Lesson 1: Reflection and its Importance

1

• Lesson 1 Reflection and its Importance
• The Role of Light to Sight
• The Line of Sight
• The Law of Reflection
• Specular vs. Diffuse Reflection

Chapter 11 reflection and refraction
Lesson 2 Image Formation in Plane Mirrors Image
Characteristics for Plane Mirrors What Portion
of a Mirror is Required to View an Image?
Lesson 4 The Mathematics of Refraction Snell's
Law Ray Tracing and Problem-Solving
Determination of n Values
Lesson 3 Refraction at a Boundary Boundary
Behavior Refraction and Sight The Cause of
Refraction Optical Density and Light Speed The
Direction of Bending
Lesson 5 Total Internal Reflection Boundary
Behavior Revisited Total Internal Reflection
The Critical Angle
2
Lesson 1 Reflection and its Importance
The Role of Light to Sight The Line of Sight
The Law of Reflection Specular vs. Diffuse
Reflection
3
The Role of Light to Sight

• Without light, there would be no sight.
• The objects which we see can be placed into one
  of two categories luminous objects and
  illuminated objects.
• Luminous objects are objects which generate their
  own light.
• Illuminated objects are objects which are capable
  of reflecting light to our eyes.
• The sun is an example of a luminous object, while
  the moon is an illuminated object.

4
The Line of Sight

• The line of sight is a straight line between your
  eye and the object. In order to view an object,
  you must sight along a straight line at that
  object and when you do, light will come from
  that object to your eye along the line of sight.

5
We use line of sight to determine image location

• In order to locate the image, two conditions must
  be satisfied

1. You must be able to see the image. One of the
   many rays of light from the object that approach
   the mirror and must reflect along your line of
   sight to your eye.

1. Since there is only one image for an object
   placed in front of a plane mirror, every sight
   line from different observing places would
   intersect in a single location. This location of
   intersection is known as the image location.

6
(No Transcript)
7

• The image is positioned directly across the
  mirror along a line which runs perpendicular to
  the mirror.
• The distance from the mirror to the object (known
  as the object distance) is equal to the distance
  from the mirror to the image (known as the image
  distance). For all plane mirrors, this equality
  holds true
• Object distance Image distance fro

8
The Law of Reflection

• The ray of light approaching the mirror is known
  as the incident ray (I). The ray of light which
  leaves the mirror is known as the reflected ray
  (R).
• At the point of incidence where the ray strikes
  the mirror, a line can be drawn perpendicular to
  the surface of the mirror. This line is known as
  a normal line (N). The normal line divides the
  angle between the incident ray and the reflected
  ray into two equal angles.
• The angle between the incident ray and the normal
  is known as the angle of incidence (?i). The
  angle between the reflected ray and the normal is
  known as the angle of reflection (?r). The law of
  reflection states that when a ray of light
  reflects off a surface, the angle of incidence is
  equal to the angle of reflection.

?i ?r
9
example

• Identify which angle is angle of incidence and
  which angle is angle of reflection.

• Incident angle is ___
• Reflected angle is _____

B
C
A
D
10
example

• A ray of light is incident towards a plane mirror
  at an angle of 30-degrees with the mirror
  surface. What will be the angle of reflection?

11
example

• A ray of light is approaching a set of three
  mirrors as shown in the diagram. The light ray is
  approaching the first mirror at an angle of
  45-degrees with the mirror surface. Trace the
  path of the light ray as it bounces off the
  mirror. Continue tracing the ray until it finally
  exits from the mirror system. How many times will
  the ray reflect before it finally exits?

12
Specular vs. Diffuse Reflection

• light reflects off surfaces in a very predictable
  manner - in accordance with the law of
  reflection. Once a normal to the surface at the
  point of incidence is drawn, the angle of
  incidence can then be determined. The light ray
  will then reflect in such a manner that the angle
  of incidence is equal to the angle of reflection.

The Law of Reflection is Always Observed
(regardless of the orientation of the surface)
13

• Specular reflection Reflection off of smooth
  surfaces such as mirrors or a calm body of water.
  
