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Title: Final Exam Lectures EM Waves and Optics

1
Final Exam Lectures EM Waves and Optics
2
Electromagnetic Spectrum
3
Traveling EM Wave
• Maxwells equations predict the existence of em
waves propagating through space at the speed of
light
• The waves consist of oscillating E and B fields
that are perpendicular to each other and the
direction of wave propagation

4
EM Waves cont
• EM waves generated with transformers and LC
circuits
• EM waves is composed of changing E and B fields
and will therefore travel in a vacuum
• Maxwells equations can be used to develop a wave
equation from which the form of the waves can be
deduced

5
Properties of EM Waves
• The solutions of Maxwells equations are
wavelike, with both B and E satisfying a wave
equation.
• EM waves travel through a vacuum at the speed of
light.
• The components of the E and B fields of plane em
waves are perpendicular to each other and to the
direction of propagation (transverse waves)
• The magnitudes of E and B in empty space are
related by the expression
• EM waves obey the principle of superposition

6
Energy Transport
• Poynting vectorthe rate of energy transport per
unit area in an em wave
• Its units are
• The direction of the Poynting vector is the
direction of wave propagation
• Intensitythe time averaged value of S over one
or more cycles

7
• Radiation pressure is the linear momentum
transported by an em wave
• If the surface absorbs all the incident energy
• An example of this type of surface is a black
body
• If the surface is perfectly reflecting for a
normally incident wave
• An example of this type of surface is a mirror

8
Optics Definitions
• Geometrical opticsthe study of the properties of
light waves under the approximation that it
travels as a straight line (plane wave)
• Reflectionwhen light hits a surface and bounces
back
• Refractiontravel of light through a surface (or
interface) that separates 2 media. Light is bent
at the surface, but inside the medium it travels
in a straight line

9
• Index of refraction nassociated with a medium of
travel. It also depends on the wavelength of
light for all media except vacuum.
• Angle of incidence ?Ithe angle the light makes
to the normal to the surface when it hits the
surface
• Angle of reflection ?r the angle the light makes
to the normal to the surface when it bounces back
• Angle of transmission ?t the angle the light
makes to the normal to the surface inside the
surface

10
Polarization
• Polarization em waves which vibrate randomly in
all directions are filtered such that they
vibrate in one direction
• An E field component parallel to the polarizing
direction is passed (transmitted) by a polarizing
sheet a component perpendicular to it is absorbed

11
Reflection
• Law of reflection the angle of incidence equals
the angle of reflection
• Total internal reflection when all light
incident on a surface is reflected

12
Refraction
• Refraction the travel of light through an
interface (bending of light by an interface)
• Law of refraction (Snell's Law)

13
Definitions
• Imagethe reproduction derived from light of an
object. Images are located either at a point
from which light rays actually diverge or at the
point from which they appear to diverge.
• Virtual imageimage perceived to be on the
opposite side of the mirror from the object and
observer (no actual light)
• Real imageimage perceived to be on the same side
of the mirror as the object and observer (light)

14
More Definitions
• Mirrora surface which reflects a beam of light
in one direction, not scattering or absorbing it
• Plane mirrora flat reflecting surface (mirror).
Light diverges after reflection from this type of
mirror.
• Spherical mirrora mirror with a reflecting
surface like a section of a sphere. This mirror
focuses incoming parallel waves to a point

15
More Definitions
• Image length (y ) the perpendicular distance
of an image from the center of the mirror
• Object length (y)the perpendicular distance of
the object from the center of the mirror
• Magnification (M)a measure of the size of the
image compared to the size of the object

16
• the angle of incidence equals the angle of
reflection
• p (s) is positive for all images. Using the
convention an object or image in front of the
mirror (or the side light or an observer is) is
positive and an object or image behind the mirror
would be negative.
• i (s) is negative for virtual images, and
positive for real images

