Optics Homework Solutions

Visual Optics Lab – Professor Jim Schwiegerling

OPTI 435/535: Visual Optics



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Section 1

  • What is vision? Anatomy of the eye. Dissection. Average and range of sizes, shapes and indices of ocular components. Overview of optical modeling. Definition of visual acuity.
  • Download Notes

Section 2

  • Schematic eye models. Gullstrand-LeGrand and Helmholtz models. First-order properties. Locations of cardinal points. Definitions of near point, far point, myopia and hyperopia. Aspheric eye models. Stiles-Crawford, photopic response, diffraction. Location of eye axes.
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Section 3

  • Spherical, Chromatic, Astigmatism (axial and oblique). Techniques for measuring aberrations. Nominal values. Derivation of these quantities from raytrace data. Retinal curvature.
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Section 4

  • Visual performance – Theoretical resolution. Vernier acuity, grating acuity, Snellen acuity. Vision charts. Specification of visual acuity. Contrast sensitivity. Fourier theory – PSF, MTF, modulation threshold. Campbell and Green experiments. Van Nes and Bouman experiments. Changes in contrast sensitivity. Square-wave response.
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Section 5

Section 6

Section 7

  • Spherical ametropia, cylindrical error, Scheiner disk, vector addition of crossed cylinders. Correction with sphero-cylindrical spectacle lenses. Correction with spherical, aspheric and toric contact lenses. prism ballast.
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Section 8

  • Optometers, Autorefractors mage analysis, retinoscopic scanning and Scheiner disk types. Fogging.
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Section 9

  • Lensmeters, Accommodation , age changes, near addition. Progressive lenses. Spherical and astigmatic considerations.
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Section 10

  • Intraocular lenses. Power calculations. Multifocal contact and intraocular lenses. Aphakia and pseudophakia. Defocus Transfer Function.
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Section 11

  • Other corrections: RK/AK, PRK, ALK/LASIK, orthokeratology, interscleral ring.
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Section 12

  • Pupillometry. Measurement of the anterior cornea. Placido disks, stereo-photogrammetry and scanning slit devices. Height, slope and curvature representations of the cornea. Derivation of relationships. Keratometric index of refraction. (Differential Geometry Notes)
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Section 13

  • Calculation of radii of curvature, astigmatic axis and conic constant from Zernike expansion coefficients. Keratoconus detection.
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Section 14

  • Miscellaneous Ocular Measurements. Measurement of corneal thickness – scanning slit, pachymetry. Measurement of the angle in glaucoma. Gonioscopy. Scheimpflug imaging. Phakometry, Purkinje images. (Scheimpflug Imaging Notes)
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Section 15

  • Visual Fields. Spatial and temporal summation. Perimetry: Tangent Screen, Goldman projection, Static and Kinetic. Scotomas
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Section 16

  • Measurement and imaging the retina. Direct and indirect ophthalmoscopy, fundus camera. Confocal scanning laser ophthalmoscope. Optical coherence tomography. Applications: glaucoma screening, nerve fiber layer measurement.
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Section 17

Section 18

  • Color matching. Additive and subtractive color mixing. Color vision – Trichromatic vs. opponent-process theories. Spectral response of cone pigments. Color blindness.
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Patent Class 1

Patent Class 2

Eye Lecture

  • Miscellaneous types of eyes found in nature.

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  • Homework 1 – Visual Acuity, Cardinal Points, Photorector Dimensions
  • Homework 2 – Power Error, Differential Geometry, Spatial Frequency, Spherical Aberration
  • Homework 3 – Zernikes, IOLs, Spectacle lens design
  • Homework 4 – Biconic surfaces, topographic maps, Munnerlyn formula, Chromatic Aberration
  • Homework 5 – Colorimetry ColorimetryData3012.txt download

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Homework Solutions

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Midterm Solutions

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Old Midterms

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Old Finals

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Final Project

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Course Information  |  Homework Schedule  |  Downloads  |  Helpful Links

Optical Design and Instrumentation I

  • Semester: Fall 2017
  • Days and Time: Monday/Wednesday – 8:00 – 9:15 a.m.
  • Location: Meinel Building, Room 307


John E. Greivenkamp

College of Optical Sciences, Rm. 741

(520) 621-2942


Office Hours:  Monday   2:00-3:00

I also maintain an open door policy related to this course.  Feel free to knock even if the door is physically closed.  If the time is bad, we will set something up.  I prefer to see you in person rather than by email!

