Download - Physics Beyond 2000
![Page 1: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/1.jpg)
Physics Beyond 2000
Chapter 11
Electromagnetic Waves
![Page 2: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/2.jpg)
What are electromagnetic waves?
• EM waves are energy emitted resulting from acceleration of electric charges.
-
![Page 3: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/3.jpg)
EM Waves
• They can travel through vacuum.
• In vacuum, their speed = 3 × 108 ms-1
• c = f.λ
• An EM wave consists of electric and magnetic fields, oscillating in phase and at right angles to each other. http://www.geo.mtu.edu/rs/back/spectrum/
![Page 4: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/4.jpg)
Electromagnetic spectrum
• The range of the wavelength of EM waves is enormous.
• 10-14 m – 1 km
• The electromagnetic spectrum is named according to the range of the wavelength and the method of production.
![Page 5: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/5.jpg)
Radio Waves• Production:
• Apply an a.c. voltage of high frequency to a pair of metal rods (dipole).
• If the rods are vertical, the radio wave is also said to be vertically polarized.
direction of propagation ofradio wave
oscillating a.c.
oscillating electric fieldtransmitter
![Page 6: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/6.jpg)
Radio Waves• Receiver:
• The receiver dipole is parallel to the direction of polarization. In this case, it is vertical.
direction of propagation ofradio wave
oscillating a.c.
oscillating electric field
transmitter receiver
![Page 7: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/7.jpg)
Spectrum of Radio WavesRadio waves Wavelength
Long waves 1 km – 10 km
Medium waves 100 m – 1 km
Short waves 10 m – 100 m
Very high frequency (VHF)
1 m – 10 m
Ultra high frequency
(UHF)
0.1 m – 1 m
![Page 8: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/8.jpg)
Microwaves
• Microwave is polarized along the length of the dipole.
direction of propagation ofmicrowave
oscillating a.c.
oscillating electric field
transmitter receiver
![Page 9: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/9.jpg)
Microwaves
• Vertical metal rod can absorb the energy of the microwave.
direction of propagation ofmicrowave
oscillating a.c.
oscillating electric field
transmitter receiver
metal rod
no response
![Page 10: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/10.jpg)
Microwaves
• Horizontal metal rod cannot absorb the energy of the microwave.
direction of propagation ofmicrowave
oscillating a.c.
oscillating electric field
transmitter receivermetal rod
![Page 11: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/11.jpg)
Interference of Microwaves• At P, the wave from the transmitter meets
the reflected wave. Interference occurs.
P
transmitter
imageof transmitter
metal plate
![Page 12: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/12.jpg)
Interference of Microwaves• We may consider it as an interference from two
coherent sources, the transmitter and its image.
P
transmitter
imageof transmitter
metal plate
![Page 13: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/13.jpg)
Interference of Microwaves• The two sources are in anti-phase because
there is a phase change of on reflection.
P
transmitter
imageof transmitter
metal plate
![Page 14: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/14.jpg)
Interference of Microwaves• If the path difference at P = n., there is
destructive interference.
P
transmitter
imageof transmitter
metal plate
![Page 15: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/15.jpg)
Interference of Microwaves
• If the path difference at P = , there is constructive interference.
P
transmitter
imageof transmitter
metal plate
)2
1( n
![Page 16: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/16.jpg)
Microwave Cooking
• One possible frequency of microwave is 2.45 GHz which is equal to the natural frequency of water molecules.
• Microwave can set water molecules into oscillation. The water molecules absorb the energy from microwave.http://www.gallawa.com/microtech/howcook.html
![Page 17: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/17.jpg)
Microwave in satellite communications
• Reading the following
http://www.s-t.au.ac.th/~supoet/satel.htm#1
![Page 18: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/18.jpg)
Infrared Radiation
• Self-reading.
![Page 19: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/19.jpg)
Ultraviolet Radiation
• Self-reading.
![Page 20: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/20.jpg)
Visible light
• Self-reading.
![Page 21: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/21.jpg)
Colored Video Pictures
• Self-reading.
![Page 22: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/22.jpg)
Scattering of Light• Light energy is absorbed by an atom or
molecule.
• The atom (molecule) re-emits the light energy in all direction.
