Chapter 37 Interference

1
Chapter 37 Interference
PHYS 2326-34
2
Concepts to Know

• Interference
• Principle of Superposition
• Monochromatic Light
• Coherent Light
• Antinodal Curves (Constructive Interference)
• Nodal Curves (Destructive Interference)
• Interference Fringes
• Phase Shift (Reflection off Slow Medium)
• Thin Films

3
Inteference

• Like sound waves, light waves can produce
  interference
• Nodes exist where there are minima (dark areas)
  from destructive interference
• Antinodes exist where there are bright areas from
  constructive interference

4

• With sound, we discussed the interference using
  examples having only one frequency and phase such
  as a pipe that resonates.
• To see such effects with light, we need to have
  one frequency as well. Otherwise the effect is
  hidden by too much going on.

5
Monochromatic Light

• Monochromatic light simply means one color
  which is 1 frequency or wavelength
• Lasers produce monochromatic light very well
• Sodium vapor lights do a fair job although they
  are producing bichromatic light but there are a
  variety of arc lamps which are monochromatic
• Lightbulbs produce a wide range of wavelengths

6
Coherent Light

• Coherent light refers to light having a
  consistent phase between sources.
• From our study of sound, we determined that
  phasing between PA system speakers could have
  negative effects on ones hearing at some
  locations
• In order to see interference effects we must have
  consistent phase.

7
Conditions for Interference

• Sources must be coherent have a constant phase
• Sources must be monochromatic, a single wavelength

8
Youngs Double-Slit Experiment

• Performed by Thomas Young in 1800
• It showed Huygenss principle of subdividing wave
  fronts into new wavelets or wave fronts to be
  correct

9

• S1 and S2 are narrow slits separated by distance
  d. Distance d is the difference in path lengths
  r1 and r2 and ? is the angle from the normal at
  the slit center line and y is the offset distance
  at the screen
• When d is a multiple of wavelength there is
  constructive interference

r1
y
S1
r2
?
d
S2
d
L
10

• d sin ?bright m?
• d sin ?dark (m ½) ?
• since tan ? y/L
• ybright L tan ?bright
• ydark L tan ?dark
• for small angles where ? sin ?
• ybright L (m ? /d)

11
Phase Shift from Reflection

• Section 37.5 refers to Lloyds mirror where our
  two sources are one source plus a reflected image
  of the source
• When an electromagnetic wave is reflected from
  the interface to a medium with a higher index of
  refraction than the one in which it is traveling,
  it undergoes a 180 degree phase reversal.

12

• When a reflection occurs at a surface where the
  index of refraction is less than that of the
  medium the wave is traveling in, there is NO
  phase reversal at the reflection
• This corresponds to a ½ wavelength displacement
  shift or a ½ integer shift

13
Thin Films

• Thin films such as oil on water or soap bubble
  surfaces exhibit interference effects by showing
  varied colors when white light is incident on the
  films.
• This occurs because the reflection from the top
  surface has a 180 degree phase shift and the
  second surface at some distance t does not have
  this phase shift and the total effective path
  difference becomes a multiple of certain
  wavelengths
• 2t (m1/2)?n where ?n ? /n (index of
  refraction)
• 2nt (m1/2) ? for constructive interference and
• 2nt m ? for destructive interference (eqn
  37.15-17)

14
Color Wavelength
500nm
400nm
600nm
700nm
blue
green
red
yellow
cyan
magenta

• Primary colors are red green and blue and have a
  range of wavelengths for each. Adding any
  combination creates other colors. Often called
  RGB
• Cyan magenta and yellow are combinations of two
  primary colors
• Wavelengths are shown in nanometers (10-9 meters)
  sometimes these are shown in Angstroms which is
  10-10

15
Example Problem 1

• In a double slit interference experiment, the
  slits are 10 micron (10-6 meters) apart and the
  screen is 2 meters away. If 500nm wavelength
  light is used, find a) the location of the first
  dark fringe, b) the location of the 3rd bright
  fringe, c) the spacing between fringes, d) the
  theoretical number of bright fringes possible.

16

• a) d sin ? (m1/2)?, 1E-5 sin ? (1/2) 5E-7 ?
  1.43
• y L tan ? 2.0 tan(1.43) 0.05m
• b) d sin ? (m)?, 1E-5 sin ? (3) 5E-7
• ? 8.63
• y L tan ? 2.0 tan(8.63) 0.30m
• c) d sin ? (1)?, ? 2.86
• y 0.10m
• d) let maximum ? 90, d sin 90 (m)?, m20.
  This is for 1 side and there is a middle fringe
  total 41

17
Example Problem 2

• What is the minimum thickness of a soap bubble
  film with index of refraction 1.33 that would
  reflect 650nm most brightly? b) What is the
  minimum thickness for an anti-reflecting coating
  of index of refraction 1.4 or a glass of index
  1.5 which would reflect no green light of
  wavelength 550nm? c) what would be the color of
  the light that is reflected off the lens

18

• n 1.33, ?o 650nm, ? ?o /n 488nm, ?m 0
  m2-m1
• m2 2d/ ?, since m1 ½ (due to 180 deg.
  inversion not present at m2) our path difference
  can be ½ wavelength. Get wavelength inside
  material and determine d m2 ?/2 ½ 488 /
  2122nm
• b) coating n1.4, glass 1.5 at 550nm ? ?o /n
  393nm, m1 ½, m2 2d/ ? ½ since both m1 and
  m2 reflect from greater index of refraction
  mediums ?m ½ m2-m1 m2 ½, m2 1
• ? 550/1.4 393,
• hence m2 1 2d/ ? ½, 2d/ ? 1/2, d ?/4
  393/4 98nm
• c) green transmitted, blue red reflected,
  magenta