17
Plane Mirrors
• The magnification is always 1.
• The image is as far behind the mirror as the
object is in front of it (o -I or s-s).
• The image is virtual and upright (same
orientation as the object).
• The image has front-back reversal

18
Finding Images
• Point Source
• Draw 2 rays extending from the object to the
mirror
• Using law of reflection, reflect the 2 rays off
the mirror
• Extend the reflections back till the point where
they join
• This is the image of the point
• Extended Source
• Do the above steps for a point at the top of the
object and for a point at the bottom of the
object
• Draw in the rest

19
Spherical Mirror Definitions
• Concavecaved in spheres, looking from the
interior of the sphere. Light rays converge to a
real point after reflection therefore there is a
real focus
• Convexflexed out spheres, looking from the
exterior of the sphere. Light rays diverge after
reflection therefore there is a virtual focus

20
More Spherical Mirror Definitions
• Central (principal) axisextends through the
center of curvature of the sphere and through the
center of the mirror
• Paraxial raysrays which diverge from the object
to make a small angle with the principal axis
• Focus (focal point)point through which all
paraxial rays parallel to central axis reflect
through (a point on the central axis), or their
extensions for a convex mirror
• Focal length (f)the distance of the focus from
the center of the mirror

21
Concave Mirror Facts
• There is a smaller field of view than with plane
mirrors.
• The image is greater in size than the object.
• The focus is real.
• As the object is moved closer to the focal point,
the real, inverted image moves to the left. When
the object is on the focal point the image is
infinitely far to the left. When the object
moves past the focal point toward the mirror, the
image is virtual, upright, and enlarged.
• For a concave mirror the image goes out to
infinity for pltf (m increases) and image comes in
from infinity for pgtf (m increases from -infinity
to 0)

22
Convex Mirror Facts
• There is a greater field of view than with plane
mirrors.
• The image is smaller in size than the object.
• The focus is virtual.
• As the object distance increases, the virtual
image decreases in size and approaches the focal
point as the object distance approaches infinity

23
Locating Images By Drawing Rays
• A ray parallel to the central axis reflects
through the focal point.
• A ray passing through the focal point reflects
parallel to the central axis.
• A ray passing through the center of curvature
reflects along itself.
• A ray reflecting at the center of the mirror is
reflected symmetrically about the central axis

24
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25
• A ray consists of two parts
• Initial line from object to device
• Final line from device extending both sides of
the device (negative side of the device should be
dotted)

26
• Two rays I use for mirrors
• Initial is parallel to principal axis while final
is through focal point
• Initial is through focal point while final is
parallel
• Remember to extend the final on both sides of the
mirror

27
Mirror Type Plane Concave Concave Convex
i -p p lt f p gt f i lt p
Magnification M 1 M gt 1 M lt 0 0 lt M lt 1
Image Virtual Virtual Real Virtual
Orientation Same Same Inverted Same
Sign of f No f -
28
Lens Definitions
• Lensa transparent object with two refracting
surfaces whose central axes coincide (image
formed by first serves as the object for the
second)
• Converging lenscauses a light ray that is
initially parallel to the central axis to
converge to a point
• Diverging lenscauses a light ray that is
initially parallel to diverge
• Thin lensthickness of lens is much less than p,
i, r1, r2 (r1 is the radius of curvature of the
first lens surface and r2 is the radius of
curvature of the other lens surface)

29
Refraction
• If
• Then
• If
• Then
• Bend toward normal
• If
• Then
• Bend away from normal

30
Refraction from Spherical Surfaces
• If rays are bent toward the central axis, they
form a real image on that axis on the opposite
side of the surface from the object ( i)
• If rays are bent away from the central axis, they
form a virtual image on that axis on the same
side of the surface from the object (- i)

31
Spherical Surface Planar Surface
32
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33
Refraction cont
• convex surface is a converging lens
• concave surface is a diverging lens