• Diffuse reflection Reflection off of rough
  surfaces such as clothing, paper, and the asphalt
  roadway.
• Each individual ray obeys the laws of reflection.

14
Why Does a Rough Surface Diffuses A Beam of Light?

• For each type of reflection, each individual ray
  follows the law of reflection. However, the
  roughness of the material means that each
  individual ray meets a surface which has a
  different orientation. The normal line at the
  point of incidence is different for different
  rays. Subsequently, when the individual rays
  reflect off the rough surface according to the
  law of reflection, they scatter in different
  directions. The result is that the rays of light
  are incident upon the surface in a concentrated
  bundle and are diffused upon reflection.

15
practice

• A ray is incident on a plane mirror at 25 degrees
  (incident angle). Draw a diagram to indicate the
• The surface of the mirror
• The line of normal
• The incident ray
• The reflected ray

16
Lesson 2 - Image Formation in Plane Mirrors

• Why is an Image Formed?
• Image Characteristics in Plane Mirrors
• Ray Diagrams for Plane Mirrors
• What Portion of a Mirror is Required to View an
  Image?

17
Why is an image formed?

• An image is formed because light gives off from
  an object in a variety of directions. Some of
  this light (which we represent by rays) reaches
  the mirror and reflects off the mirror according
  to the law of reflection. Each one of these rays
  of light can be extended backwards behind the
  mirror where they will all intersect at a point
  (the image point). Any person who is positioned
  along the line of one of these reflected rays can
  sight along the line and view the image - a
  representation of the object.

18
Image formation from plane mirrors
..\..\RealPlayer Downloads\07PPT03 Image
characteristics in a plane mirror.flv
19
Image characteristics in a plane mirror

1. An image has the same size as the object.
2. The image is as far behind the mirror as the
   object is in front of the mirror.
3. The image has the same orientation as the object.
4. The image is laterally inverted. (left and right
   reversal)
5. The image is virtual, no actual light meet at the
   image position. Virtual image can not be captured
   on a screen.

20

• the lateral inversion (left-right reversal).

21
example

• If Suzie stands 3 feet in front of a plane
  mirror, how far from the person will her image be
  located?

22
example

• If a toddler crawls towards a mirror at a rate of
  0.25 m/s, then at what speed will the toddler and
  the toddler's image approach each other?

23
Ray diagrams

• 1. Draw the image of the object.

2. Pick one extreme on the image of the object
and draw the reflected ray that will travel to
the eye as it sights at this point.
3. Draw the incident ray for light traveling from
the corresponding extreme on the object to the
mirror.
4. Repeat steps 2 and 3 for another extreme on
the object.
24
Practice draw ray diagram
25
What Portion of a Mirror is Required?

• Ray diagrams can be used to determine what
  portion of a plane mirror must be used in order
  to view an image.

• In order to view his image, the man must look as
  low as his feet, and as high as the tip of his
  head. The man only needs the portion of mirror
  extending between points X and Y in order to view
  his entire image. All other portions of the
  mirror are useless to the task of this man
  viewing his own image.

to view an image of yourself in a plane mirror,
you will need an amount of mirror equal to
one-half of your height.
26
example

• In the diagram, a light ray leaves a light source
  and reflects from a plane mirror. At which point
  does the image of the source appear to be
  located?
• A
• B
• C
• D

27
example

• When a ray of light strikes a mirror
  perpendicular to its surface, the angle of
  reflection is
• 0
• 45
• 60
• 90

28
example

• Parallel light rays are incident on the surface
  of a plane mirror. Upon reflection from the
  mirror, the light rays will
• converge
• diverge
• be parallel
• be scattered

29
example

• A plane mirror produces an image of an object.
  Compared to the object, the image appears
• inverted and the same size
• reversed and the same size
• inverted and larger
• reversed and larger

30
example

• When a student looks into a plane mirror, she
  sees a virtual image of herself.  However, when
  she looks into a sheet of paper, no such image
  forms.  Which light phenomenon occurs at the
  surface of the paper?
• regular reflection
• diffuse reflection
• polarization
• resonance

31
example

• In the diagram, a light ray, R, strikes the
  boundary of air and water.
• Look at the graph and estimate the approximate
  degree of the angle of incidence.
• 31
• 61
• 119
• 149

32
example

• A ray of light strikes a plane mirror at an angle
  of incidence equal to 45.  What is the angle
  between the incident ray and the reflected ray?

