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Exam 3 – PHYS 355 - OPTICS
Mendes, Fall 2008, Dec 15, 2008
Start time: 8:00 a.m.,
End time: 10:30 am
Open textbook, notes, homeworks, and quizzes
Calculators allowed; no other electronic device allowed
Where it is appropriate, make sure to provide physical units to your numerical answer
1/7
(10 points)
1) Sunlight is incident on an optical filter that transmits light with a center wavelength of
500 nm and a bandwidth of 1.2 nm. Determine the frequency bandwidth and the
coherence length of the transmitted light.
2/7
(10 points)
2) Here’s a way to measure the optical wavelength of a light beam by measuring a
physical distance: Monochromatic light illuminates a Michelson interferometer. One of
its mirrors (mirror 1 in Figure below) is moved by 25 µm, and it is observed that 89
fringe-pairs, bright and dark, pass by the detector during this process. Determine the
wavelength of the light beam.
Mirror 2
Beam
Splitter
Mirror 1
Light source
Detector
25 µm
3/7
(30 points)
3) A He-Cd laser (442 nm) is incident on a screen containing two very narrow horizontal
slits separated by 180 µm. A fringe pattern appears on a screen held 1.2 m away.
a) What is the distance from the central axis to the first zero of the light intensity?
b) How far in mm from the central axis is the fourth bright fringe?
c) Now consider that a 1-mm glass slide (n = 1.52) is inserted behind the top slit. How
much will the fringe pattern move along the y-axis? Is it going to move up or down?
y
442 nm
180 µm
1.2 m
4/7
(10 points)
4) An electromagnetic plane wave is incident on an opaque screen that contains a single
and long horizontal slit that is 20 cm wide in the vertical direction. As shown in the
Figure below, a detector, far away from the screen, but moving parallel to it, locates the
first minimum of light intensity at an angle of 34° above the central axis. What are the
wavelength and frequency of this electromagnetic radiation?
detector
20 cm
34°
5/7
(20 points)
5) Consider that the lenses in the human eyes form an imaging system where optical
aberrations are almost negligible. The pupil diameter in human eyes is typically around 2
mm under bright illumination. Under those conditions:
a) What is the smallest angular width that is possible to resolve with the human eyes? For
this calculation, consider the optical wavelength that our eyes are most sensitive (green,
550 nm)
b) From the angular width calculated above, determine the smallest details we can expect
to resolve for an object located at 25 cm in front of our eyes, which is typically the
closest distance that our eyes can still accommodate. State your answer in micrometers,
µm. Make sure your answer is reasonable to you: don’t tell me that you can see a
hydrogen atom or that the smallest object you can resolve is a tennis ball.
6/7
(20 points)
6) White light plane waves are incident normally (in other words, the angle of incidence
is 0°, or more precisely, the angle between the incident k-vector and the normal to the
sample surface is 0°) on a transmission diffraction grating. If the diffraction grating has
1 cm
:
2,000 lines per cm, we then know that the period of the grating is a =
2, 000
a) At what angle from the central axis will green light (550 nm) emerge in the first-order
spectrum (m = 1)?
b) Consider that 4,000 grating lines (N = 4,000) are used to disperse the incident light
beam (for example, either the light beam width or the grating region is limited to 2-cm
wide, whichever is the smallest). At about 550 nm, what is the angular width, Δθ , of the
first-order spectrum (m =1)?
c) What is the dispersion,
dθ
, of the first-order spectrum (m = 1) at about 550 nm?
dλ
d) Under the conditions considered above, what is the smallest wavelength range, Δλ ,
one can expect to resolve (to separate) at the first-order spectrum (m = 1) around the 550nm wavelength?
a
7/7