Ch 16 Interference

1
Ch 16 Interference
2
Diffraction is the bending of waves around
obstacles or the edges of an opening. Huygens
Principle - Every point on a wave front acts as a
source of tiny wavelets that move forward with
the same speed as the wave the wave front at a
later instant is the surface that is tangent to
the wavelets.
3
Interference alters the intensity (brightness) of
light, just as it effects the loudness of sound.
The waves combine following the principle of
linear superposition.
4
(No Transcript)
5
When identical waves cross in phase the waves
reinforce each other constructive interference.
When the waves are out of phase they cancel each
other destructive interference.
6
If the wave sources are coherent sources, the
interference will continue without change.
7
In 1801 Thomas Young (English) performed a
historic experiment showing that two overlapping
light waves interfere with each other.
8
Monochromatic light passes through a single
narrow slit and falls on two closely spaced
narrow slits S1 and S2. These two slits act as
coherent sources of light that interfere with
each other.
9
When both light rays travel the same distance,
they constructively interfere and produce a
bright spot.
10
When one light ray travels 1l further than the
other, they still constructively interfere and
produce a bright spot.
11
But if one light ray travels 1/2 l further than
the other, they destructively interfere and
produce a dark spot.
12
Thus a series of bright and dark areas is
produced.
13
(No Transcript)
14
If illuminated with monochromatic light,
successive pairs of slit images will appear on
either side of the principle image. The first
pair are called the first-order images, the
second pair are the second-order images.
15
(No Transcript)
16
d is the distance between the slits, and is
called the grating constantl is the
wavelength? is the diffraction angle
17
Monochromatic light is shined on two slits. The
distance between the two slits is 0.030 mm. The
second order bright fringe is measured on a
viewing screen at an angle of 2.15 from the
central maximum. Determine the wavelength of the
light.
18
Ex. 2 - Red light (l 664 nm in vacuum) is used
in Youngs experiment with the slits separated by
a distance d 1.20 x 10-4 m. The screen is
located at a distance from the slits of L 2.75
m. Find the distance y on the screen between the
central bright fringe and the third-order bright
fringe.
19
Diffraction gratings have as many as 12,000
equally spaced parallel grooves. When
illuminated with white light, each slit produces
a new wave front. These wave fronts interfere and
produce pairs of continuous spectra equally
spaced on opposite sides of the principle image.
20
If illuminated with monochromatic light,
successive pairs of slit images will appear on
either side of the principle image. The first
pair are called the first-order images, the
second pair are the second-order images.
21
(No Transcript)
22
d is the distance between the slits, and is
called the grating constantl is the
wavelength? is the diffraction angle
23
To find the location of the destructive
interference, replace m with m 1/2.l d sin
q/(m ½)
24
If white light is used rather than monochromatic
light, a central white band results. Outside the
central point, fringes of all colors result. At
the central point all colors are incident
producing white light. Outside the central white
fringe there is a bright fringe for each value of
l.
25
In these light colored bands, red is farther out
than the other colors. Violet is closest to the
white central spot. Red lights l is larger than
violets therefore by sin q ml/d (l d sin
q/m) , the red band is farther from the center.
There is one group of colored fringes for each
value of m.
26
Thin transparent soap films, oil slicks, and
wedge-shaped films of air show varying patterns
of colors when viewed by reflected white light.
Monochromatic light produces light and dark
bands.
27
(No Transcript)
28
(No Transcript)
29
Some light is reflected at the top surface, some
is refracted and then partially reflected at the
bottom surface, eventually refracted again at the
top surface and exiting parallel to the original
reflected ray.
30
If the film is 1/4 wavelength in thickness, the
second ray exits 1/2 wavelength behind the
originally reflected ray. This should
destructively interfere and the film should
appear dark.
31
If the film is 1/2 wavelength in thickness, the
second ray should be one whole wavelength behind
and constructive interference should occur.
32
Observation shows the opposite effect of that
expected. This occurs when air is on both sides
of the film. Very thin layers of soap film are
very dark, although we would expect them to be
bright.
33
Thomas Young explained this by suggesting that
one of the reflected waves undergoes a 180 phase
change during reflection.
34
The reflection where the medium beyond has a
greater index of refraction (top) undergoes the
phase shift. When the medium beyond has a lower
index of refraction there is no phase shift.
35
Thus the rule for constructive and destructive
interference for thin films bounded on both sides
by a medium of lower index of refraction is this
36
Maximum constructive interference occurs if the
optical path difference is an odd number of half
wavelengths (film thickness is an odd number of
quarter wavelengths) and
37
Maximum destructive interference occurs when the
optical path difference is a whole number of
wavelengths (film thickness is an even number of
quarter wavelengths).
38
A vertical cross section of soap film meets the
odd and even quarter wavelength thicknesses at
successive intervals down the film for different
colors.
39
Optically flat glass plates separated by a thin
film of air produce regular patterns of
interference fringes. irregular surfaces produce
irregular patterns.
40
An interferometer can be used to measure the
smoothness of glass surfaces.
41
Ex. 4 - (a) A thin film of gasoline floats on a
puddle of water. Sunlight falls almost
perpendicularly on the film and reflects into
your eyes. Destructive interference eliminates
the blue color (l 469 nm) , so the film has a
yellow hue. If the refractive indices of blue
light in gasoline and water are 1.40 and 1.33
respectively, determine the minimum nonzero
thickness t of the film. (b) Repeat part (a)
assuming that the gasoline is on glass (nglass
1.52) instead of water.
42
Ex. 5 - Under natural conditions, thin films have
a multicolored appearance that often changes
while you are watching them. Why are such films
multicolored, and what can be inferred from the
fact that the colors change in time?
43
Ex. 6 - (a) Assume that green light (l 552 nm)
strikes two glass plates (n 1.52) nearly
perpendicularly. Determine the number of bright
fringes that occur between the place where the
plates touch and the edge of the sheet of paper
(thickness 4.10 x 10-5 m). (b) Explain why
there is a dark fringe where the plates touch.
44
Single-slit diffraction - A slit that is only a
few wavelengths wide will produce alternating
light and dark bands. The very center of the
image is almost equidistant from all parts of the
slit, so it is very bright because all
interference is constructive.
45
At points below and above this bright band, where
the distance to each edge of the slit differs by
whole wavelength, the difference in the edge and
the center differs by 1/2 a wavelength.
46
For every point from the bottom of the slit to
the center, there is a point from the center to
the top that is 1/2 wavelength different in
distance from the screen. Therefore, all light is
canceled and the band is dark.
47
At two points further from the center, the
distance to each edge of the slit differs by 1.5
wavelengths. In this case three wavelets arrive,
all offset by 1/2 a wavelength. Two of these
interfere constructively, the third provides the
light band (dimmer than the center light band).
48
If the difference in distance to the two edges
is two wavelengths, a dark band results. If the
difference is 2.5 wavelengths, a light band again
results, etc. The intensity of the light bands
decreases with distance.
49
(No Transcript)
50
The angle to the normal at which the bright
fringes (constructive interference) are located
can be found using this equationsin q (m
½)l/d. d is the distance between the slits m is
the order of the image.
51
The formula for the dark fringes is sin q
ml/d. The dark fringes must be halfway between
the bright fringes.
52
The intensity of the light bands decreases with
distance.
53
A Michelson interferometer splits light rays into
two parts then reunites them after making one
part travel a longer distance. At integer 1/2
l differentials, the reunited rays destructively
interfere. At integer l differentials, the
reunited rays interfere constructively. These
distances can be measured to find the l of light.
54
(No Transcript)