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Unformatted text preview: (8) Optical Terminology
(14) Arrayed Waveguide Grating Router Name
(Please Print) (14) Fourier Transform Infrared Spectrometer
(16) Light Measurement (15) Total Internal Reﬂection (15) Paraxial Ray Approximation (18) Refraction at Convex Spherical Surface E C E 4500
First Examination
February 12, 2001 Rules for exam: 43!» UI 9°“? 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 1/2" x 11" information sheets that you have prepared.
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! h = 6.6260755 x10‘34joulesec
c = 2.99792458x108meter/sec Table 1 STANDARD LUMINOSITY DATA Wavelength Luminous eﬁicacy Wavelength Luminous eﬂicacy (8) Optical Terminology State in words the meaning of the acronyms listed below. Put your answers in the
spaces provided. DVD H DBR EDFA FWHM = (14) Arrayed Waveguide Grating Router An arrayed waveguide grating router is used as a wavelength demultiplexer. That
is, a series of wavelengths that are multiplexed together in a single ﬁber are separated
into individual waveguides by the arrayed waveguide grating router. The arrayed wave
guide output section from the combined channel waveguides of an arrayed waveguide
grating router is shown below. The output ends of the channel waveguides lie along a
circle of radius R as shown. This arrayed channel waveguide output may be well approx
imated as if it were a metallic curved reﬂection grating illuminated by a point source
from the center of curvature (indicated by the dot). Under this approximation, state quantitatively the locations of the individual fo—
cused wavelengths. This should be the locations where the output channel waveguides
are placed to receive the demultiplexed wavelengths. Do not use the paraxial ray ap
proximation. In addition to this statement, indicate these locations on the diagram. SLAB § WAVEGUIDE
:1
:l COUPUNG ARRAYED REG'ON CHANNEL
:I
WAVEGUIDES _—_:::_:I g (14) Fourier Transform Infrared Spectrometer A Fourier Transform Infrared (FTIR) spectrometer is based on a Michelson in
terferometer. An FTIR spectrometer is capable of determining the spectral content of a
light source. This is accomplished by scanning one of the mirrors of the Michelson inter—
ferometer and recording the output interferogram as a function of the optical path dif
ference between the two interfering beams. For the case of two narrow linewidth wave
lengths (represented by their wavenumbers, where wavenumber = 1 /wavelength) in the
source (upper left ﬁgure), the resulting interferogram is shown (at upper right). Zero
optical path difference is at the left edge of the graph. A Fourier transform relationship exists between the spectrum in wavenumber space and the interferogram in optical path
difference space. For the same FTIR instrument in a second case, the source is changed and now
consists of two narrow linewidth wavelengths (lower left ﬁgure) that are closer together
in wavelength (and wavenumber). Sketch the new resulting interferogram for this source
in the lower right ﬁgure. Put zero optical path difference at the left edge of the graph. INTENSITY
INTENSITY
<— INTENSITY
INTENSITY WAVENUMBER OPTICAL PATH DIFFERENCE Light Measurement Radiance An important quantity in light measurement is “radiance.” Using complete sen
tence(s), deﬁne what is meant by “radiance.” Give the mks units of “radiance.” Apparent Brightness Four light sources of freespace wavelengths 500nm, 520nm, 600 nm, and 650nm
each emit 2.0 milliwatts with the same beam divergence and beam geometry. Which
source appears brightest? Check the one correct answer below. 500 nm
520 nm
600 nm 650 nm Illuminance An illumination of 100 footcandles at a wavelength of 500nm corresponds to
which of the following irradiance values? Check the one correct answer. 2.935 x 10'4 watts/m2
3.16 x 10’3 watts/m2
0.455 watts/m2 4.90 watts /m2 (15) Total Internal Reﬂection The prism shown below is to be used in air as a totally internally reﬂecting prism. ' 45° 45° Calculate, showing all work, the range of values of the index of refraction, n, in
order for total internal reﬂection to occur for the normally incident ray shown. Express
the indices of refraction accurately to the nearest 0.0001. Put your ﬁnal answers in the
spaces provided below. (15) Paraxial Ray Approximation A thin prism of index of refraction n and apex angle <15 is used in air to deviate a
light beam. The apex angle 4) is small. The angle of incidence oz is small. Using the paraxial ray approximation, develop an expression for the angular de
viation 6 in radians for this case of small ¢ and small a. Put your ﬁnal answer in the
space provided. (18) Refraction at Convex Spherical Surface The interface between two lossless dielectric regions is a convex spherical surface
as shown in the diagram. The spherical surface has a radius of curvature of 50 mm. The
index of refraction of the lefthand region is 1.5. The index of refraction of the right
hand region is 1.0. An object is located on the axis of the optical system 200 mm to the
left of the spherical surface. Calculate, showing all work, the location of the image and the linear magniﬁca
tion. Express your answers accurately to four signiﬁcant ﬁgures. Specify whether the
image is left or right of the interface. Specify whether it is a real or virtual image. Put
your ﬁnal answers in the spaces provided. Using a distance between tick marks of 50 mm, draw on the above diagram, the
object, the parallel ray, the chief ray, the focal ray, and the image. Image distance from interface = mm
The image is to the (left) (right) of the interface. (Circle one.) Linear magniﬁcation = The image is (real) (virtual). (Circle one.) Optical Terminology DVD 2 Digital Versatile Disk or Digital Video Disk
DBR = Distributed Bragg Reﬂector EDFA = ErbiumDoped Fiber Ampliﬁer FWHM = Full Width at Half Maximum Arrayed Waveguide Grating Router Under the approximation as a metallic curved reﬂection grating illuminated by
a point source from the center of curvature, the arrayed channel waveguide outputs are
focused on the circumference of a Rowland circle. The diameter of the Rowland circle
is equal to the radius of curvature, R, of the curved grating. The center of the Rowland
circle is midway between the center of curvature and the center of the grating. Fourier Transform Infrared Spectrometer Two wavenurnbers (wavelengths) in a source constructively interfere when there
is zero optical path difference between them. However, they destructively interfere after
the optical path difference is great enough so that they are out of phase. For two wave lengths that are closer together, a greater optical path difference is required for them to
be out of phase. INTENSITY
INTENSITY
< INTENSITY
INTENSITY WAVENUMBER OPTICAL PATH DIFFERENCE Light Measurement Radiance Radiance is the radiant power output per unit solid angle per unit projected area.
The mks units of radiance are watt /steradianmeter2. Apparent Brightness
The 520nm light source appears brightest. Illuminance . _ 1001m/ft2 _ 2
Irradlance ‘ (O.323)(680lm/w)(12in/ft)2(25.4 x 10'3m/in)2 ’ 4'90 w/m Total Internal Reflection
nmm sin 61 = nmr sin 90°
nmin = l/sin 01 = 1/sin 45° 2 1.414214 nmax = 00 Paraxial Ray Approximation The deviation, 6, is given by
6 = a — ¢ + sin—1 {n sin[¢ — sin—1(sina/n)]}
In the paraxial ray approximation, 6=oz—¢+n(¢—a/n)
or 5=¢(n—1) Refraction at Convex Spherical Surface R = +50mm, m = 1.50, 712 = 1.00, s = 200mm an f1 = — = n2  721
R
f2 = L = —100mm
712 — n1
n1 n2 le—nl
s + 3’ _ R
R2 
8’ = m _ n _ m = —07.143 mm.
R s
7118, . . .
m = — = 0.4286 (uprlght vu‘tual Image) ...
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 Spring '08
 Gaylord
 Geometrical optics, paraxial ray approximation, optical path difference, Convex Spherical Surface

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