33
Objective - Refraction at a Boundary

• Refraction of Light Waves
• Refraction and Sight
• The Cause of Refraction
• Optical Density and Light Speed
• The Direction of Bending

34
Refraction of Light Waves

• Refraction is a boundary behavior. When a wave
  reaches the end of one medium and encounters
  another medium, the transmitted wave undergoes
  refraction (or bending) if it approaches the
  boundary at an angle (obliquely).
• When a beam of light approaches a boundary, it
  changes direction as it crosses the boundary
  separating two medium.
• Light only bends when incident at an angle.

Light enters the medium at an angle (obliquely)
35
The Ray Model of Light

• We will rely on the use of rays to represent the
  direction in which light is moving. The ray is
  constructed in a direction perpendicular to the
  wave fronts of the light wave this accurately
  depicts the light wave's direction. In this
  sense, we are viewing light as behaving as a
  stream of particles which head in the direction
  of the ray. The idea that the path of light can
  be represented by a ray is known as the ray model
  of light.

36
Refraction and Sight

• Every object that can be seen is seen only
  because light from that object travels to our
  eyes.
• When light passes from one medium into a second
  medium, the light path bends. Refraction takes
  place. When sighting at an object, light from
  that object changes media on the way to your eye,
  a visual distortion is likely to occur. This
  visual distortion is witnessed if you look at a
  pencil submerged in a glass half-filled with
  water.

37

• Since refraction of light occurs when it crosses
  the boundary, visual distortions often occur.
  These distortions occur when light changes medium
  as it travels from the object to our eyes.

38

• The refraction of light explains
• mirages
• visibility of the sun after it has actually
  disappeared below the horizon.

Image formed by lenses is refraction http//www.fr
eezeray.com/flashFiles/eyeDefects.htm
39
The Cause of Refraction

• The transmission of light across a boundary
  between two media is accompanied by a change in
  both the speed and wavelength of the wave.
• When light enters from denser to less dense
  (water to air), it speeds up. Since the frequency
  doesnt change, the light has a longer
  wavelength.
• When light enters from less dense to denser
  medium (air to water) it slows down and
  transforms into a wave with a shorter wavelength.
  
• The only time that a wave can be transmitted
  across a boundary, change its speed, and still
  not refract is when the light wave approaches the
  boundary in a direction which is perpendicular to
  it.
• As long as the light wave changes speed and
  approaches the boundary at an angle, refraction
  is observed. Changing speed is the cause of the
  light wave changes directions at the boundary.

40
Conditions of Refraction

• A light wave must enter the boundary at an angle
  (obliquely) in order to bend. A light wave will
  not undergo refraction if it approaches the
  boundary in a direction which is perpendicular to
  it.

41
example

• The diagram shows a ray of light passing from air
  into glass at an angle of incidence of 0. Which
  statement best describes the speed and direction
  of the light ray as it passes into the glass?
• Only speed changes.
• Only direction changes.
• Both speed and direction change.
• Neither speed nor direction changes

42
example

• A change in the speed of a wave as it enters a
  new medium produces a change in
• frequency
• period
• wavelength
• phase

43
example

• The diagram shows how an observer located at
  point P on Earth can see the Sun when it is below
  the observer's horizon.   This observation is
  possible because of the ability of the Earth's
  atmosphere to
• reflect light
• diffract light
• refract light
• polarize light

44
example

• Which phenomenon of light accounts for the
  formation of images by a lens?
• reflection
• refraction
• dispersion
• polarization

45
example

• Base your answer to the question on the diagram
  below, which represents a ray of monochromatic
  light (f 5.09 1014 hertz) in air incident on
  flint glass. what happens to the light from the
  incident ray that is not refracted?
• It is reflected and converted to mechanical
  energy.
• It is reflected, absorbed and energy is
  decreased.
• It is all destroyed.
• It is slowed down, dissolved and reflected.

