Show that fraunhofer diffraction patterns have a center of symmetry [i. e., (y, z) i( -y, -z)], regardless of the configuration of the aperture, as long as there are no phase variations in the field over the region of the hole. begin with eq. (10.41). we'll see later (chapter 11) that this restriction is equivalent to saying that the aperture function is real.

If we relied solely on the nonrenewable resources found in the u. s., which one would we run out of first at current usage levels? a. natural gas b. oil c. uranium d. coal

Consider the following position function. find (a) the velocity and the speed of the object and (b) the acceleration of the object. bold r left parenthesis t right parenthesisr(t)equals=left angle 6 t superscript 4 baseline comma 2 t cubed right angle6t4,2t3 for tgreater than or equals≥0

Wo small variable-thrust jets are actuated to keep the spacecraft angular velocity about the z-axis constant at ? 0 = 1.16 rad/s as the two telescoping booms are extended from r1 = 1.18 m to r2 = 4.69 m at a constant rate over a period of 124 seconds. the small 19-kg experiment modules at the ends of the booms may be treated as particles, and the mass of the rigid booms is negligible. determine the necessary thrust t for each jet as a function of time where t = 0 is the time when the telescoping action is begun. after you have the general expression for t, answer the questions. show work.