• The intensity of light in initial direction is reduced.
incident light
atomoscillating E-field
![Page 23: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/23.jpg)
Scattering of Light• Light energy is absorbed by an atom or
molecule.
• The atom (molecule) re-emits the light energy in all directions.
• The intensity of light in initial direction is reduced.
atom
scattered light
axis along which the atom oscillating
![Page 24: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/24.jpg)
Scattering of Light• Note that there is not any scattered light
along the direction of oscillation of the atom.
• The scattered light is maximum at right angle to the axis.
atom
scattered light
axis along which the atom oscillating
strongeststrongest
![Page 25: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/25.jpg)
Why is the sky blue at noon and red at sunrise and sunset?
• Why is the sky blue in daytime?
• http://physics.about.com/science/physics/library/weekly/aa051600a.htm
• Why is the sky red in sunset/sunrise?
• http://physics.about.com/science/physics/library/weekly/aa052300a.htm
![Page 26: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/26.jpg)
Why is the sky blue at noon and red at sunrise and sunset?
• At noon, we see the most scattered light.• Note that the natural frequency of air molecules is
in the ultraviolet region. Blue light is easily scattered by air molecules.
white light fromthe sun
Blue lightis most scattered
Red light is least scattered
![Page 27: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/27.jpg)
Why is the sky blue at noon and red at sunrise and sunset?
• At sunset, we see the least scattered light.
• Red light is least scattered. white light fromthe sun
Red lightis least scattered
Blue light is most scattered
![Page 28: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/28.jpg)
Polarization of light• Light is transverse wave so it exhibits polari
zation.• Unpolarized light: the electric field is not co
nfined to oscillate in a plane.• Plane-polarized light: the electric field at ev
ery point oscillates in the same fixed plane.• Plane of polarization: the plane in which the
electric field of a plane polarized light oscillates.
![Page 29: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/29.jpg)
Polarization of Light
• Plane polarized light:
• Unpolarised light:
electric vector
electric vector
![Page 30: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/30.jpg)
Polarization by Absorption • An array of parallel conducting wires.
• It can absorb electric field of microwave oscillating in a plane parallel to its conducting wires.
Conducting wires are verticalPlane-polarized microwave
No microwave
E-field is vertial.
![Page 31: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/31.jpg)
Polarization by Absorption • An array of parallel conducting wires.
• It cannot absorb electric field of microwave oscillating in a plane perdpndicular to its conducting wires.
Conducting wires are verticalPlane-polarized microwave
E-field is horizontal Plane-polarized microwave
![Page 32: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/32.jpg)
Polarization by Absorption • An array of parallel conducting wires.
• It can be a polarizer of microwaves
Conducting wires are verticalUnpolarized microwave
Plane-polarized microwave
![Page 33: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/33.jpg)
Polarization by Absorption • Polaroid is a plastic sheet consisting of long chains
of molecules parallel to one another.
• It can absorb electric field of light oscillating in a plane parallel to its chains of molecules.
E-field is vertical
Chains of molecules are vertical
No light
Plane-polarized light
![Page 34: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/34.jpg)
Polarization by Absorption
• Polaroid is a plastic sheet consisting of long chains of molecules parallel to one another.
• It cannot absorb electric field of light oscillating in a plane perpendicular to its chains of molecules.
E-field is horizontal
Chains of molecules are verticalPlane-polarized light
Plane-polarized light
![Page 35: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/35.jpg)
Polarization by Absorption • Polaroid is a plastic sheet consisting of long chains
of molecules parallel to one another.
• It can be a polarizer of light.
Chains of molecules are verticalUnpolarized light
Plane-polarized light
![Page 36: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/36.jpg)
Polarization by Reflection
plane-polarizedincident light
plane-polarizedrefracted light
No reflected light
air
glass
Assume that the direction of the reflected light and that of the refracted light are perpendicular.
![Page 37: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/37.jpg)
Polarization by Reflection
plane-polarizedincident light
plane-polarizedrefracted light
No reflected light
air
glass
•The electric field sets theelectrons in the glass tooscillate at right angles tothe refracted ray.•The intensity perpendicularto the axis of oscillation isstrongest The refracted ray is bright.•The intensity parallel to the axis of oscillation is zero no reflected ray.
![Page 38: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/38.jpg)
Polarization by Reflection
Unpolarizedincident light
Unpolarizedrefracted light
Polarized reflected light
air
glass
The plane of polarizationis parallel to the surface of medium.
