MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.710 Optics Solutions to Problem Set #4 Spring ' 09 Due Wednesday, April 1, 2009 Problem 1: Knocking down one dimension: the Screen Hamiltonian a) The main goal of this problem is to show how the 6 6 set of Hamiltoni
2.71 Optics
Problem Set 8 Solutions
1. (a) For a diffraction limited system the slopes of the OTF are constant. m
u=25mm-1
= 68.75% = 0.6875
1 x 1 + cos 2 2 1 1 1 ^ + Iin = (u) + u - 2 4 1 a ^ ^ Iout = Iin OTF = (u) + 2 4 1 x 1 + a cos 2 Iout (x ) = 2 1 a
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
2.710 Optics Solutions to Problem Set #7 Spring '09 Due Wednesday, Apr. 22, 2009
Problem 1: Zernicke phase mask For problem 1, general formulations for the 4f system are presented here. As shown in Fig. A in problem
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
2.71 Optics Solutions to Problem Set #6 Spring '09 Due Wednesday, Apr. 15, 2009
Problem 1: Grating with tilted plane wave illumination 1. a) In this problem, onedimensional geometry along the xaxis is considered. The
2.71 Optics 1. 2 k k | 1 | = | 2 | = 1 = 2 (sin 30 x + cos 30 z ) = 2 k ^ ^
Problem Set 5 Solutions
1 3 x+ ^ z ^ 2 2
2 = 2 (cos 45 x + sin 45 sin 30 y + sin 45 cos 30 z ) k ^ ^ ^ 2 2 6 2 = x+ ^ y+ ^ z ^ 2 4 4
Assuming |E1 | = |E2 | = 1,
i z) r 2 E1 (x
2.71 Quiz 2
50 min
8:058:55am EDT
8:058:55pm SST
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
2.71 Optics QUIZ 2 Spring '09 Monday, April 27th , 2009
1. Interference Two plane waves of wavelength are propagating on the xz plane such that their electric field
2.71 Optics
Quiz 1 Solutions
Spring `09
1. (a) Solution: Without correction, the focus is before the retina, leading to blurred vision:
With correction, the image forms (focused) on the retina:
1 1 1 1 1 1 50 - 45 5
+ = = - = = -fc + 15 50 45 -fc + 15 45
2.71 Quiz 1
50 min
8:058:55am EST
9:059:55pm SST
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
2.71 Optics QUIZ 1 Spring '09 Wednesday, March 9th , 2009
CL
EP EL
R
15
50
distances shown in mm (not to scale)
CL=corrective lens; EL=eye lens; EP=eye pupil; R=re
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.71 Optics Problem Set #8 Spring '09 Posted Wednesday, April 29, 2009 - Due Wednesday, May 6, 2009
1. In a diffractionlimited imaging system, the contrast is measured at spatial frequency 25mm-1 and it is found to be
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.71 Optics Problem Set #7 Spring '09 Posted Monday, Apr. 13, 2009 - Due Wednesday, Apr. 22, 2009
1. Zernicke phase mask. You are given an imaging system which consists of two thin transparencies T1, T2 and two thin l
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.71 Optics Problem Set #6 Spring '09 Posted Monday, Apr. 6, 2009 - Due Wednesday, Apr. 15, 2009
1. Grating with tilted plane wave illumination Consider a sinusoidal phase grating of the surface relief type with compl
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.71 Optics Problem Set #5 Spring '09 Posted Monday, March 30, 2009 - Due Wednesday, April 8, 2009
1. Two plane waves of the same wavelength are propagating along the directions of wave vectors k1 , k2 as shown in the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
2.71 Optics Problem Set #4 Spring '09 Posted March 16, 2009 - Due Wednesday, April 1, 2009
1. Particle in quadratic and linear potential Consider a particle whose Hamil tonian is given by p2 + p2 1 2 x y + kqx + mgqx
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.71 Optics Problem Set #3 Spring '09 Posted Feb. 23, 2009 - Due Wednesday, March 4, 2009
1. Wanda's world Your goldfish Wanda happens to be situated at the center of her spherical waterworld. At the same time, your f
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.71 Optics Problem Set #2 Spring '09 Posted Feb. 17, 2009 - Due Wednesday, Feb. 25, 2009
1. Wiper speed control Design an optical system which can detect the amount of water present on a car's windshield (see the sch
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.71 Optics Problem Set #1 Spring '09 Posted Feb. 9, 2009 - Due Wednesday, Feb. 18, 2009
1. Spherical waves and energy conservation We mentioned in class that the amplitude of the electric field describing a plane wav
2.71 Optics
Final Exam Solutions
Spring `09
1. Consider the following system.
(a) If we position an on-axis point source at the center of the object plane (front focal plane of L1), a collimated ray bundle will emerge to the right of L1 and its diameter i
2.71 Final examination
3 hours (9am12 noon)
Total pages: 7 (seven)
PLEASE DO NOT TURN OVER
UNTIL EXAM STARTS
Name:
PLEASE RETURN THIS BOOKLET WITH YOUR SOLUTION SHEET(S)
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
2.71 Optics FINAL EXAMINATION Spring '09 Tu
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Practice Exam 3 - Solutions
Spring `09
1. A thin bi-convex lens with the same absolute curvature on both faces is used in the two imaging systems shown below. In the first, both object and image are in air, whereas in the second the obje
2.71/2.710 Optics
Practice Exam 3
Spring `09
1. A thin bi-convex lens with the same absolute curvature on both faces is used in the two imaging systems shown below. In the first, both object and image are in air, whereas in the second the object is "immer
2.71/2.710 Optics
Practice Exam 2 - Solutions
Spring `09
1. What is the Fraunhofer diffraction pattern of a 1-D slit of size a?
Slit description (1D): Fourier transform of slit: Diffracted far field: Fraunhofer diffraction pattern (intensity):
a F(u) = as
2.71/2.710 Optics
Practice Exam 2
Spring `09
1. What is the Fraunhofer diffraction pattern of a 1-D slit of size a? 2. What is the Fraunhofer diffraction pattern of this sinusoidal amplitude grating, where is the grating period? x 1 f (x) = 1 + cos 2 2 3.
2.71/2.710 Optics
Practice Exam 1 - Solutions
Spring `09
1. Consider the two-lens system shown below. Lens L1 has focal length f , and lens L2 has focal length f /2.
(a) Set the separation distance d such that the Effective Focal Length (EFL) of the combi
2.71/2.710 Optics
Practice Exam 1
Spring `09
1. Consider the two-lens system shown below. Lens L1 has focal length f , and lens L2 has focal length f /2. (a) Set the separation distance d such that the Effective Focal Length (EFL) of the combination equal
2.710 Optics
Problem Set 8 Solutions
1. (a) For a diffraction limited system the slopes of the OTF are constant. m
u=25mm-1
= 68.75% = 0.6875
1 x 1 + cos 2 2 1 1 1 ^ + Iin = (u) + u - 2 4 1 a ^ ^ Iout = Iin OTF = (u) + 2 4 1 x 1 + a cos 2 Iout (x ) = 2 1