Teaching Assistant and Grader

Tyson Ririe


Office Hours: Revised

  • Monday: 12:00-2:00 p.m.
  • Tuesday: 3:00-5:00 p.m.
  • Wednesday: 12:00-1:00 p.m.

Office hours will be held in the 7th floor discussion area (Optical Sciences West Wing). Also available by email and appointment. Please email to set up an individual appointment.

Course Information

Goal: This course will provide the student with a fundamental understanding of optical system design and instrumentation. The course begins with the foundations of geometrical optics, which includes the first-order properties of systems, and paraxial raytracing, continues with a discussion of elementary optical systems, and concludes with an introduction to optical materials and dispersion. A special emphasis is placed upon the practical aspects of the design of optical systems.

Instructor Notes: Will be required and will be distributed on line.

Required Text: Field Guide to Geometrical Optics, J. E. Greivenkamp ISBN: 0819452947

Note that this book is available as an e-book through the UA library as well as an app for both Android and Apple (search “SPIE”)

References:A useful list of optics references

Full Course Syllabus: Syllabus – Includes Course Policies

Grading Policy and Schedule:

  • Homework 20%
  • Pop Quizzes 10%
  • Midterm Exam (In Class) 30%
    • Wednesday 10/18/17 (Lecture 17)
  • Final Exam (In Class) 40%
    • Wednesday 12/13/17, 8:00-10:00 AM

Please note the final exam date that has been assigned by the University – plan your holiday travel accordingly as the final exam will not be available prior to this date.  If the midterm date has not yet been determined, it will be announced well in advance.

Only a basic scientific calculator may be used for the in-class exams.  This calculator must not have programming or graphing capabilities.  An acceptable example is the TI-30 calculator.  Each student is responsible for obtaining their own calculator.  Please note that this type of calculator is also required for the Ph.D. Comprehensive/Preliminary Exam in Optical Sciences.

Distance Students: All course materials (including the final exam) must be received in Tucson by 5 PM on Monday December 18, 2017.  This implies that you must take the exam by Friday December 15 and ship it that same day by a priority service.  It is the Student’s responsibility to see that this requirement is met by their proctor.


A: Excellent – has demonstrated a more than acceptable understanding of the material; exceptional performance; exceeds expectations

B: Good – has demonstrated an acceptable understanding of the material; adequate performance; meets expectations

C: Average – has not demonstrated an acceptable understanding of the material; inadequate performance; does not meet expectations

D: Poor – little to no demonstrated understanding of the material; exceptionally weak performance


Pop Quizzes:

Quick quizzes will be given during the first 2-3 minutes of random classes throughout the semester.  There will be a total of about 10-15 quizzes.  The purpose of the quizzes is to monitor basic material understanding as well as to promote on-time class attendance.  Please be prepared at every class with a blank sheet of paper (8 ½ x 11) for a potential quiz.

Missed quizzes cannot be made up.

Distance students – the instructor is counting on your integrity to do the quiz during the allotted time period.  Please return the quiz as you would any homework set.


Homework Assignments & Solution Sets:

Homework and solutions will be posted as .pdf files through this website. If you need Acrobat Reader to view .pdf files, please see the Adobe website for a free download.

Homework will be assigned regularly throughout the semester, and it will usually be due in one week.  The solutions to the homework will be posted at the same time as the homework is assigned.  The purpose of the homework is for you to practice the techniques discussed in class or to reinforce this material.  Completion of the homework is important to fully master this material.  Collaboration and discussion of the homework is encouraged.

Homework is due in the classroom on the assigned day – it may not be turned in early.  Homework must be turned in before the start of class.  A student may only turn in their own homework.  No electronic submissions are permitted.

Any homework turned in to the TA will receive zero credit.

Because the homework solutions are available as a resource during the completion of the assigned homework, the grading of the homework will be based upon verification that the homework problems have been completed and turned in.  Approval for early or late homework must be obtained in advance from the instructor.