46
example

• Refraction of a wave is caused by a change in the
  wave's
• amplitude
• frequency
• phase
• speed

47
example

• The diagram represents wave fronts traveling from
  medium X into medium Y. All points on any one
  wave front shown must be
• traveling with the same speed
• traveling in the same medium
• in phase
• superposed

48
example

• What happens to the frequency and the speed of an
  electromagnetic wave as it passes from air into
  glass?
• The frequency decreases and the speed increases.
• The frequency increases and the speed decreases.
• The frequency remains the same and the speed
  increases.
• The frequency remains the same and the speed
  decreases.

49
The Direction of Bending

• Refraction is the bending of the path of a light
  wave as it passes from one material into another
  material. The refraction occurs at the boundary
  and is caused by a change in the speed and
  wavelength of the light wave upon crossing the
  boundary.
• The tendency of a ray of light to bend one
  direction or another is dependent upon whether
  the light wave speeds up or slows down upon
  crossing the boundary.
• The speed of a light wave is dependent upon the
  optical density of the material through which it
  moves.

50
Light Traveling from a Fast (less dense) to a
Slow (denser) Medium

• If a ray of light passes across the boundary from
  a material in which it travels fast into a
  material in which travels slower, then the light
  ray will bend towards the normal line.

Note the incident ray and the refracted ray are
on the opposite side of the normal line.
51
Light Traveling from a Slow (denser) to a Fast
(less dense) Medium

• If a ray of light passes across the boundary from
  a material in which it travels slow into a
  material in which travels faster, then the light
  ray will bend away from the normal line.

Note the incident ray and the refracted ray are
on the opposite side of the normal line.
52
example

• The diagram shows a ray of light, R , entering
  glass from air. Which path is the ray most likely
  to follow in the glass?
• A
• B
• C
• D

53
example

• A ray of monochromatic light is incident on an
  air-sodium chloride boundary as shown in the
  diagram below. At the boundary, part of the ray
  is reflected back into the air and part is
  refracted as it enters the sodium chloride.
• Compared to the ray's angle of incidence in the
  sodium chloride, the ray's angle of reflection in
  the air is _______ (smaller, larger, the same)
• Compared to the ray's angle of incidence in the
  sodium chloride, the ray's angle of refraction in
  the sodium chloride is ___________ (smaller,
  larger, the same)

54
example

• What occurs as light travels from alcohol into
  flint glass? (hint which material is denser?
  Check ref. tbl)
• The speed of the light decreases and the ray
  bends toward the normal.
• The speed of the light decreases and the ray
  bends away from the normal.
• The speed of the light increases and the ray
  bands toward the normal.
• The speed of the light increases and the ray
  bends away from the normal.

55
Dispersion refraction of white light

• The separation of visible light into its
  different colors is known as dispersion.

Different wavelength corresponds to different
colors. Red color bends the least, violet color
bends the most.
56
Optical Density and Light Speed

• An electromagnetic wave (i.e., a light wave) is
  produced by a vibrating electric charge. As the
  wave moves through the vacuum of empty space, it
  travels at a speed of c (3 x 108 m/s).
• When light wave moves through a medium that is
  not vacuum, its speed slows down due to the
  collision with the particles in the medium.

• the speed of the wave depends upon the optical
  density of that material. The optical density of
  a medium is not the same as its physical density.

