OPTI-202R Geometrical and Instrumental Optics John E. Greivenkamp Final Exam Page 1/14 Spring 2015

Transcription

1 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 1/14 Spring 2015 Name Closed book; closed notes. Time limit: 120 mintes. An eqation sheet is attached and can be removed. A spare ratrace sheet is also attached. Use the back sides if reqired. Assme thin lenses in air if not specified. As sal, onl the magnitde of a magnification or magnifing power ma be given. 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. 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 convention mst be applied. 1) (10 points) A 200 mm focal length achromatic doblet is to be constrcted ot of the following two glasses: Glass 1: Glass 2: Provide the two reqired focal lengths. f 1 = mm f 1 = mm

2 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 2/14 Spring ) (15 points) A doble telecentric sstem is constrcted ot of two thin lenses in air. It has a magnification of 1/5. The focal length of the first lens of the sstem is 200 mm. Provide a laot of the sstem showing the second lens, spacings and the stop. An object is located 400 mm to the left of the first lens in the sstem. Where is the image plane (location relative to the second lens element)? f 1 = 200 mm Focal length of the second lens = mm Object at 400 mm: Image is mm to the of the second lens

3 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 3/14 Spring ) (15 points) Design an object-space telecentric sstem consisting of a thin lens and a stop. The focal length of the lens is 100 mm, and the sstem operates at 1:1 conjgates. The sstem covers a field of view of ±10 mm, and it operates at a working f-nmber of 4 (f/# W = 4 or NA = 0.125). The sstem is nvignetted over this field of view. Sketch the sstem and provide the reqired spacings, the diameter of the lens and the stop diameter. The method of soltion is not specified. Contines

4 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 4/14 Spring 2015 D Stop = mm D Lens = mm Stop Location: mm to the of the lens

5 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 5/14 Spring ) (5 points) A field lens is added at the intermediate image plane of a Keplerian telescope. What is the effect of the field lens on each of the following? a) MP b) Ee Relief c) Exit Ppil Diameter d) Field of View e) Telescope Length f) Image Orientation

6 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 6/14 Spring ) (10 points) A moving train is being photographed b a fixed camera. The camera does not move dring the exposre. The train is at a distance of 100 m, and the focal length of the camera lens is 50 mm. The speed of the train is 10 m/s and the train motion is perpendiclar to the optical axis of the camera. Using reasonable approximations, what is the slowest shtter speed that can be sed so that the motion blr on the detector is 5 m? Note that this problem does NOT involve depth of focs/field or hperfocal distance. Shtter speed = sec

7 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 7/14 Spring ) (10 points) An optical sstem is comprised of two thin lenses in air. The first lens has a focal length of 100 mm and the second lens has a focal length of 200 mm. The two lenses are separated b 75 mm. An object is located 200 mm to the left of the first lens. Determine the image location relative to the second lens and the image magnification. Gassian redction and Gassian imaging mst be sed. Image is located mm to the of the lens. Magnification =

8 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 8/14 Spring ) (35 points) An f/4 reverse telephoto objective is comprised of two thin lenses in air. The sstem stop is located between the two lenses. The sstem is now to be sed with a finite conjgate object that is located 150 mm to the left of the first lens. The maximm image size is +/- 20 mm. f 1 = -50 mm Stop f 2 = 40 mm Image Plane (+/- 20 mm) 15 mm 15 mm Determine the following: - Sstem focal length and back focal distance. - Stop size; Entrance ppil and exit ppil locations and sizes. - Image location. - Object size corresponding to the image size. - Reqired diameters for the two lenses for the sstem to be nvignetted over the specified maximm image size and conjgate location. 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 object FOV mst be determined from the chief ra. Ratraces mst be done on the ratrace form. Be sre to clearl label or ras on the ratrace form. Gassian imaging methods ma not be sed for an portion of this problem. Yor answers mst be entered below. Be sre to provide details on the pages that follow to indicate or method of soltion (how did o get or answer; which ra was sed, analsis of ra data, etc.). A few things written next to the ratrace sheet is not sfficient information. Sstem Focal Length = mm Back Focal Distance = mm Entrance Ppil: mm to the of the first lens. Exit Ppil: mm to the of the second lens. D EP = mm D XP = mm D STOP = mm Object Size = +/- mm Image Location: mm to the of the second lens. Lens 1 Diameter = mm Lens 2 Diameter = mm Contines with a ratrace form on the next page

9 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 9/14 Spring 2015 Srface f t Contines

10 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 10/14 Spring 2015 Provide Method of Soltion: Contines

11 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 11/14 Spring 2015 Contines

12 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 12/14 Spring 2015

13 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 13/14 Spring 2015 Spare Ratrace Sheet: Srface f t

14 OPTI-202R Geometrical and Instrmental Optics John E. Greivenkamp Final Exam Page 14/14 Spring 2015 Spare Ratrace Sheets: Srface C t n t/n n n Srface f t

15 OPTI-202 Eqation Sheet OPL nl n sin n sin n1 dt t n (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 F2 2 R1 1 n n 2 z/n mm z/n PN PNf f F 1 2 R t n n d n 1 d n 2 BFD d f R FFD d f F n n t f/# f E NA n sin U n DEP 1 1 f/# W 1 mf/# 2NA 2n I HЖ n n tan( 1/2) 10in 250mm MP f f MP 1 m MP mrmpk mv mobjmpeye

16 a Un a and a Half a and a Fll n d n d2 DOF Bf /# W P P L H fd LH L B NEAR 2 D2.44 f /# D f /# in m sin MIN / 2 n sin / 2 1 n S C sin n R Sag 2 2R f 1 f nd 1 n n F C TA CH rp n n d C P n F n C n1 P dc fcd P f