MatSE 405: Microstructure Determination mselogo.jpg

Problem set #1; due Thursday, January 24.
  1. Show how you would use two lenses, f1=50 mm, f2=100 mm, to make i) an inverted telescope that demagnifies angles by a factor of 2; and ii) a microscope that magnifies positions by a factor of 2. You should find out that the same lens configuration will accomplish either task but for the microscope also include the position of the object and the CCD array that will detect the image. For the inverted telescope show how a ray that is parallel to the optical axis propagates through the optical system. For the microscope, show the ray propagation for a ray that starts at the point on the optical axis a distance f1 in front of the first lens but makes some finite angle with the optical axis.
  2. Modify the MatLab script fermat_snell.m to show that the law of reflection (angle of incidence equals angle of reflection) is consistent with Fermat's principle. Turn in a print-out of your script and a plot that shows that the optical path length is a minimum when the ray path is given by the law of reflection.
  3. Modify the MatLab script ray_trace.m to show how a set of parallel rays propagate through the two lens system. Plot the ray paths for sets of 5 rays that start out i) parallel to the optical axis and are positioned 0.5 mm apart; and ii) make an angle of 0.1 radians with respect to the optical axis and are positioned 0.5 mm apart. Turn in a print-out of your script and a plot of the ray paths.



File translated from TEX by TTH, version 3.74.
On 17 Jan 2008, 10:16.