Problem Set #1 ECEN 4616/5616

(Due Feb 10, 2014)

Problems from “Geometrical Optics and Optical Design”, Mouroulis & Macdonald:

Chapter 1,

Problems 1,3,4,7

Chapter 2:

Problem 4

Grad problem (extra credit for 4616):

Problem 10 (chapter 2)

Other Problems:

OP1:

Definitions:

  • C is the Z-coordinate of the radius of curvature of a mirror
  • F is the focal point of an optic in object space (i.e., before refraction or reflection)
  • F’ is the focal point in image space (after refraction/reflection)

Using graphical ray traces, determine the approximate image location and magnification in the following cases:

  1. Concave mirror, real object at C;
  2. Concave mirror, real object between C and F’;
  3. Convex mirror, virtual object between F’ and C;
  4. Negative lens, real object at F’
  5. Negative lens, virtual object at F;
  6. Positive lens, virtual object at F’
  7. Convex mirror, image object at infinity.

OP2:

A positive thin lens of 100 mm focal length is followed by a positive thin lens of 50 mm focal length. The distance between the two lenses is 150 mm.

  1. Show that this system has zero power (e.g., is afocal) using the combination of lenses formula.
  2. Also demonstrate the system is afocal using a graphical ray trace.

OP3:

Put the system described in OP2 into Zemax using paraxial surfaces for the thin lenses. Note that Zemax usually has the units set to millimeters. Set the following parameters:

  • Make the first lens the stop surface.
  • In the ‘General’ dialog box (System-General, or just the ‘Gen’ tab) set “Aperture Type” to “Entrance Pupil Diameter” with a value of 25mm.
  • Set the object distance to infinity (type ‘infinity’ or ‘inf’ into the editor).
  • In the ‘Field’ dialog box (System-Fields, or the “Fie” tab), set one field to 0,0 and the field type to “angle”.
  • Set EFFL (effective focal length) and PMAG (Paraxial magnification) values on the Status Bar. (File-Preferences-Status Bar. These values show up at the bottom of the main Zemax window.
  • Make the thickness of the second lens 50 mm. (The lens isn’t that thick, as a Paraxial lens is just a surface. This just sets the distance to the image surface for layout purposes.)
  1. Verify that the system is afocal by opening a Layout Window and using at least 3 rays. What does the Status Bar report for EFFL and PMAG? Click on the top of the layout window to make it active, then press <alt>-PrtScr to copy it to the clipboard. You can then paste it into your (electronically submitted!) homework.
  2. Repeat part A, after adding a second field with a y-field value of 5 degrees.
  3. Change the Object thickness (in the Lens Data Editor) to 100mm, the “Field Type” to “Object Height”, and update the layout window. Change the “First Surface” value in the “Settings” dialog (on the top bar of the Layout window) to start the display at surface 0.
  4. What values do you get for EFFL and PMAG now? Copy and paste the layout window into your homework.
  5. Can a lens system with zero power form an image? How would you explain this? (Consider a graphical ray trace of the on-axis field.)
  1. Grad Problem (Extra Credit for 4616):
  • Right-Click on the “Thickness” value for the second paraxial lens and select a solve type of “Marginal Ray Height” with Height and Pupil Zone both = 0. (This makes the thickness adjust to the focal plane.)
  1. With the object distance at 100mm, what is the distance from the second lens to the image?
  2. Highlight (by a single left-click) the Object distance in the LDE, then open up a slider control. (Tools-Design-Slider) Set the slider to control the Object Thickness between the values of 100 and 300 mm. Randomly go to values in this range and report the effect on the EFFL and PMAG values on the Status Bar.
  3. Where is the image, when the Object distance is 300 mm?
  1. Extra Credit: This lens is known as a “Telecentric” lens and has unusual imaging characteristics. Describe a possible use for this type of lens.