Late Homework Policy (On Campus Students):

– Homework that is turned in after the start of class is considered late.

– Late HW that is turned in on the due date will receive a 20% penalty.

– Late HW that is turned in on the day after the due date will receive a 50% penalty.

– Late HW that is turned in two or more days after the due date will receive no credit.

– All late homework must be turned in to the instructor.   In the instructor’s absence, you may turn in late HW to Cindy Gardner in Room 719.  Any HW turned in to the TA will receive zero credit.

– Homework must be turned in during normal business hours.  Do not slip late HW under the instructor’s door.

– When issues arise, please contact the instructor as soon as possible so that appropriate accommodations can be made.



It is expected that students will regularly attend class and be on time for class. Late arrivals to class are distracting to both the instructor and the other students. Attendance for this class is not specifically part of the course grade (but please note the homework and quiz policies).


The Full Course Syllabus contains:

  • Special Instructions for Distance Learning Students
  • Academic Integrity
  • Absence Policies
  • Other Policies


DRC Students:

Students who are registered with the Disability Resource Center must submit appropriate documentation to the instructor if they are requesting reasonable accommodations: http://drc.arizona.edu/teach/syllabus-statement.html.  For this course, exams will be administered here at the College of Optical Sciences rather than at the DRC.

Students requesting accommodation must contact the instructor at least two weeks in advance of the scheduled date of any exams.  However, the instructor requests that this contact be made early in the semester.

Homework Schedule

502 Homework 2017 Set 1   

Assigned  8/21/17 Lecture 1          Due  8/30/17 Lecture 4



Course Notes

502-0 Full Syllabus

502-01 Introduction

502-02 Mirrors and Prisms

502-03 Imaging with a Thin Lens

502-04 Imaging and Paraxial Optics

502-05 Gaussian Imagery

502-06 Object-Image Relationships

502-07 Gaussian Reduction

502-08 Paraxial Raytracing

502-09 Stops and Pupils

502-10 Radiative Transfer

502-11 Vignetting

502-12 Objectives

502-13 Magnifiers and Telescopes

502-14 Relays and Microscopes

502-15 Telecentric Systems

502-16 The Eye

502-17 Materials

502-18 Dispersing Prisms

502-19 Thin Prisms

502-20 Chromatic Effects

502-21 Stop and Image Quality

502-22 Illumination Systems

502-23 Camera Systems

502-A Appendices



Schott Glass Map |  Data Sheets

Hoya Glass Catalog

Ohara Glass Catalog


Blank Ray Trace Sheets


300 Year Quest for Binoculars

History of Telescopes and Binoculars


Equation Sheets – Will be Included with the Exam

Midterm  502 Equations Midterm – 2017

Final Exam  502 Equations

Old Exams and Solutions

Note that old exams and solutions are provided as study aids only. As the course has evolved, the material covered in the course has changed, so that the exams may not be representative of the material coverage on a current exam.

Midterm Exams

1999 | Solutions        2000 | Solutions

2001 | Solutions        2002 | Solutions

2003 | Solutions        2004 | Solutions

2005 | Solutions        2006 | Solutions

2007 | Solutions        2008 | Solutions

2009 | Solutions        2010 | Solutions

2011 | Solutions        2012 | Solutions

2013 | Solutions        2014 | Solutions

2015 | Solutions        2016 | Solutions

Final Exams

2000 | Solutions        2001 | Solutions

2002 | Solutions        2003 | Solutions

2004 | Solutions        2005 | Solutions

2006 | Solutions        2007 | Solutions

2008 | Solutions        2009 | Solutions

2010 | Solutions        2011 | Solutions

2012 | Solutions        2013 | Solutions

2014 | Solutions        2015 | Solutions

2016 | Solutions

Additional Project-Style Homework Problems (Optional)

Project 1 | Solution

Project 2 | Solution

Project 3 | Solution

Project 4 | Solution

Project 5 | Solution

Other Links

Museum of Optics

Lens Movies – Courtesy of Marshall Scott

     Positive Lens

     Negative Lens


SPIE – The International Society for Optics and Photonics

OSA – Optical Society of America

Surplus Shed

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