Assume that the direction of the reflected light and that of the refracted light are perpendicular.
![Page 39: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/39.jpg)
The Brewster’s Angle
p = Brewster’s angler = Angle of refraction.
p p
r
incidentray
reflected ray is completely polarized
refractedray
air
medium
![Page 40: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/40.jpg)
The Brewster’s Angle
• n = tan p where n is the refractive index of the medium.
p p
r
incidentray
reflected ray
refractedray
air
medium
Prove it!
![Page 41: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/41.jpg)
Example 1
• The Brewster’s angle for glass is about 56.3o.
![Page 42: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/42.jpg)
Polarization by Scattering
• When light energy is absorbed by an atom, the atom re-radiates the light.
The atom absorbsthe wave energy.
incident ray
atom
The atom re-radiates the wave energy.
![Page 43: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/43.jpg)
Polarization by Scattering
vertically polarizedlight
water mixed with milk
vertically polarizedlight
vertically polarizedlight
vertically polarizedlightno scattered light
no scattered light
![Page 44: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/44.jpg)
Polarization by Scattering
horizontally polarizedlight
water mixed with milk
horizontally polarizedlight
horizontally polarizedlight
horizontally polarizedlight
no scattered light
no scattered light
![Page 45: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/45.jpg)
Polarization by Scattering
unpolarizedlight
water mixed with milk
unpolarizedlight
vertically polarizedlight
vertically polarizedlight
horizontally polarizedlight
horizontally polarizedlight
![Page 46: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/46.jpg)
Polaroid Sunglasses
• Why are the polaroid sunglasses designed to absorb horizontally polarized light?
Study p.233 of the textbook.
![Page 47: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/47.jpg)
Interference of Light
• Light is a kind of wave.
• Interference is a wave property.
![Page 48: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/48.jpg)
Interference of LightConditions for an observable interference pattern of
light:• Coherent sources : two sources emit light of
the same frequency and maintain a constant phase difference.
• The light waves are of same frequency and almost equal amplitude.
• The separation of the two sources is of the same order as the wavelength.
• The path difference must be not too large.
![Page 49: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/49.jpg)
Interference of Light
• Young’s double-slit experiment
http://members.tripod.com/~vsg/interfer.htm
http://surendranath.tripod.com/DblSlt/DblSltApp.html
•The incident ray is split into two coherent sourcesS1 and S2 by the double-slit.•S1 and S2 are in phase.•The screen is far away from the slit. D>> a.•The angles are very small.
![Page 50: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/50.jpg)
Young’s double-slit experiment
a
P
S1
S2
central line
Suppose that there is a maximum at point P.A constructive interference occurs at P.
screenD
![Page 51: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/51.jpg)
Young’s double-slit experiment
a
parallel rays meet at point P
As point P is far away from the double slit,the light rays of the same fringe are parallel.
The path difference = a.sin
S1
S2central line
![Page 52: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/52.jpg)
Young’s double-slit experiment
a
parallel rays meet at point P withmaximum intensity.
The path difference = a.sin
S1
S2central line
= a.sin = m. where m = 0, 1, 2,… m is the order of the fringes.
For points with constructive interference,
![Page 53: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/53.jpg)
Young’s double-slit experiment
a
parallel rays meet at a point withminimumintensity.
The path difference = a.sin
S1
S2central line
= a.sin = (m + ). where m = 0, 1, 2,…
For points with destructive interference,
2
1
![Page 54: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/54.jpg)
separation between the fringes
a
P
S1
S2
central line
Suppose the the order of the fringe at P is m.The distance from P to the central line is ym.The distance between the double slitand the screen is D.
ym
M
D
![Page 55: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/55.jpg)
separation between the fringes
a
P
S1
S2
central line
The line from mid-point M to P makes the same angle with the central line.
ym
M
D
ym = D.tan D.sin = Da
m.
![Page 56: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/56.jpg)
separation between the fringes
ym = Da
m.
(1)
By similar consideration, for the m+1 bright fringe
ym+1= Da
m.
)1( (2)
The separation between the two fringes is
s = ym+1 – ym = a
D
![Page 57: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/57.jpg)
separation between the fringes
• The fringes are evenly separated.
