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Unformatted text preview: General Questions (18) Name Thick Lens ( 14) (Please Print)
Depth of Field (10) Polarized Light (18) Telescope (14) Waveguide (14) E C E 4500 Interference Filter ( 12) Second Examination April 25, 2001 Rules for exam: 1. may: cortex 10.
11.
12.
13. 14. 15. The time allowed is 60 minutes. The test will start at 9:00am (rather than at
9:05am) and end at 10:00am (rather than at 9:55am). Answer all questions. The value of each question is given in parentheses by the
question. There are a total of 100 points possible. All work must be shown for full credit. . Put your ﬁnal answers in the locations speciﬁed.
. You may use the six new single—sided 8 l/ " x 11" information sheets that you have prepared. In addition, you may use the six information sheets that you prepared for
the ﬁrst examination. Some physical constants are given below. You may use one "book of math tables." . You may use a "pocket calculator" that can be put in a normalsize pocket and requires no external electrical power. You may not use portable, laptop, or
notebook computers nor wireless or network connections.
You may not use any reference materials other than those listed above. Therefore,
you may not use the class notes, any other textbooks, homework problems, reprints
of papers, journals, prayer books, etc. There is to be no sharing of anything. If excess information is given in a question, ignore the unneeded information. If too little information is given in a question, assume the information needed and
clearly note this with your work. Any changes to the examination will be written on the chalk board. Check the
chalk board periodically during the examination. Any acts of dishonesty will be referred to the Dean of Students without prior
discussion. The ofﬁcial written Institute procedures on academic honesty (entitled
"Maintaining Academic Honesty" and available from the Dean of Students Ofﬁce)
will be followed in all cases. Have a happy exam! c = 2.99792458x108meter/sec General Optical Engineering Questions 1. Given a lens of focal length f, an object distance of s, and an image distance of 3’, write Newton’s thin lens equation as a function of f, s, and s’. 2. In an optical system exhibiting spherical aberration, this aberration can be reduced by (Circle all correct responses.)
a) decreasing the f—number b) increasing the f—number c) decreasing the ﬁeld of view
d) increasing the ﬁeld of View e) none of the above 3. Of the aberrations coma and astigmatism, which is more important to be corrected in a telescope objective? (Circle one.)
a) coma b) astigmatism c) none of the above 4. In the visible part of spectrum, losses in fused silica optical ﬁbers are primarily due to (Circle one.) a) Mie scattering b) Rayleigh scattering
c) none of the above 5. Compared to a multi—mode optical ﬁber, a singlemode optical ﬁber has (Circle all correct responses.) 3.) small numerical aperture
b) large numerical aperture
c) small core diameter d) large core diameter e) more dispersion f) less dispersion g) none of the above 6. If a slit of width a diffracts light whose wavelength is long compared to a, the diffrac— tion is called (Circle all correct responses.)
a) Fraunhofer diffraction b) Fresnel diffraction c) Bragg diffraction d) Kirchhoff diffraction
e) none of the above Thick Lens Imaging An object is placed to the left of the lens shown in the diagram below. All dimen— sions given are in mm. An image is formed that is 25% of the size of the object (mea sured transversely to the axis of the optical system). 63.5 38.2 Calculate, showing all work, the distance of the object from the leftmost glass
surface. Calculate, showing all work, the distance of the image from the right—most glass surface. Express your answers in mm accurately to within :l:0.1 mm. Put your answers in the spaces provided. Distance of object from left—most glass = mm Distance of image from right—most glass 2 mm Depth of Field A camera lens has a focal length of 100 mm and a minimum f—number of 2 (max
imum aperture) and a maximum fnumber of 22 (minimum aperture). It is used to im
age an object that is 2 m away. An f—number of 4 is used together with a shutter time
of 1/60 sec. It is desired to double the depth of ﬁeld in the image and simultaneously to
keep the overall exposure energy the same. Complete the following sentences to describe how to accomplish this.
The new f—number should be The new shutter time should be sec. Production of Polarized Light A randomly linearly polarized argon laser of freespace wavelength 488 nm (blue)
has an output power of 250 milliwatts. It is desired to produce linearly polarized light
from this beam. A quartz ﬂat is the only item of optics available and it is to be used as
shown in the drawing below to obtain linearly polarized light. At this wavelength, the quartz has a refractive index of 1.463. The laser and the quartz ﬂat are in air. R 1) Calculate, showing all work, the required angle ﬂ to produce linearly polarized light. Express your angle in degrees accurately to within i0.001°. Put your answer in the
space provided. 2) Indicate which beam is linearly polarized. R T (circle one) 3) Calculate, showing all work, the power in the linearly polarized beam. Express your power in milliwatts accurately to within four signiﬁcant ﬁgures. ﬂz—‘a———O Power in linearly polarized beam 2 milliwatts Catadioptric Telescope A 3.5 inch diameter, 1300 mm focal length, f / 14.4 Questar brand Maksutov cata
