last dance Chapter 26 – diffraction – part ii

1
last danceChapter 26 diffraction part ii

• InstructorCourse

2
Whats Going On??

• Today Finish (?) Diffraction
• Tuesday Nothing No room is available for a
  review session.
• Wednesday Examination 4 Material that we
  covered in chapters 24, 25 and 26.
• Friday Complete semesters material. Start
  Review
• Next Monday Wrap-up and overview of the course.
• December 12 - SATURDAY 900AM Psychology
  Building Room PSY 108. BE THERE!!!
• Last Mastering Physics Assignment Posted. No
  more! Ever!

3
Last Time Two Slit Interference
4
From another world .. sound.
Two small loudspeakers that are 5.50 m apart are
emitting sound in phase. From both of them, you
hear a singer singing C (frequency 277 Hz),
while the speed of sound in the room is 340 m/s.
Assuming that you are rather far from these
speakers, if you start out at point P equidistant
from both of them and walk around the room in
front of them, at what angles (measured relative
to the line from P to the midpoint between the
speakers) will you hear the sound (a) maximally
enhanced? Neglect any reflections from the walls.
5
Table
6
Diffraction

• Huygens principle requires that the waves spread
  out after they pass through narrow slits
• This spreading out of light from its initial line
  of travel is called diffraction
• In general, diffraction occurs when waves pass
  through small openings, around obstacles or by
  sharp edges

7
Diffraction Grating

• The diffracting grating consists of many equally
  spaced parallel slits of width d
• A typical grating contains several thousand lines
  per centimeter
• The intensity of the pattern on the screen is the
  result of the combined effects of interference
  and diffraction

8
(No Transcript)
9
Diffraction Grating

• The condition for maxima is
• d sin ?bright m ?
• m 0, 1, 2,
• The integer m is the order number of the
  diffraction pattern
• If the incident radiation contains several
  wavelengths, each wavelength deviates through a
  specific angle

10
Diffraction Grating, 3

• All the wavelengths are focused at m 0
• This is called the zeroth order maximum
• The first order maximum corresponds to m 1
• Note the sharpness of the principle maxima and
  the broad range of the dark area
• This is in contrast to the broad, bright fringes
  characteristic of the two-slit interference
  pattern

Active Figure The Diffraction Grating
11
(No Transcript)
12
DIFFRACTION GRATING PATTERN
13
CDDiffraction Grating
14
A shadow isnt simply a shadow.
15
But what about this???
16
What about shadows???
Bright Center
Fringes
Shadow of a small steel ball
Reality
This effect is called DIFFRACTION
17
Diffraction Vs. Interference

• Both involve addition of waves from different
  places and technically, both are the same
  phenomenon.
• Observation requires monochromatic light and a
  small, coherent light source.
• If you are
• close to a source (non paraxial approx) we call
  it Fresnel Diffraction or near-field diffraction.
• Far away we call it Fraunhofer or far-field
  diffraction
• Diffraction usually refers to a continuous source
  of wavelets adding up. Interference has a finite
  number of sources for which the phase is constant
  over each source.

18
Another case -
Geometrical Shadow
19
Adding waves a piece at a time..
Maxima
q
D
WHY??
Single Slit
Screen
20
WHY?
21
Single-Slit Diffraction

• A single slit placed between a distant light
  source and a screen produces a diffraction
  pattern
• It will have a broad, intense central band
  central maximum
• The central band will be flanked by a series of
  narrower, less intense secondary bands
  secondary maxima
• The central band will also be flanked by a series
  of dark bands minima
• The results of the single slit cannot be
  explained by geometric optics
• Geometric optics would say that light rays
  traveling in straight lines should cast a sharp
  image of the slit on the screen

22
Single-Slit Diffraction

• Fraunhofer Diffraction occurs when the rays leave
  the diffracting object in parallel directions
• Screen very far from the slit
• Converging lens (shown)
• A bright fringe is seen along the axis (? 0)
  with alternating bright and dark fringes on each
  side

23
Single-Slit Diffraction

• According to Huygens principle, each portion of
  the slit acts as a source of waves
• The light from one portion of the slit can
  interfere with light from another portion
• All the waves that originate at the slit are in
  phase
• Wave 1 travels farther than wave 3 by an amount
  equal to the path difference d (a/2) sin ?
• Similarly, wave 3 travels farther than wave 5 by
  an amount equal to the path difference d (a/2)
  sin ?

24
Single-Slit Diffraction

• If the path difference d is exactly a half
  wavelength, the two waves cancel each other and
  destructive interference results
• d ½ ? (a/2) sin ? ? sin ? ? / a
• In general, destructive interference occurs for a
  single slit of width a when
• sin ?dark m? / a m ?1, ?2, ?3,

25
Single-Slit Diffraction

• A broad central bright fringe is flanked by much
  weaker bright fringes alternating with dark
  fringes
• The points of constructive interference lie
  approximately halfway between the dark fringes

• ym L tan ?dark , where sin ?dark m? / a

26
25. A beam of laser light of wavelength 632.8 nm
falls on a thin slit 0.00375 mm wide. After the
light passes through the slit, at what angles
relative to the original direction of the beam is
it completely cancelled when viewed far from the
slit?
27
27. Parallel light rays with a wavelength of 600
nm fall on a single slit. On a screen 3.00 m
away, the distance between the first dark fringes
on either side of the central maximum is 4.50 mm.
What is the width of the slit?
28
30. Light of wavelength 633 nm from a distant
source is incident on a slit 0.750 mm wide, and
the resulting diffraction pattern is observed on
a screen 3.50 m away. What is the distance
between the two dark fringes on either side of
the central bright fringe?
29
35. A laser beam of wavelength 600.0 nm is
incident normally on a transmission grating
having 400.0 lines/mm. Find the angles of
deviation in the first, second, and third orders
of bright spots.
30
38. (a) What is the wavelength of light that is
deviated in the first order through an angle of
18.0 by a transmission grating having 6000
lines/cm? (b) What is the second-order deviation
for this wavelength? Assume normal incidence.
31
END