• For well separated fringes.• s D Place the screen far away from the slit.
• s Different separation for waves of different wavelength.
• s The slits should be close.
s = ym+1 – ym = a
D
a
1
![Page 58: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/58.jpg)
Variation of intensity• If the slits are sufficiently narrow, light spreads
out evenly from each slit and the bright fringes are equally bright.
![Page 59: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/59.jpg)
Variation of intensity
• If the intensity on the screen using one slit is Io,
the intensity is 4.Io at the position of bright fringes and
the intensity is 0 at the position of dark fringes.
• Energy is re-distributed on the screen.
![Page 60: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/60.jpg)
Variation of intensity
• In practice, light waves do not diffract evenly out from each slit. There is an angle of spread.
http://numerix.us.es/numex/numex2.html
http://bc1.lbl.gov/CBP_pages/educational/java/duality/duality2.html
![Page 61: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/61.jpg)
Variation of intensity• The intensity of the fringes is enclosed in an
envelope as shown.
![Page 62: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/62.jpg)
Example 2
• Separation of fringes in Young’s double-slit experiment.
![Page 63: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/63.jpg)
White light fringes
s =a
D s
Separation of violet fringes is shortest.Separation of red fringes is longest.
http://members.tripod.com/~vsg/interfer.htm
http://surendranath.tripod.com/DblSlt/DblSltApp.html
![Page 64: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/64.jpg)
Submerging in a Liquid• If the Young’s double-slit experiment is
done in a liquid, what would happen to the separation of fringes?
Liquid with refractive index n
ym
![Page 65: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/65.jpg)
Submerging in a Liquid
• The wavelength changes!
Let be the wavelength in vacuum/airand n the wavelength in liquid.Let n be the refractive index of the liquid.
nn
The fringe separation in liquid
sn =
n
s
![Page 66: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/66.jpg)
Submerging in a Liquid
• The fringe separation is reduced by a factor of n.
nn
The fringe separation in liquid
sn =
n
s
![Page 67: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/67.jpg)
Optical path
• Optical path of light in a medium is the equivalent distance travelled by light in vacuum.
medium ofrefractive index
nIncidentlight
vacuum
thickness = t
thickness = optical path
Light requires the sametime to travel throughthe two paths.
![Page 68: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/68.jpg)
Optical path
• Show that the optical path = n.t
medium ofrefractive index
nIncidentlight
vacuum
thickness = t
thickness = optical path
Light requires the sametime to travel throughthe two paths.
![Page 69: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/69.jpg)
Optical path
• The number of waves in the medium = the number of waves in the optical path
medium ofrefractive index
nIncidentlight
vacuum
thickness = t
thickness = optical path
Light requires the sametime to travel throughthe two paths.
![Page 70: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/70.jpg)
Example 3
• Note that light rays pass through different media. We need to consider their path difference in terms of the optical paths.
![Page 71: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/71.jpg)
Shifting a System of Fringes
Note that ray A has passes through a medium of refractiveindex n and thickness t.We need to find the path difference in terms of the optical path.
A
B
![Page 72: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/72.jpg)
Shifting a System of Fringes
Without the medium, the central maximum is atthe central line. (Path difference = 0)Now the central maximum shifts to another position.Find the central maximum.
The central maximum shifts through a distance
a
tDny
)1(
![Page 73: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/73.jpg)
Shifting a System of Fringes
If the central line now has the mth bright fringe,the central maximum has shifted through m fringes.
tn
m)1(
![Page 74: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/74.jpg)
Multiple-slit
• More slits than two.
3 slits
4 slits
http://bednorzmuller87.phys.cmu.edu/demonstrations/optics/interference/demo323.html
![Page 75: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/75.jpg)
Multiple-slit
• N = number of slits.
• Compare N = 2 with N = 3
http://wug.physics.uiuc.edu/courses/phys114/spring01/Discussions/html/wk3/multiple/html/3-extra2.htm
![Page 76: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/76.jpg)
Multiple-slit• N = number of slits.• Compare N = 2 with N = 3
N = 2 N = 3Maximum occurs at positions with a.sin = m.
Maximum occurs at positions with a.sin = m.
The intensity at the maximum is 4.Io
The intensity at the maximum is 9.Io
Between two maxima, it is a minimum.
Between two maxima, it is a peak.
