Examples

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Examples

• Wave Optics

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1- A double-slit experiment is set up using a
helium-neon laser ( ? 633 nm). Then a very thin
piece of glass ( n 1.50 ) is placed over one of
the slits. Afterward, the central point on the
screen is occupied by what had been the m 10
dark fringe. How thick is the glass?
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2- Light of wavelength 600 nm passes through a
double slit and is viewed on a screen 2.0 m
behind the slits. Each slit is 0.040 mm wide and
they are separated by 0.200 mm. How many bright
fringes are seen on the screen?
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• 3- Light consisting of two nearly equal
  wavelengths ? ?? and ?, where ?? ltlt ? , is
  incident on a diffraction grating. The slit
  separation of the grating is d.
• Show that the angular separation of these two
  wavelengths in the mth order is

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b. sodium atoms emit light at 589.0 nm and 589.6
nm. What are the first-order and second-order
angular separations ( in degrees) of these two
wavelengths for a 600 line/mm grating?
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4- The Figure shows two nearly overlapped
intensity peaks of the sort you might produce
with a diffraction grating . As a practical
matter, two peaks can just barely be resolved if
their spacing ?y equals the width w of each peak,
where w is measured at half of the peaks height.
Two peaks closer together than w will merge into
a single peak. We can use this idea to understand
the resolution of diffraction grating.

1. In small angle approximation, the position of the
   m1 peak of diffraction grating falls at the same
   location as the m 1 fringe of a double slit y1
   ?L/d. Suppose two wavelengths differing by ??
   pass through a grating at the same time. Find an
   expression for ?y, the separation of their
   first-order peaks.

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B. We noted that the widths of the bright fringes
are proportional to 1/N, where N is the number of
slits in the grating. Lets hypothesize that the
fringe width is w y1 / N. Show that this is
true for the double-slit pattern. Well then
assume it to be true as N increases.
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c. Use your results from parts a and b together
with the idea that ?ymin w to find an
expression for ??min, the minimum wavelength
separation ( in first order ) for which the
diffraction fringes can barely be resolved.
d. Ordinary hydrogen atoms emit red light with a
wavelength of 656.45 nm. In deuterium, which is a
heavy isotope of hydrogen, the wavelength is
656.27 nm. What is the minimum number of slits in
a diffraction grating that can barely resolve
these two wavelengths in the first-order
diffraction pattern?
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• 5. The Figure shows a plane wave approaching a
  diffraction grating at angle ?.
• Show that the angles ?m for constructive
  interference are given by the grating equation
• Angles are considered positive if they are above
  the horizontal line, negative if below it.

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b. The two first-order maxima, m 1 and m -1,
are no longer symmetrical about the center. Find
?1 and ?-1 for 500 nm light incident on a 600
line/mm grating at ? 30.