57
Optical Density and the Index of Refraction

• One indicator of the optical density of a
  material is the absolute index of refraction
  value of the material.
• Absolute index of refraction, n, is the ratio of
  the speed of light in a vacuum, c, to the speed
  of light in a material medium, v.

n c / v
A vacuum is given an n value of 1.0.
The product of the absolute index of refraction
of a material and the speed of light in that
material is 3.00 x 108 m/s, the speed of light in
vacuum.
The absolute index of refraction has no units.
The greater the value of n, the denser the
medium and the slower light travels in the
medium, the shorter the wavelength.
nv c
58
Check your reference table

• Absolute indices of refraction
• In what material the light travels slowest?
• In what material the light travels fastest?

59
example

• What occurs when light passes from water into
  flint glass? (hint which one is denser?)
• Its speed decreases, its wavelength becomes
  smaller, and its frequency remains the same.
• Its speed decreases, its wavelength becomes
  smaller, and its frequency increases.
• Its speed increases, its wavelength becomes
  larger, and its frequency remains the same.
• Its speed increases, its wavelength becomes
  larger, and its frequency decreases.

60
example

• Which quantity is equivalent to the product of
  the absolute index of refraction of water and the
  speed of light in water? (hint n c / v)
• wavelength of light in a vacuum
• frequency of light in water
• sine of the angle of incidence
• speed of light in a vacuum

61
example

• If the speed of light in a medium is 2.00 x 108
  m/s, what is the absolute index of refraction for
  the medium?

62
example

• A ray of light (f 5.09 1014 Hz) is incident on
  the boundary between air and an unknown material
  X at an angle of incidence of 55. The absolute
  index of refraction of material X is 1.66.
• Determine the speed of this ray of light in
  material X.

63
example

• A ray of light of frequency 5.09x1014 hertz is
  incident on a water-air interface. Calculate the
  speed of the light while in the water.

64
example

• The speed of light (f 5.09 1014 Hz) in a
  transparent material is 0.75 times its speed in
  air. What is the absolute index of refraction of
  the material?

65
example

• The speed of light (f 5.09 1014 Hz) in a
  transparent material is 0.75 times its speed in
  air. What is the absolute index of refraction of
  the material?

66
example

• Compared to the wavelength of a wave of green
  light in air, the wavelength of this same wave of
  green light in Lucite is
• less
• greater
• the same

67
example

• A beam of monochromatic light travels through
  flint glass, crown glass, Lucite, and water. The
  speed of the light beam is slowest in
• flint glass
• crown glass
• Lucite
• water

68
When Light travel from medium 1 to medium 2

• n1 c/v1
• n2 c/v2
• n2/n1 v1/v2
• Since frequency of the wave does not change
• v1 f?1 and v2 f?2
• v1/v2 ?1/?2

n2/n1 v1/v2 ?1/?2
69
example

• The frequency of a ray of light is 5.09 x 1014
  Hz. What is the ratio of the speed of this ray in
  diamond to its speed in zircon?

70
The Mathematics of Refraction

1. The Angle of Refraction
2. Snell's Law
3. Ray Tracing and Problem-Solving
4. Determination of n Values

71
A brief review

• Refraction is the _______________ of the path of
  a light wave as it passes across the boundary
  separating two media. Refraction is caused by the
  change in _________ experienced by a wave when it
  changes medium.
• If a light wave passes from a medium in which it
  travels slow (relatively speaking) into a medium
  in which it travels fast, then the light wave
  will refract _____________________ the normal.
• On the other hand, if a light wave passes from a
  medium in which it travels fast (relatively
  speaking) into a medium in which it travels slow,
  then the light wave will refract _______________
  the normal.

Question By how much does light refract when it
crosses a boundary?
72
The Angle of Refraction

• The amount of refraction of a ray is measured by
  the angle of refraction. It is the angle between
  a ray emerging from the interface of two media
  and the normal to that interface at the point
  where the ray emerges.
• Note the angle of refraction and the angle of
  incidence are on the opposite side of the normal.

