that there are two roots, but only one of them is physical. Which one and why? d) Write a program to solve this equation to an accuracy of = 106 using the bisection method, and hence find a value for the displacement constant