OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 1/12 Fall, 2011 Name Closed book; closed notes. Time limit: 2 hors. 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. Yo mst show or work and/or method of soltion in order to receive credit or partial credit for or answer. 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. Distance Stdents: Please retrn the original exam onl; do not scan/fax/email an additional cop. Yor proctor shold keep a cop of the completed exam. 1) (10 points) A 200 mm focal length telephoto objective is constrcted ot of two thin lenses in air. The first lens has a focal length of 150 mm. The sstem Back Focal Distance is 100 mm. Determine the focal length of the second lens and the separation between the two lenses. Use Gassian methods. Separation = mm f 2 = mm
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 2/12 Fall, 2011 2) (15 points) The design of a thin lens achromatic doblet is given b the following two eqations: φ1 ν1 φ2 ν2 = = φ ν ν φ ν ν Derive one of these two eqations. 1 2 1 2
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 3/12 Fall, 2011 3) (20 points) An object is located 100 mm to the left of a 50 mm focal length thin lens. The object has a height of 10 mm above the optical axis of the lens. The lens diameter is 20 mm, and the lens serves as the sstem stop. An additional apertre is placed 50 mm to the right of the lens. What is the reqired diameter of this apertre so that the sstem operates withot vignetting? The method of soltion is not specified. h = 10 mm 50 mm Apertre Object 100 mm f = 50 mm D STOP = 20 mm z Contines
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 4/12 Fall, 2011 Ratrace sheet, if needed: Srface f φ 0 1 2 3 4 5 6 t D APERTURE mm
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 5/12 Fall, 2011 4) (30 points) A relaed Keplarian telescope is constrcted with three thin lenses in air. All three lenses have the same diameter of 24 mm. Objective f OBJ = 125 mm Rela Lens f R = 50 mm Ee Lens f EYE = 25 mm z t 1 = 275 mm t 2 = 100 mm Determine: The Magnifing Power of the telescope. The half-vignetted Field of View in degrees in object space. The locations of the Entrance and Exit Ppils. The diameters of the Entrance and Exit Ppils. NOTE: This problem is to be worked sing ratrace methods onl. Gassian imaging methods ma not be sed for an portion of this problem. The field of view mst be determined from the chief ra. Be sre to clearl label or ras on the ratrace form. Yor answers mst be entered below. Yo mst 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.). Magnifing Power = FOV = +/- deg in object space Entrance Ppil: mm to the of the objective lens. D EP = mm Exit Ppil: mm to the of the ee lens. D XP = mm
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 6/12 Fall, 2011 Srface 0 1 2 3 4 5 6 f φ t Contines
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 7/12 Fall, 2011 Provide Method of Soltion: Contines
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 8/12 Fall, 2011 Provide Method of Soltion:
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 9/12 Fall, 2011 5) (10 points) The image in the ee is formed in an index of refraction of 1.336. The rear focal length of the ee is 22.4 mm. An object is 1 meter in front of the ee (in air) and has a height of 20 mm. What is the height of the image formed in the ee (on the retina)? Use Gassian methods. Assme that the ee changes length to keep the image in focs. Image Height = mm
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 10/12 Fall, 2011 6) (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. Two objects are located 400 mm and 100 mm to the left of the first lens in the sstem. Where are the respective image planes (located relative to the second lens element)? f 1 = 200 mm Focal length of the second lens = mm Object at 400 mm: Object at 100 mm: Image is mm to the of the second lens Image is mm to the of the second lens
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 11/12 Fall, 2011 Bons/Extra Credit (5 points) We all know that in Gassian redction, a sstem of lenses is replaced with a pair of principal planes and a sstem focal length or power. One thing we did not talk abot is what happens to the stop! Consider the following sstem which has a stop located between two thin lenses: f 1 Stop f 2 t 1 t 2 Discss how o wold inclde the optical properties of the stop in the redced sstem.
OPTI-502 Optical Design and Instrmentation I John E. Greivenkamp Final Exam In Class Page 12/12 Fall, 2011 Spare ratrace forms: Srface C t n 0 1 2 3 4 5 6 φ t/n n n Srface f φ 0 1 2 3 4 5 6 t
OPTI-502 Eqation Sheet OPL = nl n sin θ = n sin θ 1 1 2 2 γ= 2α n 1 d= t = t τ n φ= (n n)c n n = +φ z z f 1 f f R φ n n F E = = = z/n ω m = = z/n ω m f f = = f f n m= m n m N F2 2 R1 1 n = n 2 Δz/n = mm Δz/n PN = PN= f + f F 1 2 R t τ = ω= n n φ =φ 1+φ2 φφ 1 2τ d φ n φ 1 δ = = τ d n φ φ 2 δ = = τ ω =ω φ = +ωτ f/# f BFD = d + f R FFD = d + f F E NA n sin U n DEP 1 1 f/# W ( 1 m) f/# 2NA 2n I = H = n n = tan( θ 1/2) 10in 250mm MP = = f f 1 MP = m mv = mobjmpeye
M ρe L = = π π A Φ= LAΩ Ω 2 d πlo E = 2 4(f /# ) W Exposre = E Δ T a + Un a = and a Half a and a Fll DOF =± B f /# W L H fd LH = L B NEAR = 2 δ = ( n 1) α δ ε = ν = P Δ Δ α 1 ν = δ ν ν 1 1 1 2 nd1 1 α 1 ν = δ ν ν ε δ 2 2 1 2 nd2 1 P P 1 2 = ν1 ν2 ( α δmin ) sin ( α / 2) sin / 2 n = 1 n S θ C = sin nr D= 2.44λ f /# D f /# in μ m 2 Sag 2R nd 1 ν= n n n F n C d C P = n F n C δφ δf 1 = = φ f ν TA CH rp = ν φ1 ν1 φ2 ν2 = = φ ν ν φ ν ν 1 2 1 2 δφdc δfcd ΔP = = φ f Δν