OPTI-502 Optical Design and Instrumentation I John E. Greivenkamp Homework Set 5 Fall, 2018

Size: px

Start display at page:

Download "OPTI-502 Optical Design and Instrumentation I John E. Greivenkamp Homework Set 5 Fall, 2018"

Edward Nash
5 years ago
Views:

1 Homework Set 5 all, 2018 Assigned: 9/26/18 Lecture 11 Due: 10/3/18 Lecture 13 Midterm Exam: Wednesday October 24 (Lecture 19) 5-1) Te following combination of tin lenses in air is in a telepoto configuration: f1 = 75 mm f2 = -60 mm Spacing = 35 mm Use Gaussian reduction to determine te focal lengt of te system, and te locations of te rear principal plane and te rear focal point. 5-2) A tick lens in air as te following specifications: R1 = 127 mm R2 = -77 mm TH = 17 mm n = a) Wat is te focal lengt and power of tis lens? Were is te image of an object at infinity located wit respect to te rear vertex of te lens (te back focal distance)? b) Wat are te focal lengt, power and back focal distance if te index of te lens is canged to 1.853? c) Wat are te rear focal lengt, focal lengt, power and back focal distance if te original lens (n = 1.472) is immersed in water (n = 1.333)? Use Gaussian reduction for tis problem. 5-3) Use Gaussian reduction to determine te back focal distance of te following tree surface optical system: n = n 0 = 1.33 n 1 = 1.50 t 1 = 5.0 n 2 = 1.60 t 2 = 5.0 n' = n 3 = 1.33 R 1 = 25.0 R 2 = R 3 = -60.0

2 Homework Set 5 all, ) Determine te Gaussian properties of a tick lens in air wit a first surface of radius R 1, a tickness t, an index n, and a second surface of radius R 2 suc tat: a) it is concentric wit te first surface. b) it as equal but opposite power from te first surface. c) te lens as ero power. or eac of tese tree cases, determine te Gaussian properties of te lens and sketc te locations of te cardinal points (, f, f R, P, P',, ', N, N'). 5-5) Using Gaussian reduction, determine te Gaussian properties of te following eye model. Dimensions are in mm. Te front of te eye is in air. Keep a copy of your answers for future use. n0 n1 n2 n3 t1 t2 r1 r2 r3 r t n ) A concave mirror wit a radius of curvature of 100 mm is used to image a real object 200 mm away from its vertex. Were is te image and wat is te magnification? Work tis problem using te sign conventions of class. Note: You must put te above information into te proper sign convention. Don t expect your customer to know about sign conventions.

3 Homework Set 5 all, ) A mirror of curvature C is immersed in an index n. Wat is its power, and wat are te front and rear focal lengts? Wic depend on n, and wic do not? 5-8) A Gregorian objective is an all reflective system tat uses two concave mirrors: Radius 2 Radius 1 Spacing WD ' Radius 1 = 100 mm Radius 2 = 40 mm Spacing = 75 mm a) Use Gaussian reduction to determine te focal lengt and working distance (WD) for tis system. b) You sould ave found tat tis system as a negative power and focal lengt, yet it forms a real image. Explain tis result. Consider te ray pat for te ray for an object at infinity and te definitions of te cardinal points.

4 Homework Set 5 all, ) Two tick lenses in air are combined into a single imaging system. Bot lenses are 25 mm tick and bot lenses ave a focal lengt of 100 mm, owever te index of te first lens is 1.6 and te index of te second lens is 1.5. Te vertex-to-vertex spacing of te lenses is 50 mm. Te principal plane locations for te two individual lenses wit respect to surface vertices are sown in te figure. All units are in mm. f 1 = 100 t 1 = 25 n 1 = 1.6 f 2 = 100 t 2 = 25 n 2 = 1.5 R 1 R P1 P P2 P NOTE: Only Gaussian metods may be used for tis problem. 50 a) Determine te Radii of Curvature of bot surfaces of te first lens (n 1 = 1.6). b) or te system comprised of te two tick lenses, determine: System ocal Lengt Location of te Rear Principal Plane of te system relative to te rear vertex of te second lens Back ocal Distance Location of te ront Principal Plane of te system relative to te front vertex of te first lens ront ocal Distance

5 Homework Set 5 all, ) A variety of imaging configurations are given, eac sowing an object. Determine te image location and sie by using a ray construction. Make use of te properties of te focal points. Bot real and virtual objects are sown. Indicate if te image is real or virtual. Concave Mirror: f f f

6 Homework Set 5 all, 2018 Convex Mirror: f f f

h = v h 2 = height of the object is negative for inverted image and positive for erect image. is always positive. Direction of incident light

h = v h 2 = height of the object is negative for inverted image and positive for erect image. is always positive. Direction of incident light 6. C a p t e r at G l a n c e Ligt related penomena can be studied wit mirrors and lenses. A mirror is a reflecting surface wile a lens is a transparent material. Mirrors are mainly of tree types : plane