34
Images from Thin Lenses
• A ray initially parallel to the central axis will
pass through the focal point f.
• A ray initially passing through the focal point f
(or its backward extension) emerges parallel to
the central axis.
• A ray initially directed toward the center of the
lens will emerge with no direction change

35
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36
• Two rays I use for lenses
• Initial is parallel to principal axis while final
is through focal point
• Initial and final are the same and through the
center of the device
• Remember to extend the final on both sides of the
mirror

37
Lens Type Converging (Convex) Diverging (Concave)
p gt f1 p lt f1
Magnification M lt 0 M gt 1 0 lt M lt 1
Image Real Virtual Virtual
Orientation Inverted Same Same
Sign of f -
38
Object produces image in 1st lens which is the
object for the 2nd.
39
Two Lens Systems
• Find the image formed by the first lens as if the
second lens is not present
• Draw a ray diagram for the second lens with the
image of lens 1 as the object of lens 2
• The second image formed is the final image for
the system
• One configuration of this is if the image formed
by the first lens is behind the second lens and
is used as a virtual object for the second lens
• The total magnification of the system will be

40
Human Eye
41
Human Eye
• Light enters the eye through the cornea, a
transparent structure.
• Behind the cornea is a clear liquid called the
aqueous humor.
• Next is a variable aperture called the pupil,
which is an opening in the iris.

42
Human Eye cont
• Next is a crystalline lens. The purpose of the
crystalline lens is to allow the eye to focus on
an object through a process called accommodation.
The ciliary muscle is situated in a circle
around the lens. Thin filaments called zonules
run from the muscle to the lens
• To focus the eye on a far object, the ciliary
muscle is relaxed which tightens the zonules on
the lens forcing it to flatten and increase its
focal length
• To focus the eye on a near object, the ciliary
muscle is tightened which relaxes the zonules on
the lens allowing it to bulge and decrease its
focal length

43
Human Eye cont
• Most refraction occurs at the outer surface of
the eye, where the cornea is covered with a film
of tears. Very little occurs in the lens because
the aqueous humor and the lens have very similar
index of refractions
• The iris is a muscular diaphragm that controls
the pupil size and therefore the intensity of
light that gets into the eye
• The cornea lens system of the eye focuses light
onto the back surface of the eye called the
retina, consisting of millions of little
receptors called rods and cones. When these
receptors are stimulated by light they send a
signal to the brain by way of the optic nerve
• In the brain the image is perceived and analyzed

44
Nearsightedness
• In nearsightedness the rays converge before they
meet the retina. A nearsighted person sees close
objects but not far. This means the far point is
much closer than infinity. A diverging lens
before the eye corrects this condition

45
Farsightedness
• In farsightedness the light rays reach the retina
before they converge. A farsighted person can
see far away objects but not near objects. That
means their near point is much farther away than
25 cm. The condition is corrected by putting a
converging lens before the eye

46
Two Lens Systems
• Find the image formed by the first lens as if the
second lens is not present
• Draw a ray diagram for the second lens with the
image of lens 1 as the object of lens 2
• The second image formed is the final image for
the system
• One configuration of this is if the image formed
by the first lens is behind the second lens and
is used as a virtual object for the second lens
• The total magnification of the system will be

47
Microscope
• Microscope used to view small objects with a
combination of two lenses to get greater
magnification
• One lens is called the objective and has a very
short focal length (lt 1 cm)
• The second lens is called the eyepiece and has a
longer focal length of a few centimeters

48
Telescope
• Two types of telescopes are used to view distant
objects, such as the planets in our Solar System
• The refracting telescope uses a combination of
lenses to form an image (uses two lenses, the
objective and the eyepiece)
• The reflecting telescope uses a curved mirror and
a lens

49
Aberrations
• Two types
• Spherical aberrations occur because the focal
points of rays far from the principal axis of a
spherical lens are different from the focal
points of rays of the same wavelength passing
near the axis (paraxial rays) Minimized by
surfaces
• Chromatic aberrations occur because different
wavelengths of light refracted from a lens focus
at different points Minimized by use of a
combination of a converging lens made of one type
of glass and a diverging lens made of another
type of glass

50
Interference
• Interference phenomena occur when 2 waves
combine.
• The effects occur where light reflected from the
front and back surfaces of a film interfere with
each other.
• Examples are colors seen in oil films or soap
bubbles.