?i is the angle of incidence - the angle which
the incident ray makes with the normal line. ?r
is the angle of refraction - the angle which the
refracted ray makes with the normal line.
The amount of angle of refraction depends upon
the properties of the two media at the interface.
73
Snells law

• The general relationship governs the refraction
  of light as it passes obliquely from one medium
  to another of different optical density is known
  as Snells Law
• Angles ?1 and ?2 are the angles of incidence and
  refraction respectively, and n1 and n2 are the
  absolute indices of the incident and refractive
  media, respectively.
• ..\..\RealPlayer Downloads\Snell's Law.flv

n1sin?1 n2sin?2
n1/n2 sin?2/ sin?1
74

• Snell's law applies to the refraction of light in
  any situation, regardless of what the two media
  are.
• Snells law can be rearranged in this way
• sin?1/sin?2 n2/n1
• The ratio n2/n1 is called the relative index of
  refraction for the two media.

75
Using Snell's Law to Predict An Angle Value

• Use Snell's law, a protractor, and the index of
  refraction values to complete the following
  diagrams. Measure ?i, calculate ?r, and draw in
  the refracted ray with the calculated angle of
  refraction.

76
example

• A ray of light in air is approaching the boundary
  with water at an angle of 52 degrees. Determine
  the angle of refraction of the light ray.

77
example

• A ray of light in air is approaching the a layer
  of crown glass at an angle of 42.0o. Determine
  the angle of refraction of the light ray upon
  entering the crown glass and upon leaving the
  crown glass.

78
An important concept

• When light approaches a layer which has the shape
  of a parallelogram that is bounded on both sides
  by the same material, then the angle at which the
  light enters the material is equal to the angle
  at which light exits the layer.

79
example

• The diagram shows a ray of light passing from a
  medium X into air. What is the absolute index of
  refraction of medium X?

80
example

• A ray of light (? 5.9 10-7 meter) traveling
  in crown glass is incident on a diamond interface
  at an angle of 30.. What is the angle of
  refraction for the light ray?

81
example

• What is the speed of light in glycerol?

82
example

• A ray of light (? 5.9 10-7 meter) traveling
  in air is incident on an interface with medium X
  at an angle of 30.. The angle of refraction for
  the light ray in medium X is 12. What could be
  the medium X?

83
example

• A ray of light (? 5.9 10-7 meter) traveling
  in air is incident on a diamond interface at an
  angle of 60.
• Draw the reflected ray.
• Determine the angle of refraction for the light
  ray. show work
• Draw this refracted ray.

84
example

• A beam of monochromatic light (f 5.09 1014
  hertz) passes through parallel sections of
  glycerol, medium X, and medium Y as shown in the
  diagram below. What could medium X and medium Y
  be?
• X could be flint glass and Y could be corn oil.
• X could be corn oil and Y could be flint glass.
• X could be water and Y could be glycerol.
• X could be glycerol and Y could be water.

85
example
A ray of monochromatic light traveling in air
enters a rectangular glass block obliquely and
strikes a plane mirror at the bottom.  Then the
ray travels back through the glass and strikes
the air-glass interface.  Which diagram best
represents the path of this light ray?  N
represents the normal to the surface.
1
3
2
4
86
example

• In the diagram, a ray of monochromatic light (?
  5.9 10-7 meter) reaches the boundary between
  medium X and air and follows the path shown.
  Which medium is most likely medium X?
• diamond
• flint glass
• Lucite
• water

87
example

• A beam of monochromatic light (? 5.9 10-7
  meter) crosses a boundary from air into Lucite at
  an angle of incidence of 45.  What is the angle
  of refraction?

88
Determination of n Values
89
example
90
example

• A monochromatic ray of light (f  5.09
  1014 hertz) traveling in air is incident upon
  medium A at an angle of 45. If the angle of
  refraction is 29, what could medium A be?

91
Total internal reflectionBoundary Behavior
Revisited

• A light wave, like any wave, is an
  energy-transport phenomenon. A light wave
  transports ________ from one location to another.
  
