4/22 do now – on a new sheet
• A car travels 80. meters due north in 15 seconds. Then
the car turns around and travels 40. meters due south in
5.0 seconds. What is the magnitude of the average
velocity of the car during this 20.-second interval? [show
work]
15-1 Refraction Objective
• Recognize situations in which refraction will
occur.
• Identify which direction light will bend when it
passes from once medium to another.
• Solve problems using Snell’s law
• Homework due:
1. Project
2. Castle learning review corrections
3. 15.1 reading assignment
4. Lab 19: wave on a string
• Homework assignment:
1. Castle learning
Broken pencil observation
• Every object that can be seen is seen only because light from that
object travels to our eyes.
Refraction of Light Waves
• Refraction is the bending of a wave disturbance as
it passes at an angle from one medium into
another.
• When a beam of light approaches a boundary at an
angle, it changes direction as it crosses the
boundary separating two medium.
Light enters the medium at an
angle (obliquely)
• 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.
Atmospheric Refraction
• 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/eyeDefec
ts.htm
The Cause of Refraction
• Refraction occurs across a boundary between two
media is caused 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.
The Ray Model of Light explains refreaction
• The ray of wave is constructed in a direction perpendicular to
the wave fronts of the light wave, which is the light wave's
direction. The idea that the path of light can be represented
by a ray is known as the ray model of light.
All wave
fronts are in
phase
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.
What we learned
• 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 Direction of Bending
The speed of a light wave is dependent upon the optical density of
the material through which it moves. Light travels faster in less
optically dense medium.
If a ray of light passes across the
boundary from a denser material into a
less dense material, such as from water
to air, the light ray will bend away from
the normal line.
If a ray of light passes across the
boundary from a less dense material
into a denser material, such as from air
to water, 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.
Class work – today’s date
1.
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?
a. Only speed changes.
b. Only direction changes.
c. Both speed and direction change.
d. Neither speed nor direction changes
2.
A change in the speed of a wave as it enters a new medium
produces a change in
frequency
period
wavelength
phase
a.
b.
c.
d.
3. 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
a. reflect light
b. diffract light
c. refract light
d. polarize light
4. What happens to the frequency and the speed of an
electromagnetic wave as it passes from air into glass?
a. The frequency decreases and the speed increases.
b. The frequency increases and the speed decreases.
c. The frequency remains the same and the speed increases.
d. The frequency remains the same and the speed decreases.
5.
a.
b.
c.
d.
6.
a.
b.
c.
d.
Which phenomenon of light accounts for the formation of
images by a lens?
reflection
refraction
dispersion
Polarization
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.
7.
a.
b.
c.
d.
Refraction of a wave is caused by a change in the
wave's
amplitude
frequency
phase
speed
8. The diagram represents wave fronts traveling from
medium X into medium Y. All points on any one wave
front shown must be
a. traveling with the same speed
b. traveling in the same medium
c. in phase
d. superposed
9.
a.
b.
c.
d.
•
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
A ray of monochromatic light is incident on an air-sodium
chloride boundary. At the boundary, part of the ray is reflected
back into the air and part is refracted as it enters the sodium
chloride.
10. 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)
11. 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
12. What occurs as light travels from alcohol into flint
glass? (hint: which material is denser? Check ref. tbl)
a. The speed of the light decreases and the ray bends
toward the normal.
b. The speed of the light decreases and the ray bends
away from the normal.
c. The speed of the light increases and the ray bands
toward the normal.
d. The speed of the light increases and the ray bends
away from the normal.
4/23 do now
• A child kicks a ball with an initial velocity of 8.5 meters
per second at an angle of 35º with the horizontal, as
shown in the diagram. The ball has an initial vertical
velocity of 4.9 m/s and a total time of flight of 1.0 second.
[Neglect air resistance.] What is the maximum height
reached by the ball? [show work]
Finish class work from yesterday
15-1 Refraction Objective
• Determine the relationship between optical
density and index of refraction.
• Define dispersion
• Solve problems using Snell’s law
• Homework assignment:
1. Castle learning
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?
diamond
• In what material the light travels fastest?
air
Index of refraction and ratio of wavelength
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
Dispersion – refraction of white light
• The separation of visible light into its different
colors is known as dispersion.
Wavelength affects index of refraction.
Index of red light is the smallest, it bends the least. While index
of violet light is greatest, it bends the most.
A brief review
bending
• Refraction is the _______________
of the path of a light
wave as it passes across the boundary separating two
speed
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
away from
_____________________
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.
towards
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 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.
• If θ1 is zero, θ2 will be zero, which means when light enters
perpendicularly to the boundary, it is not changing direction.
• 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.
45o
60o
32o
35o
Examples
1. 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.
2. 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.
Class work – today’s date
1. What occurs when light passes from water into flint
glass? (hint: which one is denser?)
a. Its speed decreases, its wavelength becomes smaller,
and its frequency remains the same.
b. Its speed decreases, its wavelength becomes smaller,
and its frequency increases.
c. Its speed increases, its wavelength becomes larger,
and its frequency remains the same.
d. Its speed increases, its wavelength becomes larger,
and its frequency decreases.
2.