51
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53
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54
Diffraction
• Diffraction occurs when many sources are present.
• These effect occur whenever a wave passes through
an aperture or around an obstacle.

55
Relativity Lecture
• Relativity
• Time Dilation
• Length Contraction
• Transformation Equations
• Review

56
Postulates
• Relativity postulate the laws of physics are
the same for observers in all inertial reference
frames
• Einstein extended this from Galileo (laws of
mechanics) to include electromagnetism and optics
• Speed of light postulate the speed of light in
vacuum has the same value c in all directions and
in all inertial reference frames
• Ultimate speed-no entity which carries energy or
information can exceed this limit c299792458
• Inertial reference frame frames in which
Newtons laws are valid (nonaccelerating)

57
Events
• Event something that happens to which an
observer can assign a set of coordinates
• Space, time, or spacetime

Construction to help picture spacetime X
coordinate from measuring rods and time
coordinate from clocks
58
Relativity
• Relativity deals with the measurement of events
and how they are related
• If two observers are in relative motion, they
will not, in general, agree as to whether two
events are simultaneous

59
Relativity - Simultaneity
• Consider Sam and Sally to the left
• Blue and Red events occur
• Sam sees them as simultaneous
• Sally sees the red event first (before Sam does),
and the blue event later
• Note both measure themselves halfway in between
(Sam conclude simultaneous and Sally concludes
red event happens first)

60
Time Dilation
• The time interval between two events depends on
how far apart they occur, in both space and time
• Proper time interval the time interval between
two events, which occur at the same location in
an inertial reference frame, measured in that
frame
• Measurements of the same time interval in any
other inertial reference frame are always greater

61
Time Dilation cont
62
Length Contraction
• The length of an object depends on which
reference frame it is measured in
• Proper length (rest length) the length of an
object measured in the rest frame of the object
• Measurements of the same length in any other
inertial reference frame are always less
• Length contraction occurs only along the
direction of relative motion

63
Transformation Equations
Lorentz Transformation Equations
Galilean Transformation Equations
64
Velocities
• Using the Lorentz eqs. we can compare the
velocities observed by 2 observers in frames
moving relative to each other

65
Momentum
• Momentum is also effected by speed
• Classically pmv
• Relativistically

66
Mass Energy
• Mass and energy are conserved together not
separately as assumed classically
• Nuclear reactions show us this
• Rest energy or mass energy
• Use units

67
Energy cont
It is impossible to increase speed to c because
it would require an infinite amount of energy
• The total energy (without potential energy)

68
Definitions
• Photon-packages of definite size containing the
energy of light that is emitted or absorbed.
• Energy levels-the possible energy values of the
internal energy of an atom.
• Photoelectric effect-the emission of electrons
from a surface of a conductor when light strikes
it.
• Threshold frequency-the minimum frequency of
monochromatic light which must strike a cathode
to produce a current.

69
Definitions continued
• Stopping potential (V0)-the reversed potential
difference required to stop the electron flow
completely in the photoelectric effect.
• Balmer series-the series of energy levels in
hydrogen discovered by Balmer.