The width of bright fringes is large.
The width of bright fringes is less
![Page 77: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/77.jpg)
Multiple-slit• N = number of slits.• Compare N = 2 with large N.
N = 2 Large N Maximum occurs at positions with a.sin = m.
Maximum occurs at positions with a.sin = m.
The intensity at the maximum is 4.Io
The intensity at the maximum is N2.Io
Between two maxima, it is a minimum.
Between two maxima, there are (N-2) peaks. The intensity of the peak is almost zero
The width of bright fringes is very narrow
![Page 78: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/78.jpg)
Multiple-slit• N = 3• Maximum occurs at a.sin = m. (same as N = 2).
Central maximum 1st order maximum
m= 0 = 0All three rays are in phase.
m= 1 a.sin = All three rays are in phase.
a
a
a
a
phase difference= 0
phase difference= 0
![Page 79: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/79.jpg)
Multiple-slit
• Textbook, p.238. Fig. 30.
• Position of maximum when N = 2 is still a maximum.
• There are peak(s) between two successive maxima.
• The number of peaks = N – 2.
• The intensity of peaks drops with N.
![Page 80: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/80.jpg)
Multiple-slit (N = 3)m = 0m = 1 m = 1
0sin a
sina
sin
a2sin
a2
sin
Why is there a peak between two maxima when N = 3?
![Page 81: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/81.jpg)
Multiple-slit (N = 3)
a2sin
There is a peak at position with
a
a
θθ
Δ1
Δ2
Δ1 = 2
phase difference = π
Δ2 =λ phase difference = 0
Add three rotating vectors for the resultant wave.
![Page 82: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/82.jpg)
Multiple-slit (N = 3)
Why are there 2 minima between two maxima when N = 3?
m = 0m = 1 m = 1
0sin a
sina3
2sin
a2sin
a2
sin
a3sin
![Page 83: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/83.jpg)
Multiple-slit (N = 3)
a3sin
There is a minimum at position with
a
a
θθ
Δ1
Δ2
3
Add three rotating vectors for the resultant wave.
Δ1 = phase difference
= 3
2
Δ2 = phase difference =
3
43
2
![Page 84: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/84.jpg)
Multiple-slit (N = 3)
a3
2sin
There is a minimum at position with
a
a
θθ
Δ1
Δ2
Add three rotating vectors for the resultant wave.
3
2Δ1 = phase difference
= 3
4
Δ2 = phase difference =
3
83
4
![Page 85: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/85.jpg)
Diffraction grating
• A diffraction grating is a piece of glass with many equidistant parallel lines.
![Page 86: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/86.jpg)
Diffraction grating• The mth order maximum is given by
a.sin = m.
m = 0
m = 1
m = 1
m = 2
m = 2
m = 3
m = 3
![Page 87: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/87.jpg)
Diffraction grating• The maximum order is given by
m = 0
m = 1
m = 1
m = 2
m = 2
m = 3
m = 3
a
m max
![Page 88: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/88.jpg)
Intensity of diffraction grating
![Page 89: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/89.jpg)
coarse grating and fine grating
• The separation between lines on a coarse grating is longer than that of a fine grating.
• Example of a coarse grating: 300 lines/cm.
• Example of a fine grating: 3000 lines/cm.
Find the maximum order of the above two gratings.
![Page 90: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/90.jpg)
Colour Spectrum from a Diffraction Grating
m = 0
m = 1
m = 1
m = 2
m = 2
m = 3
m = 3
m = 1
m = 2
m = 3
white light
m = 1
m = 2
m = 3
a..sinm = m. The spatial angle m depends on
![Page 91: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/91.jpg)
Example 4
• Monochromatic light = light with only one colour (frequency)
![Page 92: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/92.jpg)
Example 5
• Overlapping of colour spectrum
![Page 93: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/93.jpg)
Blooming of lenses
• Coat a thin film on a lens to reduce the reflection of light.
without coating
incident rayreflected ray
with coating
incident ray
no reflected ray
glass glassfilm
![Page 94: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/94.jpg)
Blooming of lenses
• Ray A is reflected at the boundary between air and the film.
with coating
incident rayReflected ray A
![Page 95: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/95.jpg)
Blooming of lenses
• Ray B is reflected at the boundary between the thin film and the glass.
with coating
incident rayReflected ray A
Reflected ray B
![Page 96: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/96.jpg)
Blooming of lenses
• It is designed to have destructive interference for the reflected light rays. No reflected light ray.
with coating
incident rayReflected ray A
Reflected ray B
![Page 97: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/97.jpg)
Blooming of lenses• Suppose that the incident ray is normal to
the lens.• The reflected light rays are also along the
normal.
incident ray reflected rays
film
glass glass
film
![Page 98: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/98.jpg)
Blooming of lenses• Let n’ be the refractive index and t be the
thickness of the thin film.
