OPTI-502 Optical Design and Instrumentation I John E. Greivenkamp Final Exam In Class Page 1/14 Fall, 2017

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1 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 1/14 Fall, 017 Name Closed book; closed notes. Time limit: 10 mintes. An eqation sheet is attached and can be removed. Spare ratrace sheets are attached. Use the back sides if reqired. Assme thin lenses in air if not specified. If a method of soltion is specified in the problem, that method mst be sed. Ratraces mst be done on the ratrace form. Be sre to indicate the initial conditions for or ras. Yo mst show or work and/or method of soltion in order to receive credit or partial credit for or answer. Provide or answers in a neat and orderl fashion. No credit if it can t be read/followed. Use a rler or straight edge! Onl a basic scientific calclator ma be sed. This calclator mst not have programming or graphing capabilities. An acceptable example is the TI-30 calclator. Each stdent is responsible for obtaining their own calclator. Note: On some qantities, onl the magnitde of the qantit is provided. The proper sign conventions and reference definitions mst be applied. Distance Stdents: Please retrn the original exam onl; do not scan/fax/ an additional cop. Yor proctor shold keep a cop of the completed exam. 1) (10 points) Design a Galilean telescope constrcted ot of two thin lenses in air. The telescope mst have a magnifing power of 3X and a length of 75 mm. f OBJ = mm f EYE = mm

2 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page /14 Fall, 017 ) (15 points) Design a spectacle lens for a patient with corneal astigmatism. The patient reqires a lens that has powers of -4 D and -6 D in orthogonal meridians on the lens. The lens has an index of 1.5, and the shape of this thin lens in air is a meniscs. The concave spherical srface of the lens has a radis of crvatre of 80 mm. The convex srface of the lens is toroidal prodcing the reqired power variation. a) Determine the two principal radii of crvatre for the convex srface of the lens. b) What is the srface sag difference of the convex srface along the two principal meridians? Determine this sag at a radis of 0 mm from the srface vertex. R1 = mm R = mm Sag = mm

3 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 3/14 Fall, 017 3) (15 points) As shown below, a 100 mm focal length thin lens is sed to image an object at infinit. The lens has a diameter of 40 mm. The sensor sed with the lens has a width of 10 mm (± 5 mm). The sstem stop is at the lens. A right angle prism is to be inserted between the lens and the sensor. The exit face of the prism mst be spaced 0 mm from sensor. The prism has an index of refraction of 1.5. What is the smallest prism that can be sed in the sstem with no vignetting? In other words, the sstem is nvignetted over the fll width of the sensor. Let H be the width of the face of the prism. Yo ma consider this to be a onedimensional problem and consider vignetting onl in the plane of the paper. D lens = 40 mm D Sensor = 10 mm f = 100 mm Contines

4 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 4/14 Fall, 017 Minimm Prism Size H = mm

5 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 5/14 Fall, 017 4) (5 points) The following diagram shows the design of an objective that is comprised of two thin lenses in air. The sstem stop is located between the two lenses. The sstem operates at f/4. The object is at infinit. The maximm image size is +/- 30 mm. f 1 = -00 mm Stop Dia =???? f = 100 mm Image Plane (+/- 30 mm) 40 mm 40 mm Determine the following: - Entrance ppil and exit ppil locations and sizes. - Sstem focal length and back focal distance. - Stop diameter. - Anglar field of view (in object space). - Reqired diameters for the two lenses for the sstem to be nvignetted over the specified maximm image size. NOTE: This problem is to be worked sing ratrace methods onl. All answers mst be determined directl from the ras o trace; for example, the FOV mst be determined from a ratrace. Ratraces mst be done on the ratrace form. Be sre to clearl label or ras on the ratrace form. A method of soltion explaining or procedre and calclations mst be provided. Calclations ma NOT be done in the margins of the ratrace sheet. Gassian imaging methods ma not be sed for an portion of this problem. Entrance Ppil: mm to the of the first lens. Exit Ppil: mm to the of the second lens. D EP = mm D XP = mm Sstem Focal Length = mm Stop Diameter = mm Lens 1 Diameter = mm Back Focal Distance = mm FOV = +/- deg in object space Lens Diameter = mm

6 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 6/14 Fall, 017 Srface f t Contines

7 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 7/14 Fall, 017 Provide Method of Soltion: Contines

8 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 8/14 Fall, 017 Provide Method of Soltion:

9 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 9/14 Fall, 017 5) (10 points) An optical sstem is comprised of two elements separating indices of refraction n 1, n and n 3. Sbscript 1 designates element 1, sbscript designates element, and qantities withot sbscripts (EP, XP, P and P ) are associated with the total sstem. n1 n 3 Stop XP 1 EP n P P P 1 1 P P P z Circle the index of refraction (and therefore the corresponding optical space) associated with each of the following: EP: n 1 n n 3 XP: n 1 n n 3 P 1 : n 1 n n 3 P 1 : n 1 n n 3 P : n 1 n n 3 P : n 1 n n 3 P : n 1 n n 3 P: n 1 n n 3

10 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 10/14 Fall, 017 6) (15 points) A dobl telecentric sstem is constrcted ot of two thin lenses in air. The spacing between the lenses is 50 mm, and the magnitde of the magnification m is 1/4. a) Design and sketch the laot of the sstem. Provide the reqired focal lengths. f 1 = mm f = mm Contine to Part b

11 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 11/14 Fall, 017 b) A 1 mm high object is located 100 mm to the left of the first lens of this sstem. Determine the location and size of the image. Cascaded imaging ma not be sed (o ma not image throgh one lens and then se this image as an object for the other lens). Ratrace methods ma not be sed for this problem. The image is mm to the of L. The image height is mm.

12 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 1/14 Fall, 017 7) (10 points) Prove the nlikel reslt that for a general optical sstem, the distance from the rear nodal point of the sstem to the rear focal point of the sstem NF is eqal to mins the front focal length of the sstem. f F Prove NF f for a general sstem. F

13 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 13/14 Fall, 017 Spare Ratrace Sheet: Srface f t

14 OPTI-50 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 14/14 Fall, 017 Spare Ratrace Sheets: Srface C t n t/n n n Srface f t

15 OPTI-50 Eqation Sheet OPL nl n sin n sin 1 1 n1 dt t n t n n 1 1 d n 1 d n BFD d f R FFD d f F (n n)c n n z z f 1 f f R n n F E z/n m z/n f f m f f n m m n m N F R1 1 n n z/n mm z/n PN PNf f F 1 R n n k 1 t f/# f E NA n sin U n DEP 1 1 f/# W 1 mf/# NA n I HЖ n n tan( 1/) 10in 50mm MP f f MP 1 m MP mrmpk mv mobjmpeye

16 M E L A LA d LO E 4(f /# ) W Exposre H E T a Un a and a Half a and a Fll DOF Bf /# W L H fd LH L B NEAR n1 P n 1 1 d1 1 n 1 1 d P P 1 1 sin MIN / n sin / 1 n S C sin n R D.44 f /# D f /# in m Sag R nd 1 n n n F n C d C P n F n C f 1 f TA CH rp dc fcd P f

OPTI-502 Optical Design and Instrumentation I John E. Greivenkamp Final Exam In Class Page 1/16 Fall, 2015

OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 1/16 Fall, 2015 Name Closed book; closed notes. Time limit: 120 mintes. An eqation sheet is attached and can be