OPTI-502 Final Exam In Class John E. Greivenkamp Page 1/13 Fall, 2008

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1 Page 1/13 Fall, 2008 Name Closed book; closed notes. The time limit is 2 hors. Eqation sheets are attached and can be removed. Spare ratrace forms are also attached. Use the back sides if reqired. Do not se an pre-stored information or programs in or calclator. Assme thin lenses in air if not specified. If a method of soltion is specified in the problem, it mst be sed. Yo mst show or work and/or method of soltion in order to receive credit or partial credit for or answer. Distance Stdents: Please retrn the original exam onl; do not scan/fax/ an additional cop. 1) (10 points) The following list identifies six optical glasses b their six-digit glass code. Identif which of these glasses is a crown (K) or a flint (F) b circling the appropriate letter K F K F K F K F K F K F Which of these two glasses shold be sed to prodce a first-order achromatic doblet with the least excess power? Crown Glass: Flint Glass:

2 Page 2/13 Fall, ) (20 points) Dring the semester, we have discssed a variet of optical sstems, components and concepts. For each of the topics that is listed, provide a brief description and discss some of the featres or properties of this item. (for example, from a design perspective, what does it mean for the performance of the sstem or the se of the sstem?). Tr to be practical, I am looking for concepts not eqations. Limit or answers to the space provided. Legibilit does cont I need to be able to read it! a) Field Lenses b) Reverse Telephoto Lens

3 Page 3/13 Fall, 2008 c) Right angle Roof Prism (Amici) d) Speclar Illmination Sstem

4 Page 4/13 Fall, ) (15 points) Using onl 50 mm focal length thin lenses, provide the laot of a doble-telecentric sstem with a lateral magnification of Yo ma se p to for of these thin lenses in or design. Provide a sketch of the sstem clearl indicating the spacings of the lenses and the location of the sstem stop. Note: The sstem magnification mst be POSITIVE. The lens diameters are not reqired. There are several possible designs o need to provide onl one.

5 Page 5/13 Fall, ) (20 points) In a 3X Galilean telescope, the separation between the objective lens and the ee lens is 100 mm. The objective lens diameter is 30 mm and the ee lens diameter is 12 mm. The telescope is to be sed with an ee that has a 4 mm diameter entrance ppil. The separation between the ee lens and the ee ppil is 15 mm. The object is at infinit. What is the nvignetted object space Field of View of this sstem in degrees? Which element limits the nvignetted Field of View? Contines

6 Page 6/13 Fall, 2008 Unvignetted Field of View = +/- degrees in object space FOV Limited b Ra Trace Form Follows

7 Page 7/13 Fall, 2008 Srface f φ t

8 Page 8/13 Fall, ) (15 points) A swimming pool has a sloped bottom (i.e. deeper on one end than the other). Yo notice that at noon on a snn da, an interesting light pattern has formed on the bottom of the pool. The pattern is de to imaging of the sn b the waves on the pool srface. Especiall sharp line images of the sn occr at a depth of 2 m, and the spacing of the lines is abot 300 mm. Using reasonable, simple assmptions, what can o sa abot the waves on the srface of the water? In particlar, what are the approximate amplitde and period of the waves? State or assmptions. n water = 1.33 Contines

9 Page 9/13 Fall, 2008 Wave period = mm Wave peak-to-valle amplitde mm

10 Page 10/13 Fall, ) (20 points) In cataract srger, the natral lens of the ee (now white and opaqe) is removed and replaced b an artificial intraoclar lens (IOL). The goal of this lens is to work with the cornea to focs images of distant objects on the retina. The cornea can be assmed to be a single refracting srface (R C = 8.0 mm), and the IOL is assmed to be a thin lens. The IOL is sall made of plastic and it is immersed in the aqeos of the ee (n AQ = 1.333). The IOL is located 4 mm behind the cornea, and the retina is 24 mm behind the cornea. Both parts of this problem are to be done sing Gassian methods. No credit will be given for ratrace analsis. R C = 8.0 mm IOL Retina n = 1.0 n AQ = mm 24 mm a) What is the power and focal length of the IOL reqired to image distant objects onto the retina? This power and focal length are for the thin lens immersed in the aqeos. Contines

11 Page 11/13 Fall, 2008 φ IOL = /mm f IOL = mm Contines

12 Page 12/13 Fall, 2008 b) If the plastic IOL is removed from the aqeos, what are its power and focal length in air? The index of the IOL is 1.5. n IOL = 1.5 φ Air = /mm f Air = mm

13 Page 13/13 Fall, 2008 Spare ratrace forms: Srface C t n φ t/n n n Srface f φ t

14 OPTI-502 Eqation Sheet OPL = nl n sin θ = n sin θ 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

15 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 nd1 1 α 1 ν = δ ν ν ε δ 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 δφdc δfcd ΔP = = φ f Δν