• Let be the wavelength of the incident light.
incident ray reflected rays
film
glass glass
film
![Page 99: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/99.jpg)
Blooming of lenses• To have destructive interference for the
reflected rays,
incident ray reflected rays
film
glass glass
film
'4min nt
![Page 100: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/100.jpg)
Blooming of lenses• Energy is conserved. As there is not any
reflected light rays, the energy goes to the transmitted light ray.
incident ray No reflected rays
film
glass glass
film
transmitted ray
![Page 101: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/101.jpg)
Blooming of lenses• The reflected ray from the bottom of the
glass is so dim that it can be ignored.
incident ray
This reflected rayis ignored.
film
glass glass
film
![Page 102: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/102.jpg)
Blooming of lenses• Limitation:
• For normal incident ray only.
• For wave of one particular wavelength only.
incident ray
This reflected rayis ignored.
film
glass glass
film
![Page 103: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/103.jpg)
Examples
• Example 6
Find the minimum thickness of the thin film.
• Example 7
Find the wavelength.
![Page 104: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/104.jpg)
Air Wedge:Experimental setup
![Page 105: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/105.jpg)
Air Wedge
reflected ray A
normal incidentray
air wedge
A normal incident ray is reflected at the boundarybetween the slide and the air wedge.
slide
glass block
![Page 106: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/106.jpg)
Air Wedge
reflected ray A
reflected ray Bnormal incidentray
air wedget
The normal incident ray goes into the wedge, passingthrough a distance t and reflected at the boundary betweenthe air wedge and the glass block.
slide
glass block
![Page 107: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/107.jpg)
Air Wedge
reflected ray A
reflected ray Bnormal incidentray
air wedget
The ray into the glass block is ignored.
slide
glass block
![Page 108: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/108.jpg)
Air Wedge
normal incidentray
air wedge
The ray reflected at the top of the slide is ignored.
slide
glass block
![Page 109: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/109.jpg)
Air Wedge
• Depending on the the distance t and the wavelength of the incident wave, the two reflected rays may have interference.
• The pattern is a series of bright and dark fringes when we view through the travelling microscope.
![Page 110: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/110.jpg)
Air Wedge
reflected ray A
reflected ray Bnormal incidentray
air wedget
To produce bright fringes, 2.t = (m - )., m = 1, 2, 3,…
slide
glass block
2
1
constructiveinterference
![Page 111: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/111.jpg)
Air Wedge
reflected ray A
reflected ray Bnormal incidentray
air wedget
slide
glass block
constructiveinterference
•Ray B has a phase change on reflection.•The path difference must be m.
![Page 112: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/112.jpg)
Air Wedge
reflected ray A
reflected ray Bnormal incidentray
air wedget
To produce dark fringes, 2.t = m ., m = 0, 1, 2,…
slide
glass block
destructiveinterference
Note that ray B has a phase change on reflection.
![Page 113: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/113.jpg)
Air Wedge
reflected ray A
reflected ray Bnormal incidentray
air wedget
slide
glass block
destructiveinterference
Note that ray B has a phase change on reflection.
•Ray B has a phase change on reflection.•The path difference must be (m + ).
2
1
![Page 114: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/114.jpg)
Air Wedge
reflected ray A
reflected ray Bnormal incidentray
air wedget
slide
glass block
destructiveinterference
Note that ray B has a phase change on reflection.
• At the vertex, t = 0 m = 0 dark fringe.
![Page 115: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/115.jpg)
Air WedgeTo find the separation s between two successive bright fringes
air wedgetN
slide
glass block
Nth fringe (N+1)th fringe
stN+1
DL
Let D be the height of the high end of the slide.Let L be the length of the slide.