70
Dual Nature of Light
• Controversy on Dual nature of light
• Wave nature supported by some phenomena
• Interference, Diffraction, Polarization
• Particle nature supported by other phenomena
• Emission and absorption of electromagnetic

71
Three main ideas
• Tells us energy associated with the emission and
absorption of light is quantized
• Existence of discrete energy levels in an atom
• Tells us energy associated with internal motion
of atoms is quantized
• Dual wave/particle nature of both particles of
• Electrons behave like waves in an atom they are
spatially spread out and obey a wave function
describing the distribution of the electron in
space.
• Cloudlike-more dense in some regions and less in
others

72
Photoelectric Effect
73
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74
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75
Energy Levels
76
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77
• Nuclear Physics
• Nuclear Properties

78
Nuclear Physics History
• Nuclear Physics the study of the nucleus of the
atom
• Plum pudding model the original theory of atom
structure, postulated by JJ Thompson. The
positive charge of the atom is spread throughout
the entire atom volume. The electrons vibrated
at fixed points within the sphere of positive
charge.
• Nuclear model positive charge of atom is
densely concentrated at the center of the atom
(nucleus), postulated by Ernest Rutherford.

79
Experiment for Nuclear model
• An alpha particle source (radon gas) shot alpha
particles at a gold foil.
• The angle of deflection of these particles was
studied.
• Most particles were deflected through small
angles
• A few were deflected through large angles
approaching 180 degrees.
• Analysis of the data implied the radius of the
nucleus was 104 times smaller than the radius of
the atom

80
Nuclear Properties
• Nucleus made up of protons and neutrons
• Atomic number Z - of protons
• Neutron number N - of neutrons
• Mass number A - of both protons neutrons

or
Gold for example
81
Isotopes
• Isotopes nuclide with same Z but different A
(different of neutrons)
• For a given element, they have the same
electrons and therefore the same chemical
properties
• The nuclear properties vary from 1 isotope to
another.
• Usually an element has one stable isotope and the
rest are radioactive and decay by emitting a
particle.

82
Nuclidic Chart
• There is a well defined band of stable nuclides
(green) with unstable above, below, and the upper
end of the chart.
• Light stable NZ
• Heavy stable NgtZ

83
Binding Energy
• Binding energy difference between mass M of a
nucleus and the sum of the masses of its
individual protons and neutrons
• Binding energy is a convenient measure of how
well a nucleus is held together

84
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85
• The nuclei high on the plot are very tightly
bound. (Ni)
• Those low on the plot are less tightly bound. (H
U)
• Consequence
• Right side nuclei would be more tightly bound if
split into 2 nuclei farther up the plot in the
process fission.
• Left side nuclei would be more tightly bound if
combined to form nucleus closer to top in the
process fusion

86
• Radioactive decay follows statistical laws.
• A 1 mg sample of U has ?1018 atoms. During any
second only 12 of them will decay and it is
impossible to predict which 12 will do it. All
have the same chance.
• Decay rate
• is decay constant (value is characteristic of
• N is in the sample at a given time
• R is the decay rate at a given time

87
Activity of a Sample
• R is called the activity of a sample
• 1 bacquerel 1 Bq 1 decay/s
• 1 curie 1 Ci 3.7x1010 Bq
• Half life ( ) the amount of time in which
both N R are reduced to half their original
value
• Mean life (?) the amount of time in which both
N R are reduced to e of their original value

88
Decay
• Alpha Decay nucleus emits an alpha particle
• Beta Decay nucleus emits an electron or
positron
• Gamma Decay nucleus emits a photon or gamma ray

89
Alpha Decay
• The nucleus emits an alpha particle and
transforms to a different nuclide.
• Spontaneous because total mass of the decay
products is less than the mass of the original
• Disintegration energy (Q) the difference
between the initial mass energy and the total
final mass energy

90
Beta Decay
• The nucleus emits an electron or positron
• ? is a neutrino

91
• Absorbed Dose a measure of the radiation dose
actually absorbed by a specific object
• SI unit 1 gray 1Gy 1 J/kg
• Dose Equivalent the biological effect of a
radiation source (found by multiplying absorbed
dose by RBE)
• SI unit 1 sievert 1 Sv 100 rem
• RBE (Relative Biological Factor)