Final%20Exam%20Lectures%20EM%20Waves%20and%20Optics

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Final Exam LecturesEM Waves and Optics
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Electromagnetic Spectrum
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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

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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

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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

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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

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Radiation Pressure

• 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

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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

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• 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

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Polarization

• Polarization em waves which vibrate randomly in
  all directions are made to 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

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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

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Refraction

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

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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)

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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

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More Definitions

• Image length (i ) the perpendicular distance of
  an image from the center of the mirror
• Object length (p)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

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Facts About all Mirrors

• the angle of incidence equals the angle of
  reflection
• p 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 is negative for virtual images, and positive
  for real images

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Plane Mirrors

• The magnification is always 1.
• The image is as far behind the mirror as the
  object is in front of it (p -i).
• The image is virtual and upright (same
  orientation as the object).
• The image has front-back reversal

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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

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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

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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

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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)

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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

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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

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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 -
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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)

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Refraction

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

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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)

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Spherical Surface Planar Surface
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Refraction cont

• convex surface is a converging lens
• concave surface is a diverging lens

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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

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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 -
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Object produces image in 1st lens which is the
object for the 2nd.
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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

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Human Eye
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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.

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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

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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

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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

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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

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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

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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

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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

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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
  adjustable apertures or parabolic reflecting
  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

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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.

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Diffraction

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

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Relativity Lecture

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

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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)

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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
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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

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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)

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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

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Time Dilation cont
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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

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Transformation Equations
Lorentz Transformation Equations
Galilean Transformation Equations
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Velocities

• Using the Lorentz eqs. we can compare the
  velocities observed by 2 observers in frames
  moving relative to each other

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Momentum

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

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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

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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)

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Review

• Ch 22 26 deals with electrostatics (charges
  that are not moving)
• Ch 26 28 deals with electrodynamics (moving
  charges)
• Ch 29 31 are dealing with magnetism an effect
  of moving charges
• Ch 32 33 deals with combining electricity and
  magnetism plus some of the uses of these concepts
• Ch 34 37 deals with geometric optics
• Ch 38 deals with relativity

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Radiation Lecture

• Nuclear Physics
• Nuclear Properties
• Radioactive Decay
• Radioactive Dating
• Radiation Dosage

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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.

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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

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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
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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.

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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

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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

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• 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

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Radioactive Decay

• 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
  every radio nuclide
• N is in the sample at a given time
• R is the decay rate at a given time

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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

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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

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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

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Beta Decay

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

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Radiation Dosage

• 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)
• Radiation RBE
• Electron x rays 1
• Slow neutrons 5
• Alpha particles 10

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• A whole body short term gamma ray dose of 3 Gy
  will cause death in 50 of the population exposed
  to it.
• Recommended radiation exposure is lt
  5mSv in a year.