![Page 116: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/116.jpg)
Air WedgeTo find the separation s between two successive bright fringes
air wedgetN
slide
glass block
Nth fringe (N+1)th fringe
stN+1
DL
Angle of inclination of the slide can be found from
L
Dsin
![Page 117: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/117.jpg)
Air Wedge
Separation s between two successive bright fringes
tN+1 – tN = 2
tN
tN+1
s
ss .2
2tan
![Page 118: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/118.jpg)
Air Wedge
Separation s between two successive bright fringes
tN
tN+1
s
s.2tan
L
Dsin
and
For small angle , sin tan
D
Ls
.2
.
![Page 119: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/119.jpg)
Air Wedge
• For flat surfaces of glass block and slide– the fringes are parallel and evenly spaced.
![Page 120: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/120.jpg)
Air Wedge
• For flat surface of glass block and slide with surface curved upwards– the fringes are parallel and become more
closely packed at higher orders.
![Page 121: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/121.jpg)
Air Wedge• For flat surface of glass block and slide with
surface curved downwards– the fringes are parallel and become more
widely separated at higher orders.
![Page 122: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/122.jpg)
Air Wedge• We can use this method to check a flat glass
surface.
The surface is flat. The surface is not flat.
![Page 123: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/123.jpg)
Measuring the Diameter D of a Wire
air wedgeD
s
LD
.2
. Measure the quantities on the right
hand side and calculate D.
L
![Page 124: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/124.jpg)
Example 8
• There are 20 dark fringes m = 19.
• L 19.s s = D = 2
.19
m = 0m = 19
DL
19.s
19
L
![Page 125: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/125.jpg)
Soap film
• Why soap film is coloured?
http://www.cs.utah.edu/~zhukov/applets/film/applet.html
![Page 126: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/126.jpg)
Soap film
ray A
ray B
incident ray
The two transmitted rays A and B may have interferencedepending on the thickness t of the film and the wavelength.
t
soapwater
![Page 127: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/127.jpg)
Soap film
ray A
ray B
incident ray
Note that ray B has two reflections. No phase change is dueto reflection.
t
![Page 128: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/128.jpg)
Soap film
ray A
ray B
incident ray
To observe bright fringes, the path difference = m. 2.t = m.
tconstructiveinterference
![Page 129: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/129.jpg)
Soap film
ray A
ray B
incident ray
To observe dark fringes, the path difference = (m+ ). 2.t = (m+ ).
tconstructiveinterference
2
1
2
1
![Page 130: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/130.jpg)
Soap filmThe two reflected rays A and B may have interferencedepending on the thickness t of the film and the wavelength.
ray A
ray B
incident rayt
soapwater
![Page 131: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/131.jpg)
Soap filmNote that this time there is a phase change due to reflection.
ray A
ray B
incident rayt
soapwater
![Page 132: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/132.jpg)
Soap film
Find out how the interference depends on t and
ray A
ray B
incident rayt
soapwater
interference
![Page 133: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/133.jpg)
Soap film
• As the interference depends on , there will be a colour band for white incident light.
• In each colour band, violet is at the top and red is at the bottom.
![Page 134: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/134.jpg)
Soap film • Soap water tends to move downwards due
to gravity.
• The soap film has a thin vertex and a thick base. The fringes are not evenly spaced.
• The fringes are dense near the bottom and less dense near the vertex.
![Page 135: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/135.jpg)
Soap film
• The pattern of the reflected rays and that of the transmitted rays are complementary.
incident ray
C
C
C
C
D
D
D
D
C: constructiveinterferenceD: destructive interference
reflected rays transmitted rays
![Page 136: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/136.jpg)
Example 9
• The reflected rays have constructive interference.
• Note that there is a phase change on reflection.
![Page 137: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/137.jpg)
Newton’s rings:Experimental setup
![Page 138: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/138.jpg)
Newton’s rings• What do we see through the travelling micr
oscope with white incident light?
![Page 139: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/139.jpg)
Newton’s rings
• If we use red incident light,
http://www.cs.utah.edu/~zhukov/applets/film/applet.html
![Page 140: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/140.jpg)
Newton’s rings
reflected ray A
air
lens
glass block
reflected ray Bincident ray
tt = thickness of air gap
interference
The two reflected rays have interference depending onthe thickness t of the air gap and the wavelength .
