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 3: Refraction at a Boundary
Boundary Behavior
Refraction and Sight
The Cause of Refraction
Optical Density and Light Speed
The Direction of Bending
Lesson 4: The Mathematics of
Refraction
Snell's Law
Ray Tracing and ProblemSolving
Determination of n Values
Lesson 5: Total Internal Reflection
Boundary Behavior Revisited
Total Internal Reflection
The Critical Angle
Lesson 1: Reflection and its
Importance
The Role of Light to Sight
The Line of Sight
The Law of Reflection
Specular vs. Diffuse Reflection
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.
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.
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.
2. 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.
• 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
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 (θi). The angle between the reflected ray and the
normal is known as the angle of reflection (θr). 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.
θi = θr
example
• Identify which angle is angle of incidence
and which angle is angle of reflection.
• Incident angle
is ___
• Reflected angle
is _____
A
B
C
D
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?
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?
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)
• 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.
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.
practice
•
1.
2.
3.
4.
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
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?
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.
Image formation from plane mirrors
..\..\RealPlayer Downloads\07PPT03 Image
characteristics in a plane mirror.flv
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.
• the lateral inversion (left-right reversal).
example
• If Suzie stands 3 feet in front of a plane
mirror, how far from the person will her
image be located?
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?
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.
Practice – draw ray diagram
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
to view an image of yourself in a plane own image.
mirror, you will need an amount of
mirror equal to one-half of your
height.
example
•
1.
2.
3.
4.
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
example
•
1.
2.
3.
4.
When a ray of light strikes a mirror
perpendicular to its surface, the angle
of reflection is
0°
45°
60°
90°
example
•
1.
2.
3.
4.
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
example
•
1.
2.
3.
4.
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
example
•
1.
2.
3.
4.
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
example
•
•
1.
2.
3.
4.
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°
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?
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
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)
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.
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.
• 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.
• 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.freezeray.com/flashFiles/eyeDefects.htm
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 doesn’t 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.
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.
example
•
1.
2.
3.
4.
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
example
•
1.
2.
3.
4.
A change in the speed of a wave as it
enters a new medium produces a
change in
frequency
period
wavelength
phase
example
•
1.
2.
3.
4.
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
example
•
1.
2.
3.
4.
Which phenomenon of light accounts for
the formation of images by a lens?
reflection
refraction
dispersion
polarization
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?
1. It is reflected and converted to mechanical energy.
2. It is reflected, absorbed and energy is decreased.
3. It is all destroyed.
4. It is slowed down, dissolved and reflected.
example
•
1.
2.
3.
4.
Refraction of a wave is caused by a
change in the wave's
amplitude
frequency
phase
speed
example
•
1.
2.
3.
4.
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
example
• What happens to the frequency and the speed of an
electromagnetic wave as it passes from air into glass?
1. The frequency decreases and the speed increases.
2. The frequency increases and the speed decreases.
3. The frequency remains the same and the speed
increases.
4. The frequency remains the same and the speed
decreases.
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.
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.
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.
example
•
1.
2.
3.
4.
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
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.
1. 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)
2. 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)
example
•
1.
2.
3.
4.
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.
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.
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.
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 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.
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.
n∙v = c
Check your reference table
• Absolute indices of refraction:
• In what material the light travels slowest?
• In what material the light travels fastest?
example
•
1.
2.
3.
4.
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.
example
•
1.
2.
3.
4.
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
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?
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.
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.
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?
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?
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
1. less
2. greater
3. the same
example
•
1.
2.
3.
4.
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
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 = fλ1 and v2 = fλ2
v1/v2 = λ1/λ2
n2/n1 = v1/v2 = λ1/λ2
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?
The Mathematics of Refraction
1.
2.
3.
4.
The Angle of Refraction
Snell's Law
Ray Tracing and Problem-Solving
Determination of n Values
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?
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.
θi is the angle of incidence - the angle
which the incident ray makes with the
normal line.
θr 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.
Snell’s 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 Snell’s Law
n1/n2 = sinθ2/ sinθ1
n1sinθ1 = n2sinθ2
• Angles θ1 and θ2 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
• Snell's law applies to the refraction of light in any situation,
regardless of what the two media are.
• Snell’s law can be rearranged in this way
sinθ1/sinθ2 = n2/n1
• The ratio n2/n1 is called the relative index of refraction for the
two media.
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 θi, calculate θr, and draw in
the refracted ray with the calculated angle of
refraction.
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.
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.
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.
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?
example
•
A ray of light (λ = 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?
example
•
What is the speed of light in glycerol?
example
-7
• A ray of light (λ = 5.9 × 10 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?
example
•
1.
2.
3.
A ray of light (λ = 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.
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?
1. X could be flint glass and Y could
be corn oil.
2. X could be corn oil and Y could be
flint glass.
3. X could be water and Y could be
glycerol.
4. X could be glycerol and Y could be
water.
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
example
•
1.
2.
3.
4.
In the diagram, a ray of monochromatic light (λ = 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
example
• A beam of monochromatic light (λ = 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?
Determination of n Values
example
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?
Total internal reflection
Boundary Behavior Revisited
• A light wave, like any wave, is an energy-transport
phenomenon. A light wave transports ________
energy from one
location to another.
• When a light wave strikes a boundary between two distinct
transmitted
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
reflected
original medium.
Reflection
• _____________
of a light wave involves the bouncing of a
refraction
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
medium
wave, but only refraction involves a change in __________.
• 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:
n1sinθ1 = n2sinθ2
total internal reflection
http://www.upscale.utoronto.ca/PVB/Harrison/Flash/Optics/Refracti
on/Refraction.html
..\..\RealPlayer
Downloads\Light
refraction.flv
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:
n1sinθ1 = n2sinθ2
n1sinθcritical = n2sin90o
Example
• A laser beam is shining from water into air, what is the
critical angle of water?
Two Requirements for Total
Internal Reflection
•
1.
2.
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.
example
•
For the following situations, indicate if
TIR will happen or not:
1. light traveling from water towards air;
2. light traveling from air towards water;
3. light traveling from water towards crown
glass.
example
• Calculate the critical angle for the crown
glass-air boundary.
example
• Calculate the critical angle for the
diamond-air boundary.
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.
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.
example
•
1.
2.
3.
4.
A monochromatic light ray is passing from
medium A into medium B. The angle of
incidence,θ, is varied by moving the light
source, S. When the angle θ equals the critical
angle, the angle of refraction will be
0°
between 0° and 90°
between θ and 90°
90°
example
•
1.
2.
3.
4.
Total internal reflection can occur as light
waves pass from
water to air
Lucite to crown glass
alcohol to glycerol
air to crown glass
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?
A
B
C
D
example
•
1.
2.
3.
4.
In the diagram, a ray of monochromatic light (λ = 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
example
•
The diagram represents a beam of
monochromatic light (λ = 5.9 × 10-7 meter)
traveling from Lucite into air. What is the
critical angle for the Lucite-air boundary?
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?
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]