Lecture 4: Interference and diffraction of light (I)

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Lecture 4 Interference and diffraction of light
(I)
Youngs two slit experiment (YF 35.2)

• To observe interference of light one needs to
  set-up two independent, coherent, monochromatic
  (same frequency) light sources.
• Coherent light sources are difficult to make
  since light is emitted by the random agitation of
  atoms (we will see later on that lasers can be
  sources of coherent light).
• To achieve two coherent sources of light, we can
  use a common source and split it such that the
  light emerges from two secondary sources, so the
  relative phase between them is always the same.

S1
S0
S2
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Youngs two slit experiment (Cont.)

• Young (1800) set up an experiment to demonstrate
  the wave nature of light.
• A monochromatic beam of light is incident on a
  single slit S0. This acts as a source of
  wavefronts onto two slits S1 and S2.
• The coherent waves interfere with each other
  forming a pattern of light and dark bands on a
  screen some distance from the two slits.

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Geometry of Youngs two slit experiment

• The triangle S1S2Q means that S1Q d sin q
• If the screen is at a distance R which is much
  larger than the separation d of the two slits (R
  could be a few metres and d a few millimetres)
  then r1 and r2 are nearly parallel to each other
  and q is small

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• Constructive interference bright fringes
• Destructive interference dark fringes

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• Example 35-1 (YF)
• In a two slit interference experiment, the slits
  are 0.20 mm apart, and the screen at a distance
  of 1.0 m. The third bright fringe (not counting
  the central bright fringe) is displaced by 7.5
  mm. Find the wavelength of light used.
• Third fringe m3, R1.0 m, d0.2 mm, Rgtgtd

Another possibility m -3 ym -7.5 mm
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• Example L61 (Example book)
• Light from a source containing 2 wavelengths of
  567 nm and 486 nm illuminates a double slit
  arrangement with d1.0 mm and R1.50 m. At what
  distance from the central fringe on the screen
  will a bright fringe from one interference
  pattern coincide with the bright fringe from the
  other interference pattern.
• Bright fringes

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Intensity in interference patterns (YF, 35.3)

• The waves associated with light are called
  electromagnetic waves. Unlike the other waves we
  have encountered, they dont need a medium to
  propagate. They can propagate in vacuum.
• In the two slit experiment we have an electric
  field coming from S1
• and another coming from S2
• (frequency and amplitude are the same since the
  two sources are coherent).
• Principle of superposition
• P.1463 YF
• Since
  Trigonometric
  functions

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• Since
• Then

• Phase difference between two waves
• r2-r1 is called the path difference.
• New wave

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• New wave has angular frequency w and wave
  number k but the new amplitude is
• with

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• Intensity of light is the average power per unit
  area (energy per unit area per unit time)
• The intensity of light is proportional to the
  square of the amplitude of the electric field

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Lloyds mirror

• Lloyds mirror is just like Youngs two slit
  experiment but with only one source of light and
  a mirror used to create a second virtual source
  of light.

• The source interferes with its own image in the
  mirror.

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• There is a phase change of p radians due to the
  reflection of the mirror (equivalent to a path
  difference of l/2).
• The constructive and destructive conditions are
  reversed with respect to Youngs experiment and
  there is a dark fringe next to the mirror.
• Constructive interference bright fringes
• Destructive interference dark fringes