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201 OPTI - Geometrical and Instrumental Optics Exam IV Monday, December 9, 2002 6:00 9:00 PM One 8 1/2 x 11 Crib Sheet and a calculator may be used. PLEASE USE SEPARATE SHEET OF PAPER FOR ANSWERS ONLY ON ONE SIDE AND CIRCLE ANSWERS The following items may be helpful: h = 6.625 x10 e = 16 x10 . 34 J s = 4.134 x10 15 eV s ( + ) = + = + div(F + G) = divF + divG curl(F + G) = curlF + curlG 19 8 Coul c = 3.0 x10 m / sec k = 138 x10 . 23 8 J/K 4 2 = 5.67 x10 W /K m F/m (F G) = (F )G + (G )F + F curlG + G curlF div F = divF + F div(F G) = G curlF F curlG divcurlF = 0 curl F = curlF + F curl(F G) = FdivG GdivF + ( G )F (F )G curlcurlF = graddivF F curl = 0 sF n da = v divFd x cF dl = x curlF n da s n da = v d x sF(G n)da = v F div G d x + v (G )Fd x sn F da = v curlF d x 3 3 3 3 3 2 o = 8.85 x10 o = 126 x10 . 12 6 H/m sin( A B) = sin A cos B cos A sin B cos( A B) = cos A cos B sin A sin B 2 cos A cos B = cos( A B) + cos( A + B) 2 sin A sin B = cos( A B) cos( A + B) 2 sin A cos B = sin( A + B) + sin( A B) 2 cos A sin B = sin( A + B) sin( A B) sin 2A = 2 sin A cos A cos 2A = 2 cos A 1 cos 2A = 1 2 sin A d = 587.6nm c = 656.3 nm F = 486.1nm nd = 1.5168 nc = 15143 . nF = 15224 . 2 2 1 Instructor: Dr. Eustace Dereniak OPTI 201R, F/2002 Exam IV December 9, 2002 OPL = c = h n= c Vn 1 n 1 l1 n ' n = n '+ n 2 4n ' n = 2 (n '+ n ) zs = y2 2R n ' n R s in I c = n' n V # nd 1 = nf nc P= n ' u ' = n u yP y 2 = y1 + t' ( n ' u ') n' t P1 P 2 n n' n = +P s' s P= n' n = f* f s '/ n ' s/n P = P1 + P 2 C1 + C 2 C1 C 2 R 2 + R1 R 2 R1 MT = S= 2 Mz = MT xx* = ff * S= d P2 = n n ' P * d P1 = n '' n' P HN = H * N* = f * +f z2 y2 =1 a 2 b2 z2 y2 + =1 a 2 b2 2 OPTI 201R, F/2002 Exam IV December 9, 2002 E.IV.1. The telephoto system is used with the design shown (all dimensions in mm). Refractive index of the glasses = 1.5: a) What is the effective focal length of this lens system? b) If the efl is assumed to be 20 mm, what is a design for a similar lens with an efl of 50 mm? R3= -30 R4= 30 Air Air 3 6 3 R1 = 15 R2 = -15 E.IV.2 If the FFOV is 20 for a Cooke Triplett Optical System an with entrance pupil diameter of 50 mm and the image space f/# is four [(F/4]. The object fills the full field of view. a) What is the image height? b) If the chief ray angle in image space is 0.1 radian, what is the diameter of the exit pupil? 3 OPTI 201R, F/2002 Exam IV December 9, 2002 E.IV.3. For the thin lens optical system below, (all dimensions in mm) with object at infinity. 5 7.5 7.5 3 CA = 12 CA = 8 CA = 10 CA = 15 ef l = 30 CA = 10 ef l = 15 a) What is the exit pupil diameter? b) What is the (F/#) of this system 4 OPTI 201R, F/2002 Exam IV December 9, 2002 E.IV.4. For the thin lens system, show with a 2 mm height object 20 mm in front of the lens: 7.5 20 Object ef l = 15 CA = 6 CA = 10 a) What is the numerical aperture in object space? b) What is the diameter transverse magnification of the image? c) What is the working F/# in image space? E.IV.5. Two thin lenses with 5 cm diameters have effective focal length of 10 and -40 cm but are cemented together to form a doublet. A 3 cm diameter aperture is placed at the back focal point (F*): a) What is the (F/# ) of this lens system? b) What is the full field of view? E.IV.6. For a thin lens with efl of 15 (efl = 15 mm) and the initial object distance of 35 mm from the lens, how much does the object need to be moved and in what direction to shift the image by -3mm? 5 OPTI 201R, F/2002 Exam IV December 9, 2002 Questions 7-10 pertain to the attached ray trace sheet with the marginal ray unscaled. All units are in millimeters. E.IV.7. Answer the following questions using the ray trace sheet attached. a) b) c) d) What is the efl of the system? What is the back focal distance (BFD)? What is the image height? What is the location of the back principle plane (H*) relative to the last surface (7)? E.IV.8. Answer the following questions using the ray trace sheet attached: a) Where is the entrance pupil located relative to the first surface (1) and what it its diameter? b) Which surface is the stop? c) What is the FFOV in degrees E.IV.9. Answer the following questions using the ray trace sheet attached. a) b) c) d) E.IV.10. What is the scale factor to get a full field of view of 30 ? What is the LaGrange Invariant? Which surfaces vignette with this new FFOV? Where is the back nodal point relative to H*? Answer the following questions using the ray trace sheet attached: a) Where is the exit pupil located relative to the last surface and what is its diameter? b) What is the (F/#) ? c) What is the entire system scale factor to get a ( F/# ) of ( F/2 ) ? 6

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