Download Fall 2010

OPSE FINAL EXAM – Fall 2007
NAME_____________________________
OPEN BOOK. CLOSED NOTES.
YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE
GIVEN ZERO CREDIT.
ALL NUMERICAL ANSERS MUST HAVE UNITS INDICATED. (Except dimensionless units
like index of refraction).
Problem 1:
(a) How many “yellow” light wavelengths (λ=580nm) will fit into a distance in space equal to
the thickness of 1mm?
(b) How far will the same number of microwaves of frequency 94GHZ extend?
Problem 3: A laser beam impinges on an air-liquid interface at an angle of 50 degrees. The
refracted ray is observed to be transmitted at 35 degrees what is the refractive index of the
liquid?
Problem 5: An object is 30cm from a f = -15cm negative lens shown in the figure below,
(a)
On the diagram DRAW a ray diagram locating the image.
(b)
(c)
(d)
Calculate the location of the image relative to the lens.
Is the image to the left or to the right or the lens?
What is the magnification of the image?
Problem 6: An object is 30cm from a f = -15cm negative lens as in the previous problem (you
can use the results of Problem 5 here). In addition a f=10cm lens is added to the optical system as
shown in the figure below. The distance between the two lenses is 20cm.
Page 1 of 5
OPSE FINAL EXAM – Fall 2007
(a)
(b)
(c)
NAME_____________________________
Calculate the location of the FINAL image relative to the f=10cm lens.
Is the image to the left or to the right or the f=10cm lens?
What is the TOTAL magnification of the image after passing through both lenses?
Problem 7: Referring to Figure 4, which is the SHORTEST focal length lens that will optimally
focus the light into the fiber? The fiber has a Numerical Aperture of 0.3. The initial diameter D
of the laser beam is 5mm.
Figure 1: Focusing a laser beam into an optical fiber.
Problem 8: Two light waves are overlapping in space and time. The equation for one of the
waves is
(1)
E1 = Eo1 sin(ωt ) .
Which of the following waves is OUT OF PHASE with respect to E1? [NOTE: in this problem
OUT OF PHASE means that if the two waves where overlapped, the Principle of Superposition
would indicate that the TOTAL wave would be zero.] CIRCLE YOUR ANSWER
E2 Eo 2 cos(ωt +=
π ) E2 Eo 2 sin(ωt + π )
E2 = Eo 2 cos(ωt )=
E2 Eo 2 sin(ωt + π / 4) =
Problem 9: For the figure below, Wave A and Wave B start out in-phase from the start line.
Wave A passes through a plastic box filled with a clear liquid. The refractive index of the liquid
is 1.8. The index of refraction of the plastic is 1.52. The thickness of the plastic wall is 2mm. The
inner dimension of the box (in which the liquid is present) is 7.5cm.
(a)
Determine the optical path difference (in meters) at the finish line for the two
waves assuming that the wavelength is 633nm.
(b)
Based on your answer to (a), what is the relative phase difference (in radians) of
the two waves at the finish line?
Page 2 of 5
OPSE FINAL EXAM – Fall 2007
NAME_____________________________
Problem 11: Red plane waves from a helium-neon laser (wavelength of 632.8nm) in air impinge
on two parallel slits in an opaque screen. A fringe pattern forms on a distant wall, and you see
the 2nd bright band 0.5 degrees above the central axis. Kindly calculate the separation between
the slits.
Problem 12: A thin film of grease (n=1.2) spread on a flat glass plate (n=1.5) and illuminated
with white light shows a color pattern in reflection. If a region of the film reflects only red light
(600nm) strongly, how thick is it?
Problem 13: Suppose that we have a laser emitting a diffraction-limited 2-mm diameter beam
with a wavelength 514nm. If the laser is located on the roof of the parking deck at NJIT, how big
a light spot would be produced on a wall of a tall building in New York City which is 13km
away?
Problem 14: A 400nm harmonic EM-wave whose electric field is in the z-direction at t=0 is
traveling in the y direction in vacuum.
(a) What is the frequency (in hertz) of the wave?
(b) Determine ω and k for this wave.
Page 3 of 5
OPSE FINAL EXAM – Fall 2007
NAME_____________________________
(c) If the electric field amplitude is 250V/m what is the amplitude of the magnetic field?
(d) In what direction does the magnetic field point at t=0?
Problem 16: A beam of linearly polarized light incident in air on a glass (n=1.5) interface at 50
degrees is partially reflected. The electric field of in incident beam of light is polarized
perpendicular to the plane of incidence. Kindly compute the reflectance.
Problem 17: Do ONE of the FOLLOWING TWO PROBLEMS (Problems A or B):
Problem A: Using the following data (no=1.7 and ne=1.5 at 514nm) for the very rare NJITium
crystal, compute the MINIMUM thickness of NJITium required for a ½ waveplate.
Problem B: Using the specific rotation of glucose (41.89 degrees for a 10cm path length in a
1g/100ml solution at a wavelength of 656nm), what would be the net angular rotation of a
linearly polarized laser beam (through a 5cm path length) for a solution of
(a) d-glucose: 4g/L mixed with a solution of l-glucose: 8g/L
(b) In what direction would the polarization rotate? EXPLAIN YOUR REASONING. YOU
MUST SPECIFY THE ROTATION RELATIVE TO THE LASER BEAM MOVING
AWAY FROM YOU.
Problem 21: A thin sheet of clear tissue (cornea of the eye) with an index of refraction of 1.33 is
inserted normally into one beam of a Michelson interferometer. Using a 589nm light source, the
fringe pattern is found to shift by 50 fringes. Determine the thickness of the tissue section.
Problem 22: Green light (514nm) passes through a block of material that is partially absorbing.
If 10% is transmitted through 5cm of material, Estimate (You can neglect reflection for your
calculation)
(a) the Absorption coefficient of the material (in units of cm-1).
(b) The corresponding imaginary index of fraction.
Page 4 of 5
OPSE FINAL EXAM – Fall 2007
NAME_____________________________
Problem 23: Using a block of transparent, unknown material, it is found that when the material
is immersed in water (n=1.33) a beam of light inside of the material is totally internally reflected
at the block-water interface at an angle of 60.0 degrees. What is the index of refraction of the
block?
Problem 24: You are flying in an airplane and observing out the window the headlights of cars
on a roadway. You are able to just distinguish the two individual headlights on the cars. Given
that the pupil diameter is 4mm and the headlights are 2m apart, estimate the distance from your
airplane to the car.
Page 5 of 5