Issues in Modern Physics, Optics, Statistical Mechanics & Thermodynamics Sept. 2006, Exams of Physics

Download Issues in Modern Physics, Optics, Statistical Mechanics & Thermodynamics Sept. 2006 and more Exams Physics in PDF only on Docsity! Modern Physics, Optics, Statistical Mechanics and Thermodynamics September, 2006 Pick 4 out of 6 problems 1) A flashlight, in its own rest frame, is directed at an angle θ of 45 degrees to the x-axis in the xy plane. What angle will the light beam appear to make to an observer moving towards the flashlight along the x-axis at velocity β ? a. Now consider a relativistic electron traveling in a circular orbit. Explain why the radiation from the electron will be confined to a narrow cone, and calculate the opening angle of the cone. b. 2) A simple model of a rubber band is a one-dimensional (horizontal) chain consisting of N ( 1N ) linked segments, as shown schematically in the diagram. Each segment has two possible states: horizontal with length a, or vertical, contributing nothing to the length. The segments are linked such that they cannot come apart. The chain is in thermal contact with a reservoir at temperature T. a. If there is no energy difference between the two states, what is the average length of the chain? b. Fix chain at one end and hang weight from the other end, supplying a force F as shown. Determine the average length of the chain at any temperature T . Find the length in the limits 0T → andT →∞ . c. In which temperature limit is the extension proportional to F (Hooke’law)? Calculate the constant of proportionality. 3) The complete formula for multislit diffraction pattern in Fraunhofer diffraction is given by the expression 2 2 0 sin sin( ) sin NI I β αθ β α    =       where 0I is the flux density in the 0θ = direction for one slit,