OPTI-502 Optical Design and Instrumentation I John E. Greivenkamp Homework Set 9 Fall, 2018

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1 OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Assigned: 10/31/18 Lectre 21 De: 11/7/18 Lectre 23 Note that in man 502 homework and exam problems (as in the real world!!), onl the magnitde of the magnification or MP is given. Yo need to determine the sign based pon the configration. 9-1) 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 size 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. 9-2) Design a thin-lens telephoto lens with a back focal distance of 50 mm and an effective focal length of 200 mm.

2 OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp 9-3) The goal of this problem is to design a variable focal length lens sing a plano-convex lens, a plane parallel plate, and a flid that has a variable index of refraction. The flid is placed between the lens and the plane parallel plate to prodce a sandwich of thin lenses. There are no moving parts, and the finished sstem is in air. Plano-convex lens: focal length = 100 mm n = Plane parallel plate: thickness = 2 mm n = a) Sketch the arrangement of elements and give the eqation for the sstem focal length as a fnction of the index of the flid. b) If the index of this flid can var from 1.3 to 1.7, what range of power or focal length can be obtained with the sstem? Note that this is a fictitios flid! 9-4) A medim-format digital single lens reflex (DSLR) is to be designed sing a monochrome (B&W) image sensor in the DX or APS-C format. The sensor size is 24 x 16 mm. a) The first task is to specif the focal length of the camera objective. The field of view for distant objects shold be eqivalent to a 35 mm film based camera with a 38 mm focal length lens. The 35 mm film format is 24 x 36 mm. b) The next task is to determine the lens focs positions needed to cover a range of object positions from infinit to 500 mm. The camera lens will operate at f/4. One criteria for good image focs is that the blr diameter de to defocs matches the pixel width on the sensor. For this problem, diffraction and aberrations are to be ignored. (Note that this criterion is ver conservative, and significantl more blr ma still prodce good images.) The pixels on the image sensor are 10.0 x 10.0 m. The first focs zone extends from infinit to its L NEAR. The next zone starts at this position as L FAR and contines to a new L NEAR. The zones contine ntil the entire object range is covered. At each zone, give the reqired sensor location relative to the rear focal point of the lens. These vales actall provide the amont of lens motion that is reqired to go from zone to zone (as the lens is actall moved, not the sensor). This problem is best done b setting p a spread sheet. This also allows the varios parameters to be varied to investigate sstem changes. Examine how does the nmber of reqired zones var with Focal length? Blr? F/#?

3 OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp 9-5) Design a two-element reverse telephoto zoom lens: Focal length range: Lens configration: Element focal lengths: 30 to 80 mm Two-element zoom lens Reverse-telephoto configration (negative-positive) f 1 = -50 mm f 2 = 50 mm Assme an object at infinit. Both elements are thin lenses in air. Provide the eqations for the element separation and the back focal distance as a fnction of the sstem focal length. Also provide a table giving these two spacings and the total sstem length at the maximm and minimm focal lengths as well as at reglar 10 mm increments of focal length (30 mm, 40 mm, 50 mm, etc.). Plot the lens positions relative to the image plane as a fnction of focal length (similar to the plot fond in the class notes). Note that the reqirement for the two elements having eqal bt opposite focal lengths is given for comptational ease. This is an arbitrar bt sefl choice. 9-6) A 5X Keplerian telescope has a 200 mm focal length objective. a) Determine the focal length of the ee lens and the overall telescope length. b) If the stop of the telescope is the objective, what is the ee relief? 9-7) A pair of 6x30 binoclars (Keplerian) have 150 mm focal length objectives. What is the size of the exit ppil and how mch ee relief is obtained? 9-8) Design a Galilean telescope with a magnifing power of 5 and a length of 100 mm. Specif the two focal lengths. 9-9) Design a Keplerian telescope with a magnifing power of 10 and an ee relief of 11 mm. Specif the two focal lengths and the separation. 9-10) Two stars are separated b 2.0 arc seconds. Assming the ee has a resoltion of 1 arc minte, what magnifing power is reqired for a telescope in order to visall resolve the stars? If diffraction is inclded, what is the minimm reqired entrance ppil diameter?

4 OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp 9-11) A magnifier that is marked 10X is sed to examine an object. The magnifier lens has a diameter of 10 mm, and the magnifier is sed with a relaxed ee. This implies that the ee is focsed at infinit, and that the virtal image prodced b the magnifier is also at infinit. a) The magnifier is first sed as an ee lope. The separation between the magnifier lens and the ee is 25 mm. What is the diameter of the half-vignetted field of view (object size in mm) seen throgh the magnifier? Assme that the ee has a ppil diameter of 4 mm. b) The magnifier is now sed as a magnifing glass b increasing the separation between the magnifier lens and the ee to 250 mm. What is the diameter of the half-vignetted field of view (object size in mm) seen throgh the magnifier? Once again, assme that the ee has a ppil diameter of 4 mm. c) What do these reslts impl abot the wa a magnifier is best sed? 9-12) A Keplerian telescope has the following specifications: Magnifing Power = 12 X Length = 260 mm (objective to ee lens) Unvignetted Field of View = +/- 2 degrees Ee Relief = 15 mm Entrance Ppil Diameter = 40 mm The stop is located at the objective lens of the telescope The object is at infinit All elements are thin lenses Design the telescope. How man elements are reqired? Provide element focal lengths, diameters and spacings. Be sre to verif that all of the above specifications are met exactl.

5 OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Srface f t