# Tutorial 1 2019

```FUNDAMENTALS
OF
PHOTONICS
Mandoli, D. F., and W. R. Briggs. “Fiber Optics in Plants,” Scientific American (August
1984): 90.
Wehner, R. “Polarized Light Navigation by Insects,” Scientific American (July 1976): 106.
Weisskopf, Victor F. “How Light Interacts with Matter,” Lasers and Light, Readings from
Scientific American. W. H. Freeman and Company, 1969, pp 14-26.
Optical Manufacturing Companies
Optics and Optical Instruments Catalog. Edmund Scientific, Industrial Optics Division,
Barrington, New Jersey.
Melles-Griot Catalog. Melles-Griot Optical Systems, Rochester, New York, and MellesGriot Photonics Components, Irvine, California.
Problem Exercises
1. A HeNe laser in air emits light at
632.8 nanometers. The beam passes into a
glass substance of index 1.35. What are
the speed, wavelength, and frequency of
the laser light in the glass substance?
2. Use the principle of superposition to
sketch a picture of the resultant waveform
for the two waves shown at the right. Does
the resultant wave ever reach an amplitude
of 2A?
3. A Young’s double-slit interference
experiment is carried out with blue-green
argon laser light. The interference pattern
formed on a screen 3.3 m away contains the
first-order (m = 1) bright fringe 3.4 mm from
the center of the pattern. If the separation of
the double slits is 0.50 mm, what is the
wavelength of the argon laser light?
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4. Suppose you are asked to design a nonreflecting
surface for a Stealth aircraft. Your goal is to
select an antireflective polymer of index 1.6 and
of optimum thickness, so that radar waves of
wavelength λ = 3.5 cm will not be reflected from
the aircraft surface. What is the thinnest layer of
polymer you can apply to achieve your goal?
5. Solar cells made of silicon (Si) are designed
with nonreflecting, thin-film coatings such as
silicon monoxide (SiO) to minimize the
reflection of incident light. Determine the
thickness of the thinnest film of SiO that will
cause the least reflection of sunlight. Take the
average wavelength of sunlight to be near
550 nanometers.
6. An oil spill on an ocean coastline near you
produces an oil slick on the water for miles
around. After a few days, you take a
helicopter ride out over the water and
notice—with the help of a handheld
spectrometer—that the oil slick produces a
first-order maximum of reflected light of
wavelength 550 nanometers. What is the
thickness of the oil slick at that time? Assume
the oil has n = 1.25 and saltwater has
n = 1.34.
7. A laser beam of unknown wavelength is incident on a single slit of width 0.25 mm and
forms a Fraunhofer diffraction pattern on a screen 2.0 m away. The width of the central
bright fringe is measured to be about 7 mm. What is the wavelength of the laser light?
What might the laser be?
8. A thin layer of liquid (methylene iodide) is
sandwiched between two glass microscope slides,
as shown in the accompanying sketch. Light of
wavelength λ = 550 nm is incident on the glassliquid interface. The liquid has an index of
refraction of n = 1.76. (a) Is there an automatic
phase shift of λ/2 for the light reflected at the top face of the liquid film? (b) Is there an
automatic phase shift of λ/2 for the light reflected at the bottom of the film? (c) What is
the minimum thickness of liquid film required if the light incident perpendicularly on the
sandwich is to be strongly reflected?
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9. Nearly plane waves of C02 laser light of wavelength λ = 10.6 µm emerge from a circular
aperture 10 cm in diameter. If the C02 laser light is to be examined on a target in the far
field, about how far from the aperture should this examination take place?
10. Refer to Figure 4-20, which shows a Fraunhofer diffraction pattern for a circular aperture.
If the aperture is of diameter 150 µm and a helium-cadmium laser of wavelength
λ = 442 nm is used to illuminate the aperture, determine (a) an approximate far-field
distance from aperture to screen for a Fraunhofer pattern, (b) the half-angle beam
divergence of the laser beam in the far field, and (c) the radius of the airy disk on the
screen.
11. If one were to send a laser beam of wavelength 694 nm through a telescope aperture of
diameter 2.5 meters on toward the moon, 3.84 × 105 km away, what would be the
diameter of the laser beam when it hit the moon’s surface?
12. What is the angular separation in second order between light of wavelength 400 nm and
700 nm when the light is incident normally (perpendicularly) on a diffraction grating of
5000 grooves/cm?
13. Vertically polarized light of intensity I0 is
incident on a polarizer whose TA makes an
angle of 30° with the vertical. The light then
passes through a second polarizer whose TA
makes an angle of 90° with the vertical, as
shown in the sketch. (a) What is the intensity
of the light, in terms of I0 , that passes through
the second polarizer? (b) What is its
orientation?
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14. A submarine floating on
the ocean (n = 1.34)
transmits a message to a
cliff located at the
coastline. The submarine’s
antenna extends 5.5 m
above the ocean surface.
(a) If the transmitted
signal is completely
polarized by reflection
from the ocean surface,
how far must the
submarine’s antenna be
from the coastline?
(b) Relative to the ocean
surface, what is the
direction of polarization of
the polarized signal?
15. Figure 4-30 shows the two Brewster
windows tilted toward one another, each
at the appropriate angle with the
horizontal. See sketch (a). What would be
gained or lost by having the windows
parallel to each other, as in sketch (b)?
Hint: Use your knowledge of Snell’s law
to draw a center ray completely through
both windows from M1 to M2. Use
Figure 4-31 to help with details at each
window. What happens to the center ray
for each sketch?
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16.
White light contains all wavelengths from deep blue at 400 nm to deep red at 700 nm. A
narrow beam of collimated white light is sent through a prism of apex angle 20° as shown.
The prism is made of light flint glass whose refractive index at 400 nm is 1.60 and at 700 nm
is 1.565. What is the angular spread between the red and blue light at the minimum angle of
deviation for each?
17.
What is the light cone acceptance angle for an optical fiber of diameter 100 µ, located in air,
having a plastic core of index 1.49 and a plastic cladding of index 1.39? Make a sketch of the
fiber, showing a limiting ray along the surface of the acceptance cone entering the fiber and
refracting appropriately.
18.
A laser beam is incident on the end face of a cylindrical rod of material as shown in the
sketch. The refractive index of the rod is 1.49. How many internal reflections does the laser
beam experience before it exits the rod?
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