OPTI-202R Geometrical and Instrumental Optics John E. Greivenkamp Midterm II Page 1/8 Spring 2017

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1 OPTI-0R Geometrical and Instrumental Optics John E. Greivenkamp Midterm II Page /8 Spring 07 Name SOLUTIONS Closed book; closed notes. Time limit: 50 minutes. An equation sheet is attached and can be removed. A spare raytrace sheet is also attached. Use the back sides i required. Assume thin lenses in air i not speciied. As usual, only the magnitude o a magniication or magniying power may be given. I a method o solution is speciied in the problem, that method must be used. Raytraces must be done on the raytrace orm. Be sure to indicate the initial conditions or your rays. You must show your work and/or method o solution in order to receive credit or partial credit or your answer. Provide your answers in a neat and orderly ashion. No credit i it can t be read/ollowed. Only a basic scientiic calculator may be used. This calculator must not have programming or graphing capabilities. An acceptable example is the TI-30 calculator. Each student is responsible or obtaining their own calculator. Note: On some quantities, only the magnitude o the quantity is provided. The proper sign convention must be applied. ) (0 points) An optical system is comprised o two elements separating indices o reraction n, n and n 3. Subscript designates element, subscript designates element, and quantities without subscripts (EP, XP, P and P ) are associated with the total system. n n n XP EP 3 Stop P P P P P P Circle the index o reraction (and thereore the corresponding optical space) associated with each o the ollowing: EP: n n n 3 XP: n n n 3 P : n n n 3 P : n n n 3 P : n n n 3 P : n n n 3 P : n n n 3 P : n n n 3

2 OPTI-0R Geometrical and Instrumental Optics John E. Greivenkamp Midterm II Page /8 Spring 07 ) (40 points) A 5X Keplerian telescope is comprised o two thin lenses separated by 0 mm. The objective lens has a ocal length o 00 mm and it is 50 mm in diameter. The eye lens has a ocal length o 0 mm and it is mm in diameter. This telescope is to be used with a human eye, and the eye is placed at the exit pupil o the telescope. The eye has a 4 mm diameter entrance pupil. For distant objects, what is the unvignetted object ield o view (in degrees) o this system including the eye? A blank raytrace sheet is on the next page. OBJ D OBJ 00mm 50mm D 0mm mm DEYE 4mm t 0mm OBJ EYE ER Because DOBJ 5D, the objective lens is the stop o the telescope. The eye relie is ound by imaging the objective through the eye lens: OBJ t 0mm ER OBJ ER 4mm D XP DOBJ 50mm 0mm MP 5 The exit pupil o the telescope (0 mm) is larger than the entrance pupil o the eye (4 mm). When the eye is included in the system, the eye serves as the system stop.

3 OPTI-0R Geometrical and Instrumental Optics John E. Greivenkamp Midterm II Page 3/8 Spring 07 These results can be conirmed by tracing a potential chie ray and a potential marginal ray. The potential chie ray starts at the center o the objective lens and will cross the axis at the XP o the telescope and determines the ER. The potential marginal ray is launched at the edge o the objective lens (y = 5 mm) with a ero slope. As expected the potential marginal ray has a height o -5 mm at the eye. The system marginal ray is ound by scaling the potential marginal ray to the radius o the eye pupil ( mm). The scale actor is mm Scale Factor 0.4 5mm The system EP is at the objective lens with a diameter o 0 mm. Continues

4 OPTI-0R Geometrical and Instrumental Optics John E. Greivenkamp Midterm II Page 4/8 Spring 07 Since vignetting cannot occur at a stop or pupil, the ield o view is limited by the eye lens. The condition or no vignetting must be satisied at the eye lens using a scaled chie ray: a y y y C y y.0mm y.0mm a D 6.0mm a 6.0mm.0mm C.0 C Scale Factor The scaled chie ray has a height o 4.0mm at the eye lens. The chie ray slope in object space is uo This slope can be converted into the unvignetted FOV o the system: FOV tan u O.9deg FOV.9deg 3.8deg Unvignetted FOV = +/-.9 degrees

5 OPTI-0R Geometrical and Instrumental Optics John E. Greivenkamp Midterm II Page 5/8 Spring 07 3) (5 points) A doubly telecentric system is constructed out o two thin lenses in air. The spacing between the lenses is 50 mm, and the magnitude o the magniication m is /4. a) Design and sketch the layout o the system. Provide the required ocal lengths. A doubly telecentric system must be aocal (two positive lenses) with the stop at the common ocal point. The system magniication must be negative. m 4 t 50mm 4 00mm 50mm STOP F F F F 00mm 00mm 50mm 50mm = 00 mm = 50 mm Continue to Part b

6 OPTI-0R Geometrical and Instrumental Optics John E. Greivenkamp Midterm II Page 6/8 Spring 07 b) A mm high object is located 00 mm to the let o the irst lens o this system. Determine the location and sie o the image. Cascaded imaging may not be used (you may not image through one lens and then use this image as an object or the other lens). Raytrace methods may not be used or this problem. h STOP F F s A 00mm F 00mm 50mm F A 50mm h For imaging, use the longitudinal magniication with the ocal points as the reerence points. s m m m 4 6 h mm h mh 3.0mm The object is 00 mm to the let o the irst lens: s 00mm 00mm m 6.5mm A s 50mm 6.5mm 56.5mm A A A The image is to the right o the second lens. The image is 56.5_ mm to the R o L. The image height is -3.0 mm.

7 OPTI-0R Geometrical and Instrumental Optics John E. Greivenkamp Midterm II Page 7/8 Spring 07 4) (5 points) A ixed ocus camera uses a detector with 0 m x 0 m pixels. The camera lens has a ocal length o 5 mm. Objects rom m to ininity are imaged with acceptable image quality. The acceptable blur on the detector equals the pixel width. Assume a thin lens with the stop at the lens. Determine the required /# o the lens Determine the location o the detector relative to the rear ocal point o the lens. The hyperocal condition must be met: 5mm B 0 m 0.0mm L m L L m 000mm NEAR NEAR L D B B L D D.33mm / # / D /.5 To determine the detector location, image the hyperocal distance: 000mm 5.3mm The detector should be located 0.3 mm or 3 m to the right o the rear ocal point o the lens. System /# =.5 The detector is located _0.3_ mm to the _R_ o Fˊ.

8 OPTI-0R Geometrical and Instrumental Optics John E. Greivenkamp Midterm II Page 8/8 Spring 07 5) (0 points) A 50 mm ocal length relay lens is to be added to a simple 0X Keplerian telescope. In addition to erecting the image, the relay lens will also increase the magniying power o the telescope to 0X. ow much longer will the new telescope be as compared to the original Kelperian telescope? The original Keplerian telescope: The desired inal MP is 0X MP 0 LK OBJ EYE MP MP mrmpk mr.0 MP R m R R R R 3 R 50mm R R R 75mm 50mm R R K L 5mm L 5mm R OBJ EYE R R OBJ EYE K The 0X relayed Keplerian telescope is 5 mm longer than the original 0X Keplerian telescope. Increase in the length o the telescope = 5 mm

OPTI-202R Geometrical and Instrumental Optics John E. Greivenkamp Final Exam Page 1/11 Spring 2017

OPTI-202R Geometrical and Instrumental Optics John E. Greivenkamp Final Exam Page 1/11 Spring 2017 Final Exam Page 1/11 Spring 2017 Name SOLUTIONS Closed book; closed notes. Time limit: 120 minutes. An equation sheet is attached and can be removed. A spare raytrace sheet is also attached. Use the back