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)
a. wavelength of light in a vacuum
b. frequency of light in water
c. sine of the angle of incidence
d. speed of light in a vacuum
3. 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?
4. 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.
5. 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.
6. 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?
7. Compared to the wavelength of a wave of green light in air,
the wavelength of this same wave of green light in Lucite is
a. less
b. greater
c. the same
8. A beam of monochromatic light travels through flint glass,
crown glass, Lucite, and water. In which material is the
speed of the light beam slowest?
9. 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?
Class work – today’s date
1.
The diagram shows a ray of light passing from a medium
X into air. What is the absolute index of refraction of
medium X?
2.
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?
What is the speed of light in
glycerol?
3.
4. A ray of light (λ = 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?
5.
a.
b.
c.
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.
6. 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?
a. X could be flint glass and Y could
be corn oil.
b. X could be corn oil and Y could be
flint glass.
c. X could be water and Y could be Medium Y has the same index as
glycerol.
glycerol, so it could be glycerol or
d. X could be glycerol and Y could be corn oil.
water.
Medium x has index higher than
glycerol, it could be flint glass
7. 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.]
a
c
b
d
8. 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?
9. 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?
10. 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?
4/24 do now
• A child kicks a ball with an initial velocity of 9.8 meters
per second at an angle of 30º with the horizontal.
[Neglect air resistance.] What is the maximum height
reached by the ball? [show work]
Finish class work from yesterday
15-1 Refraction Objective
• Define critical angle
• Determine conditions for total internal reflection
• Solve problems using Snell’s law
• Homework assignment:
1. Castle learning
2. Quiz on Hooke’s law on Friday
3. Lab 19 is overdue
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
The complete reflection of light at the boundary of two transparent
media; this effect occurs when the angle of incidence exceeds the
critical angle.
Critical angle
• The minimum angle of incidence for which total internal
reflection occurs.
• Since the maximum possible angle of refraction is 90o, the
corresponding incident angle is critical angle.
• 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?
• Given: (ni = 1.33, nr = 1.00, θr = 90o,
• Unknown: θi = ?
Solve: n1sinθ1 = n2sinθ2
1.33sinθi = (1.00)sin90o
θi = 48.7o
When the angles of incidence is greater than 48.6o (the
critical angle), all of the energy (the total energy) carried by
the incident wave to the boundary stays within the water
(internal to the original medium) and undergoes reflection
off the boundary.
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.
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 in an optical instrument will allow
light to undergo TIR 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.
Rainbows and bubbles – interference through TIR
Ray 1 & 2 interfere
Lens Aberrations
• Aberrations occurs when light rays enters the lens does not
focus on the same point.
• Spherical aberrations
happens due to the quality of
lens.
• Chromatic aberrations
happens due to different color
of light.
Class work – today’s date
1. For the following situations, indicate if TIR will happen or
not:
a. light traveling from water towards air;
b. light traveling from air towards water;
c. light traveling from water towards crown glass.
2. Calculate the critical angle for the crown glass-air
boundary.
3. Calculate the critical angle for the diamond-air boundary.
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, what is the angle of refraction?
5.
Total internal reflection can occur as light waves pass from
a. water to air
c. Lucite to crown glass
b. alcohol to glycerol
d. air to crown glass
6.
What is the critical angle for the Lucite-air boundary?
7.
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?
8.
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
9. 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
10. 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 1.50.
a. Determine the speed of this ray of light in material X.
b. Determine the frequency of this light in material X.
c. Determine the wavelength of this light in material X.
d. Draw a diagram to indicate the boundary, the normal,
the incident ray, the reflected ray and the refracted
ray.
Lab 36 – finding index of refraction
Purpose (5 pt): Determine the index of refraction of an unknown
material
Material (5 pt): Rectangular prism with unknown index of
refraction, Pins, Pencil, Plain paper, Cardboard,
Straightedge, Protractor
Data section (20 pt):
– should contain colomns of measured and calculated data.
The rows and columns should be labeled; units should be
identified. Work should be shown for one calculation; the
work should be labeled and easy to follow.
Conclusion/discussion of results (10 pt): Calculate the index
of refraction using Snell’s Law. Record your values for n in
the data table and calculate the average value of n.
1. Trace the prism on the white paper which is
placed on top of the card board.
2. Line up two pins obliquely to the prism, the
beam will refract into the prism and then the
beam will refract again into the air.
3. Use pins to mark the points of the refracted ray
by lining them up with the images of the pins
inside the prism. Trace incident ray to the prism
and refracted ray out of the prism. Connect two
points at the intersections with the prism.
Normal
Procedure: For each person in the group, trace the prism on a blank sheet of paper.
θi
Surface 1
θri
Surface 2
θi
3. Each person in the group must draw two diagrams to indicate incident rays and
refracted rays.
4. Measure the angles of incident and refracted rays. Read the angles to the nearest
1/10th of a degree.
5. Record each person’s data in the group on the data table. Every one in your group
should have a data table.
6. Calculate the index of refraction using Snell’s Law. Record your values for n in the
data table and calculate the average value of n.
Data table
trials
θi
θr
n
1
2
3
4
5
6
Average n is
nisinθi = nrsinθr
______________________