dioptric telescope is used with a 12 mm focal length Erfle wideﬁeld eyepiece to view dis tant objects under room lighting conditions. Calculate, showing all work, the angular magniﬁcation obtained with this conﬁg
uration. Express your answer accurately to three signiﬁcant ﬁgures. Calculate, showing
all work, the minimum angle (measured from the telescope to the distant object) that
can be resolved with this conﬁguration. Express your answer in degrees accurately to three signiﬁcant ﬁgures. Put your answers in the spaces provided. Angular magniﬁcation 2 Minimum angle resolved 2 Slab Waveguide A slab waveguide consists of a glass ﬁlm of 5 pm thickness with a refractive index
of 1.515. This ﬁlm is surrounded by a substrate and cover both with a refractive index
of 1.500. Light of freespace wavelength 1.00 pm is launched into the waveguide. The po—
larization of the light is such that it excites TE modes in the waveguide. By solving the
dispersion equation (using program SLWG), the TE modes are found to have character istics be as listed below. For a freespace wavelength of 1.000 mm TEO, 6 = 87.103493°, N = 1.513064, 6 = 9.506864um—1
TEl, 6 = 84.313614°, N = 1.507545, 6 = 9.472183/rm‘1
TE2, 6 = 82.031273°, N = 1.500371, [3 = 9.427108um_1
For a freespace wavelength of 0.995 ,um TEO, 6 = 87.114479°, N = 1.513079, [3 = 9.554729pm‘1
TEl, 6 = 84.333702°, N = 1.507597, 6 = 9.520114,um_1
TEg, 6 = 82.045410°, N = 1.500423, 6 : 9.474808;rm_1
For a freespace wavelength of 1.005 pm TE), 6 : 87.092537°, N = 1.513050, 6 = 9.459475um"1
TEl, 6 = 84.293602°, N = 1.507492, 6 = 9.42473011771—1
TE2, 6 = 82.017838°, N = 1.500322, 6 = 9.379900,um"1 For the lowestorder TE mode, calculate, showing all work, the phase velocity and the
group velocity. Give the velocity in m/ sec. Express your answers accurately to within ﬁve signiﬁcant ﬁgures. Put your ﬁnal answers in the spaces provided below. Phase velocity = m / sec Group velocity = m / sec Interference Filter One “half wavelength” thick interference ﬁlter is speciﬁed to pass 510nm wave
length light at normal incidence. Another is speciﬁed to pass 520nm wavelength light at
normal incidence. By rotating the angle of incidence of one of these ﬁlters it is desired to
pass only 514.5 nm green light from an argon laser as shown in the ﬁgure. The one “half
wavelength” thick layers have a refractive index of 1.400. The surrounding regions have a refractive index of 1.500. Specify which ﬁlter should be used. Calculate, showing all work, the required an
gular rotation a in degrees that is required. Express your answer accurately to within :i:0.01°. Put your answer in the space provided. The ﬁlter to be used is 510 nm ﬁlter 520nm ﬁlter Circle one. General Optical Engineering Questions
1. Newton’s thin lens equation is (s  f ) (3/ — f) = f2. 2. In an optical system exhibiting spherical aberration, this aberration can be reduced by
b) increasing the ﬁnumber 3. Of the aberrations coma and astigmatism, which is more important to be corrected in a telescope objective?
a) coma 4. In the visible part of spectrum, losses in fused silica optical ﬁbers are primarily due to
b) Rayleigh scattering 5. Compared to a multimode optical ﬁber, a singlemode optical ﬁber has a) small numerical aperture
c) small core diameter
f) less dispersion 6. If a slit of width a diffracts light whose wavelength is long compared to a, the diffrac tion is called (Circle all correct responses.)
a) Fi‘aunhofer diffraction Thick Lens Imaging . Real image, m < 0 Linear magniﬁcation, m ll —o.25 = —1/4 Focal length, f = 20.4 mm
Object distance
1
,s = (1 — E)f = 5f = 5(20.4mm) 2 102mm
Distance of object from left—most glass = 102 — (63.5 + 38.2 — 44 — 20.4) = 64.7mm Image distance I s = —m3 = —(1/4) 102mm = 25.5mm Distance of image from rightmost glass = 25.5 + (38.2 — 20.4) = 43.3 mm Depth of Field
The new fnumber should be 8. The new shutter time should be 1 / 15 sec. Production of Polarized Light Incidence should be at the Brewster angle 91 = tan'1(n2/n1) tan—1(1.463) = = ,6 The angle of refraction is
02 = (nl/n2)sin01 = 34.35366°
The fraction of the TE amplitude reﬂected is : n100361—n200302 : _0.36313
Ei TE n1 cos 61 + 712 cos 62 The fraction of the TE power reﬂected is E 2
(mm = = 0.131865 The fraction of the total power reﬂected is (Pr)polam'zed = PTotal (PT)TE/2 = (250 771W) 0.065933 = 16.483 mW Catadioptric Telescope D = 35inch f0 2 1300mm f8 2 12mm M = fo/fe = W = 108.3X
A 9min = 1.221)— Use A = 0.5 pm
D = 3.5 in (25.4 mm/in) (1000 pm) = 88, 900 ,um 6mm 26.86 X 10‘6rad (180°/7rrad) = 3.93 X 10‘4 degrees Slab Waveguide h 2 5pm nf = 1.515 ns = nc = 1.500 A = 1.00pm The lowestorder TE mode is T E0 and it is characterized by 0 = 87.103493°, N = 1.513064, 6 = 9.506864pm"1.
vph = $0 = 0.6609100 W = 1.981359 x 108m/sec The group velocity dw d 27rc 27rc dA 27m AA “ m = 2173(7): ‘VW “ —7\7A—ﬂ
/\ = 1.005um, ﬂ = 9.459475pm‘1.
A = 0.995pm, [3 = 9.554729pm‘1.
and so
119? = 065962430 1.977527 X 108 m/sec. Interference Filter Use the 520 nm wavelength ﬁlter and tune it to the shorter wavelength of 514.5 nm. The tuning characteristic is
2 n d cos ,8 = m A For one half wavelength ﬁlters at normal incidence
2nd = A and so 2nd :2 520nm For tuning to 514.5 nm 14.
c033 = ————5 5nm and so ﬂ = 8.3407°
520nm Parallel. glass plates do not affect the ray direction in air. Thus from Snell’s law 1.03ina = 1.4sinﬁ and so a = 11.7172°. ...
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 Spring '08
 Gaylord
 Diffraction, refractive index, linearly polarized light, freespace wavelength

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