Midterm II Page 1/7 Spring 2018 Name SOUTIONS 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. 1) (15 points) An ininity-corrected microscope is constructed out o an objective lens OBJ, a tube lens TUBE, and an eye lens or eyepiece. In terms o these three ocal lengths, what is the visual magniication o this microscope? The objective lens and the tube lens combine to create a magniied intermediate image: Object Ininity Corrected Objective m OBJ / Tube ens u u y - OBJ TUBE u y u y / OBJ TUBE TUBE OBJ Intermediate Image The eye lens works as a magniier viewing this intermediate image: The net visual magniication is the product o these two magniications: MP 250mm m m MP V OBJ TUBE OBJ 250mm m V = TUBE OBJ 250mm
Midterm II Page 2/7 Spring 2018 2) (20 points) A 5 mm diameter extended source is used to project a spot o light onto a distant wall. A 500 mm ocal length lens with a diameter o 100 mm is to be used. The source is placed at the ront ocal point o the lens to collimate it. What is the projected spot sie on a wall 100 m away? Note: Compute the maximum extent o the projected spot. Do not determine the irradiance proile o the spot. This is a geometrical optics problem do not consider diraction or aberrations. ight collimated rom an extended source diverges due to the source sie. This situation can be treated as a vignetting problem. By using the condition or no vignetting at the wall, all o the light in the pattern will be contained in a circle o the determined diameter. y 2.5 mm 50 mm u SOURCE u y 500 mm u0 y D /250mm ENS DSOURCE /2 2.5mm u u 0.005 500mm ENS yu 100m y0.5m500mm a y y 50mm500mm550mm SPOT D 2a 1100mm SPOT SPOT Spot Dia at 100 m = _1100_mm
Midterm II Page 3/7 Spring 2018 3) (20 points) Design a doubly telecentric system using two thin lenses (in air). The overall object-to-image distance is required to be 200 mm, and the image sie is one third the object sie. The object and image must both be real. Determine the ocal lengths, the lens separation, a pair o conjugate object and image positions, and the stop location. Provide a neat sketch the system showing these distances. The system must be aocal with the lens separation equal to the sum o the ocal lengths. The stop must be located at the common ocal point. Two positive lenses must be used, and the system magniication is negative. There are many possible object/image locations (and resulting systems), but the obvious solution places the object at the ront ocal point o the irst lens and the image at the rear ocal point o the second lens. h F1 F2 s 1 75mm 1 F 1 75mm 2 25mm 2 F 2 h 25mm t 100mm 200mm s ength 2 2 200mm 1 1 2 2 m 1 32 3 1 1 2 1 2 75mm 25mm t 100mm 1 = 75 mm 2 = 25 mm t = 100_ mm Stop ocation: Common Focal Point 75 mm to the Right o the First ens Object: _75 mm to the o the irst lens Image: _25 mm to the _R_ o the second lens
Midterm II Page 4/7 Spring 2018 4) (20 points) You are using a camera with a 20 mm ocal length lens to take a picture on large-ormat solid state detector (total image sie is 23.7 mm x 15.6 mm). The long dimension o the detector is oriented horiontally. You are photographing a house against a very distant mountain backdrop, and the distance to the house is 15 m. The camera is ocused on the house. The house is 10 m wide and has a peaked roo that is 8 m high. Assume that the lens is a thin lens with the stop at the lens. 8 m 10 m a) How ar behind the lens must the detector be located? How big is the image o the house on the detector? Sketch the image ormed on the detector (as seen through the back o the sensor). Image the house: 15m 15000mm 20mm 1 1 1 1 1 15000mm 20mm 20.0267mm This is the lens house separation. Now or the image sie: m 0.001335 h mh H : h 10m h 13.35mm V : h 8m h 10.68mm The image is inverted and reverted or rotated 180 degrees. ens-detector separation = 20.0267 mm Image sie: _13.35_mm x _10.68_ mm Detector 13.35 mm 10.68 mm 23.7 mm 15.6 mm
Midterm II Page 5/7 Spring 2018 b) The pixels on the sensor are 7 m square. I this is the limiting image blur in the system (produces acceptable image quality), what is the astest /# lens that can be used so that the distant mountains are also considered to be in ocus along with the house? Remember that the camera is ocused on the house. For the mountains to also be in ocus, set the hyperocal distance equal to the distance to the house (the camera is ocused on the house): D H 15m 15000mm B B 7m 0.007mm 20mm D 5.25mm /# /D3.8 /# = _/3.8 c) With this /#, what is the closest object that will be considered to be in ocus? 15m 2 2 H NEAR 7.5m The closest in-ocus object is 7.5 m rom the camera.
Midterm II Page 6/7 Spring 2018 5) (25 points) Design an object-space telecentric imaging system consisting o a 100 mm ocal length thin lens and a stop. The object is 300 mm to the let o the lens. The system images a 20 mm diameter object onto a 10 mm square detector. The system operates at a working -number o 4 (/# W = 4 or NA = 0.125) and is unvignetted or this object. Provide the diameter o the lens, the stop diameter, and the required spacings. Provide a neat sketch o the system showing these distances. For object-space telecentricity, the stop must be located at the rear ocal point o the lens. h F h 100mm Determine the image location: 300mm 100mm 1 1 1 1 1 300mm 100mm 150mm This could also be determined by noting that the speciied magniication is -0.5 and the image distance must thereore be minus hal the object distance. Continues
Midterm II Page 7/7 Spring 2018 Now the stop diameter D S must be determined using the working /# or the NA. Examine the marginal ray that goes through the edge o the stop and the axial image location. 150mm 100mm 50mm D S / 2 F u D / 2 1 S u / # W 4 2NA NA 0.125 u D S 12.5mm Note that the relationship /# W = (1 m)/# is not appropriate to use here as this system does not have an /#. The EP is at ininity. The working /# must be converted to the NA to determine the marginal ray slope in image space. The lens diameter as determined by vignetting. At the lens: y Object Radius h 10mm y u or y D / 2 S y 18.75mm For no vignetting: a y y a D 28.75mm 57.5mm ens Diameter = 57.5 mm Stop Diameter = 12.5 mm Stop ocation: 100 mm to the R o the ens Image ocation: 150 mm to the R o the ens