• When a light wave strikes a boundary between two
  distinct media, a portion of the energy will be
  _____________ into the new medium and a portion
  of the energy will be ________________ off the
  boundary and stay within the original medium.
• _____________ of a light wave involves the
  bouncing of a light wave off the boundary, while
  ______________ of a light wave involves the
  bending of the path of a light wave upon crossing
  a boundary and entering a new medium. Both
  reflection and refraction involve a change in
  direction of a wave, but only refraction involves
  a change in __________.

energy
transmitted
reflected
Reflection
refraction
medium
92

• The fundamental law which governs the reflection
  of light is called the law of reflection - When a
  light ray reflects off a surface, the angle of
  incidence is equal to the angle of reflection.

• The fundamental law which governs the refraction
  of light is Snell's Law

n1sin?1 n2sin?2
93
total internal reflection
http//www.upscale.utoronto.ca/PVB/Harrison/Flash/
Optics/Refraction/Refraction.html
..\..\RealPlayer Downloads\Light refraction.flv
94
Critical angle

• The maximum possible angle of refraction is 90o.
• There is some specific value for the angle of
  incidence (we'll call it the critical angle)
  which yields an angle of refraction of 90o.
• This particular value for the angle of incidence
  could be calculated using Snell's Law

n1sin?1 n2sin?2
n1sin?critical n2sin90o
95
Example

• A laser beam is shining from water into air, what
  is the critical angle of water?

96
Two Requirements for Total Internal Reflection

• Total internal reflection (TIR) is the phenomenon
  which involves the reflection of all the incident
  light off the boundary. TIR only takes place when
  both of the following two conditions are met
• the light is in the denser medium and approaching
  the less dense medium.
• the angle of incidence is greater than the
  so-called critical angle.

97
example

• For the following situations, indicate if TIR
  will happen or not
• light traveling from water towards air
• light traveling from air towards water
• light traveling from water towards crown glass.

98
example

• Calculate the critical angle for the crown
  glass-air boundary.

99
example

• Calculate the critical angle for the diamond-air
  boundary.

100
TIR and the Sparkle of Diamonds

• Relatively speaking, the critical angle for the
  diamond-air boundary is an extremely small
  number. This property about the diamond-air
  boundary plays an important role in the
  brilliance of a diamond gemstone. Having a small
  critical angle, light has the tendency to become
  "trapped" inside of a diamond once it enters. A
  light ray will typically undergo TIR several
  times before finally refracting out of the
  diamond.

101
More examples of TIR
A prism will allow light to undergo total
internal reflection whereas a mirror allows light
to both reflect and refract. So for a prism, 100
percent of the light is reflected. But for a
mirror, only about 95 percent of the light is
reflected.
102
example

• A monochromatic light ray is passing from medium
  A into medium B.  The angle of incidence,?, is
  varied by moving the light source, S. When the
  angle ? equals the critical angle, the angle of
  refraction will be
• 0
• between 0 and 90
• between ? and 90
• 90

103
example

• Total internal reflection can occur as light
  waves pass from
• water to air
• Lucite to crown glass
• alcohol to glycerol
• air to crown glass

104
example
A ray of monochromatic light is traveling in
flint glass.  The ray strikes the flint glass-air
interface at an angle of incidence greater than
the critical angle for flint glass.  Which
diagram best represents the path of this light
ray? 
B
A
C
D
105
example

• In the diagram, a ray of monochromatic light (?
  5.9 10-7 meter) reaches the boundary between
  medium X and air and follows the path shown.
  Which medium is most likely medium X?
• diamond
• flint glass
• Lucite
• water

106
example

• The diagram represents a beam of monochromatic
  light (? 5.9 10-7 meter) traveling from
  Lucite into air. What is the critical angle for
  the Lucite-air boundary?

107
example

• The absolute index of refraction for a substance
  is 2.0 for light having a wavelength of 5.9
  10-7 meter.  In this substance, what is the
  critical angle for light incident on a boundary
  with air?

108
example

• A ray of light (f  5.09 1014 Hz) is incident on
  the boundary between air and an unknown
  material X at an angle of incidence of 55, as
  shown. The absolute index of refraction of
  material X is 1.66. Determine the speed of this
  ray of light in material X. show all work,
  including equation and substitution with units