WAVE OPTICS AND OPTICAL INSTRUMENTS

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WAVE OPTICS AND OPTICAL INSTRUMENTS
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• Understanding how these rainbows are made and how
  certain scientific intruments can determine
  wavelength is the domain of wave optics.
• Light can able viewed as either a particle or a
  wave.
• The three primary topics we examine are
  interference, diffraction and polarization.

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The Interference of Light

• Two waves could add together either
  constructively or destructively
• In constructive interference- the amplitude of
  the resultant wave is greater than that of
  independent waves
• In destructive interference- the resultant
  amplitude is less than that of either individual
  waves
• Conditions for interference
• 1. The sources must be coherent, which means the
  waves they emit must maintain a constant phase
  with respect to each other
• 2. The waves must have identical wavelengths
  (monochromatic)

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Youngs Double-Slit Experiment

• The light from the two slits produces a visible
  pattern on screen consisting of a series of
  bright and dark parallel bands called fringes

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• The light intensity on the screen at P is the
  result of light from both slits
• A light from the lower slit, travels further then
  the light from the upper slit, the path
  difference
• d(s) r2-r1 d sin ?

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• Condition for constructive interference (for
  bright fringes) dd sin ?bright m?
• Condition for destructive interference (for dark
  fringes) dd sin ?dark (m ½)?
• m0, 1, 2. . . order number

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• m 0, the first bright fringe at ?bright0 is
  called zeroth-order maximum
• m1 is called first-order maximum
• m0, the path difference d?/2 condition of
  location of the first dark fringe on either side
  of the central (bright maximum)
• m1 , d3?/2 condition for the second dark
  fringe on either side
• Position of the bright fringes
• ybright(?L /d) m
• Position of the dark fringes
• ydark(?L /d)(m½)
• m 0, 1, 2,

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Interference in thin films
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• 1. An electromagnetic wave traveling from a
  medium of index of refraction n1 toward a medium
  of refraction n2 undergoes a 180o phase change on
  reflection when n2gtn1, there is no phase change
  in the reflected wave if n2ltn1
• The wavelength of light ?n in a medium with index
  of refraction n is ?n ?/n
• where ? is the wavelength of light in vacuum

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• If 2t ?n /2, then rays 1 and 2 recombine in
  phase and constructive interference results
• Condition for constructive interference in thin
  films
• 2t(m½) ?n
• m 0, 1, 2,
• 2nt(m½) ? (1)

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• The general equation for destructoive
  interference in thin films is
• 2 n t m ? (2)
• m 0, 1, 2,

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• Equation (1) and (2) for constructive and
  destructive interference are valid when there is
  only one phase reversal (when the media above and
  below the thin film both have indices of
  refraction greater (respectively less) than the
  film
• If the film is placed between two different
  media, one of lower refractive index than the
  film and one of higher refractive index, equation
  (1) and (2) are reversed
• 2nt(m½) ? destructive
• 2 n t m ? - constructive

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Diffraction

• Diffraction the spreading out of light from its
  initial line of travel

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Single Slit Diffraction
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• sin ? darkm ?/d
• m 1, 2, 3,
• This equation gives the values of ? for which the
  diffraction pattern has zero intensity, where a
  dark fringe form

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The Diffraction Grating

• The condition of maxima in the interference
  pattern at the angle ? is
• d sin ?bright m?
• m0, 1, 2,
• Diffraction grating is use in CD tracking

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Polarization of Light Waves
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Polarizing by Reflection

• ?p90o?2180o
• ?290o-?p sin?2sin(90o-?p)cos?p
• nsin?1/sin?2sin?p/sin?2sin?p/cos?ptan?p
  -Brewsters Law
• ?p?B- Brewsters angle

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Optical instruments

• The Eye
• The Power P of a lens in diopters is
• P1/f
• Ex
• f20cm, P5
• f-40cm, P -2.5

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• The simple magnifier
• Angular magnification mß/a
• tanah/25 tanßh/p
• mmaxß/a(h/p)/(h/25)125/f
• If q8, than pf, m25/f

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• The Compound Microscope
• The overall magnification of the compound
  microscope mM1 me-L/fo(25cm/fe)
• M1 lateral magnification (-q1/p1-L/fo)
• me- angular magnification(25cm/fe)of the
  eyepiece for an object (corresponding to the
  image at q1)placed at the focal point

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• The Telescope
• m a/ß (h/fe)/(h/fo)fo/fe

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