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:
a.
Concave mirror, real object at C;
b.
Concave mirror, real object between C and F’;
c.
Convex mirror, virtual object between F’ and C;
d.
Negative lens, real object at F’
e.
Negative lens, virtual object at F;
f.
Positive lens, virtual object at F’
g.
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.
a. Show that this system has zero power (e.g., is afocal) using
the combination of lenses formula.
b. 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-PreferencesStatus 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.)
A. 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.
B. Repeat part A, after adding a second field with a y-field
value of 5 degrees.
C. 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.
1. What values do you get for EFFL and PMAG now?
Copy and paste the layout window into your
homework.
2. 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.)
D. 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. (ToolsDesign-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?
E. Extra Credit: This lens is known as a “Telecentric” lens
and has unusual imaging characteristics. Describe a
possible use for this type of lens.