HongKongPolytechnicUniversityLightControithroughOpticalSystemExample: Consider an optical system made up of two positive thin lenses with a stop Slocated between them as shown in the figure. (a) Locate the position and size of the finalimage. (b)Locate the AS, E.P, and E,P for the system. ()Locate the FS, E,W, and E,W forthe systemL1sL2f,=40cm1=20cm-330.5cmdiam=2cmdiam=2cm0FFF,F2ObjectL40cm20cm10cm1111s's'=20 cm,Solution: s,=-40 cm,f=40/3cm,ms'fiSi2S111$2-2s,=20cmS2=-10 cm;f2=20/3cm;m2s2J2S2S220cmsPP1cmKPVOOOFP2ObjectOpImageO"pD20cm10cmL1ImageO'pL2(0.5cmhigh)6Optics1----byDr.H.Huang,DepartmentofAppliedPhysics
Hong Kong Polytechnic University Optics 1-by Dr.H.Huang, Department of Applied Physics 6 Light Control through Optical System Example: Consider an optical system made up of two positive thin lenses with a stop S located between them as shown in the figure. (a) Locate the position and size of the final image. (b) Locate the AS, EnP, and ExP for the system. (c) Locate the FS, EnW, and ExW for the system. Solution: s1=−40 cm; f1=40/3 cm; s1 =20 cm; s2=−10 cm; f2=20/3 cm; s2 =20 cm; 1 1 1 1 1 1 s s f − = 2 1 1 1 1 = − = s s m 2 2 2 1 1 1 s s f − = 2 2 2 2 = − = s s m
HongKongPolytechnicUniversityLightControithroughOpticalSystemEPE,WE,w8.57cmASMRPFSE,P0″2.0cm002.0cmImageObjectplaneplane(b) Lens L1 is AS and E,P. Using thin lens equation, E,P is located 8.57 cm to the right oflensL2withandiameterof4/7cm.(c) To find FS, we must determine the angles subtended at the center of the entrance pupilEyeThestopSisFS.E,Wislocated inthepupilobject plane witha diameter of 2 cmTemporalE,W is located at the image plane withsideadiameterof2cmFovea+Optical axisHEaF2E.NEAschematiceye:VisualaxisNasalsideEPEP7Optics1----byDr.H.Huang,DepartmentofAppliedPhysics
Hong Kong Polytechnic University Optics 1-by Dr.H.Huang, Department of Applied Physics 7 Light Control through Optical System (b) Lens L1 is AS and EnP. Using thin lens equation, ExP is located 8.57 cm to the right of lens L2 with an diameter of 4/7 cm. (c) To find FS, we must determine the angles subtended at the center of the entrance pupil. The stop S is FS. EnW is located in the object plane with a diameter of 2 cm. ExW is located at the image plane with a diameter of 2 cm. A schematic eye:
HongKongPolytechnicUniversityLightControithroughOpticalSystemHomework:1.Twopositivelenses, each of diameter 5 cm and focal length15 cm,are separated byadistance of 10 cm. For what range of object positions along the optical axis will (a) thefirst lens and (b) the second lens control the amount of light passing through the system?2. An aperture of opening 5 cm in diameter is positioned 15 cm to the left of a positive lensof rim diameter 10 cm and focal length 12 cm.Each element is centered on the opticalaxis. (a) For an object located 6 cm to the left ofthe aperture, which element serves as As?(b) Where aretheentrance andexit pupils located?3. An aperture of 5-cm opening is located 8 cm to the right of a positive lens of diameter 10cm and focal length 12 cm. (a) For an object located 6 cm to the left of the lens, whichelement is AS? (b)Where is E.P?What is its size?(c)Where is E,P? What is its size?4. An object measures 2 cm high above the axis of an optical system of a 2-cm AS and a thinconvex lens of 5-cm focal length and 5-cm aperture. The object is 10 cm and the AS is 2cm in front of the lens. Determine the position and size of the entrance and exit pupils, aswell as theimage.5. An optical system, centered on an optical axis, consists of (left to right): object plane, thinlens L, 30 cm from the object plane, aperture A 15 cm farther from Lr, thin lens L, 10 cmfarther from A, and image plane. Lens L, has a focal length of 10 cm and a diameter 6 cmL2 has a focal length of 5 cm and a diameter of 6 cm; aperture A has a centered, circularopening of 2.0 cm in diameter. Locate (a) image plane, (b) AS and E,P, (c) E,P and (d) FSE,WandE,W.8Optics1----byDr.H.Huang,DepartmentofAppliedPhysics
Hong Kong Polytechnic University Optics 1-by Dr.H.Huang, Department of Applied Physics 8 Light Control through Optical System Homework: 1. Two positive lenses, each of diameter 5 cm and focal length 15 cm, are separated by a distance of 10 cm. For what range of object positions along the optical axis will (a) the first lens and (b) the second lens control the amount of light passing through the system? 2. An aperture of opening 5 cm in diameter is positioned 15 cm to the left of a positive lens of rim diameter 10 cm and focal length 12 cm. Each element is centered on the optical axis. (a) For an object located 6 cm to the left of the aperture, which element serves as AS? (b) Where are the entrance and exit pupils located? 3. An aperture of 5-cm opening is located 8 cm to the right of a positive lens of diameter 10 cm and focal length 12 cm. (a) For an object located 6 cm to the left of the lens, which element is AS? (b) Where is EnP? What is its size? (c) Where is ExP? What is its size? 4. An object measures 2 cm high above the axis of an optical system of a 2-cm AS and a thin convex lens of 5-cm focal length and 5-cm aperture. The object is 10 cm and the AS is 2 cm in front of the lens. Determine the position and size of the entrance and exit pupils, as well as the image. 5. An optical system, centered on an optical axis, consists of (left to right): object plane, thin lens L1 30 cm from the object plane, aperture A 15 cm farther from L1 , thin lens L2 10 cm farther from A, and image plane. Lens L1 has a focal length of 10 cm and a diameter 6 cm; L2 has a focal length of 5 cm and a diameter of 6 cm; aperture A has a centered, circular opening of 2.0 cm in diameter. Locate (a) image plane, (b) AS and EnP, (c) ExP and (d) FS, EnW and ExW
HongKongPolytechnicUniversityOpticallnstrumentationPrisms: generally not used aloneAngular deviation:A=0' +0,8=8 +8, =0 +0--A+SmnsinMinimum deviation occurs when2n=the ray of light passes through theAsinprism symmetrically.2(A + 8m. )/2For small prism angle: n =A/21a1Smin = A(n-1)Or:Virtualimage&Ophthalmic Prisms:Small angleprisms areused inophthalmologyto correct doublevision.Whentwo eyesObjectdonot aim simultaneously at anobject correctly,townonoverlapping images are perceived.Base9Optics1----byDr.H.Huang,DepartmentofAppliedPhysics
Hong Kong Polytechnic University Optics 1-by Dr.H.Huang, Department of Applied Physics 9 Optical Instrumentation Prisms: generally not used alone Angular deviation: Minimum deviation occurs when the ray of light passes through the prism symmetrically. 1 2 1 2 1 2 = + = + − − 2 sin 2 sin min A A n + = 1 2 A = + For small prism angle: Or: ( ) 2 2 min A A n + ( 1) min = A n− Ophthalmic Prisms: Small angle prisms are used in ophthalmology to correct double vision. When two eyes do not aim simultaneously at an object correctly, tow nonoverlapping images are perceived