![Page 141: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/141.jpg)
Newton’s rings
reflected ray A
air
lens
glass block
reflected ray Bincident ray
tt = thickness of air gap
interference
For bright fringes, 4
).12(
mt
![Page 142: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/142.jpg)
Newton’s rings
reflected ray A
air
lens
glass block
reflected ray Bincident ray
tt = thickness of air gap
interference
For dark fringes, 2
.mt
![Page 143: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/143.jpg)
Newton’s rings
reflected ray A
air
lens
glass block
reflected ray Bincident ray
tt = thickness of air gap
interference
At the center of the lens, there is a dark spot.
![Page 144: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/144.jpg)
Newton’s rings
• The spacing of the rings are not even.
• Near the center, the rings are widely separated.
• Near the edge, the rings are close together.
![Page 145: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/145.jpg)
Newton’s rings
• Find the radius of the mth dark ring.
Rm
![Page 146: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/146.jpg)
Newton’s rings
air
lens
glass block
t t = thickness of air gap
R = radius of curvature of the lens
Rm
C
O
A B
tRtRRRm 2)( 22
t
![Page 147: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/147.jpg)
Newton’s rings
air
lens
glass block
t t = thickness of air gap
R = radius of curvature of the lens
Rm
C
O
A B
t
tRRm 2
2
mt for the mth dark fringe
![Page 148: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/148.jpg)
Newton’s rings
air
lens
glass block
t t = thickness of air gap
R = radius of curvature of the lens
Rm
C
O
A B
t
mRRm
![Page 149: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/149.jpg)
Newton’s rings
• Separation between two successive ringss = Rm+1 – Rm = Rmm ).1(
The separation approaches zero for high orders.
![Page 150: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/150.jpg)
Example 10
• To find the radius of curvature of a lens by Newton’s rings.
• If there is distortion of the Newton’s rings, the lens is not a good one.
![Page 151: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/151.jpg)
Thin filmsLight is incident obliquely onto a thin film of refractive index n and thickness t.
thin filmtn
incidentray
![Page 152: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/152.jpg)
Thin films
The reflected rays have interference depending on the angleof view and wavelength .
thin filmtn
incidentray
![Page 153: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/153.jpg)
Thin film
incident white lightcolouredspectrum
http://www.cs.utah.edu/~zhukov/applets/film/applet.html
![Page 154: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/154.jpg)
Diffraction of Light
single slitlaser tube
screen
http://surendranath.tripod.com/SnglSlt/SnglSltApp.html
![Page 155: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/155.jpg)
Diffraction of Light
• Intensity variation
http://arborsci.com/Oscillations_Waves/Diffraction.htm
![Page 156: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/156.jpg)
Diffraction of Light
• Consider a light source which is far away from the single slit and the light is normal to the slit.
• In general, the position of the mth dark fringe due to a slit of width d is given by
d.sinm = m.
http://www-optics.unine.ch/research/microoptics/RigDiffraction/aper/aper.html
![Page 157: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/157.jpg)
Diffraction of Light
• Variation of intensity
• http://www.fed.cuhk.edu.hk/sci_lab/download/project/javapm/java/slitdiffr/Default.htm
![Page 158: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/158.jpg)
Theory of diffractionFormation of 1st order dark fringe.
Divide the slit into two equal sections A1 and A2.The light from section A1 cancels the light from section A2
d
A1
A2
1
1
Prove that d
1sin
![Page 159: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/159.jpg)
Theory of diffractionFormation of 2nd order dark fringe.
Divide the slit into 4 equal sections A1 , A2, A3 and A4.The light from section A1 cancels the light from section A2.
The light from section A3 cancels the light from section A4
d
A1
A2
Prove that d
2sin 2
A3
A4
2
![Page 160: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/160.jpg)
Theory of diffractionFormation of 2nd order dark fringe.
d
A1
A2
d
mm
sin
A3
A4
2
In general for the mth dark fringe,
![Page 161: Physics Beyond 2000](https://reader034.vdocuments.site/reader034/viewer/2022051401/5681367d550346895d9e0b58/html5/thumbnails/161.jpg)
Diffraction of Light• Consider a light source which is far away
from the single slit and the light is normal to the slit.
• For a circular hole with diameter d, the center is a bright spot and the 1st dark ring is given by
d
22.1sin 1