Refraction of Light

1
Refraction of Light
2
Substance Index of
Refraction Solids at 20ºC Diamonds
2.419 Glass, crown 1.52 Ice
(0ºC) 1.309 Sodium chloride
1.544 Quartz Crystalline 1.544
Fused 1.458 Liquids at
20ºC Benzene 1.501 Carbon
tetrachloride1.461 Ethyl alcohol
1.362 Water 1.333 Gases at
0ºC, 1 atm Air
1.00029 Carbon dioxide 1.00045 Oxygen, O2
1.00027 Hydrogen H2 1.00013
bending
Recall that refraction is the __________ of light
as it crosses a boundary between two media due to
the light beam traveling at different speeds in
each medium.
Optical Density- a property of a material which
indicates the ________ with which light travels
through it. A large optical density
indicates that light travels ___________ through
the material. (the opposite is true for a small
index of refraction). Index of Refraction ( )
the ratio of speed of light in a vacuum (Cv)
to the speed of light in a certain material (
). n Cv/ Cm n has ___ units because it is
a ratio of speeds
speed
slowly
n
Cm
no

• Since light travels faster in a vacuum than any
  material, n will
• always be ___________ than 1. (See table to the
  right)
• Visual look at Refraction
• As light travels from a less optically dense
  medium
• ( ________ speed) to a more optically dense
  medium (slower
• speed), the light bends __________ the normal to
  the surface.
• This is like light traveling through the air and
  striking a water surface. Interactive figure
  28.14

greater
faster
towards
3
2. Some of the light that strikes the boundary
will be reflected back into the original medium
(about ___ for light striking water from air). 3.
Note that the angles of incidence and refraction
are measured relative to the ________of the
surface. 4. As light travels from a more
optically dense medium to a less optically dense
medium, the light bends ___________ from the
normal of the surface. Again, some of the light
rays are reflected back into the original medium.
Interactive figure 28.36 Snells Law shows the
relationship of the angle of incidence and the
angle of refraction through the __________ of
refraction of light in each medium (n).
2
normal
away
index
n1 sin ?1 n2 sin ?2 ?1 angle of
incidence ?2 angle of refraction Example A
ray of light strikes an air/water interface at an
angle of 46o to the normal. Determine the angle
of refraction if the direction of the wave is
from a. air into water b. water into air
n1 sin ?1 n2 sin ?2 b. ?2 sin -1( n1 sin ?1/
n2) ?2 sin-1(1.333 sin (46o) / 1.00029) ?2
73o

• n1 sin ?1 n2 sin ?2
• ?2 sin -1(n1 sin ?1/ n2)
• ?2 sin-1(1.00029 sin (46o) / 1.333)
• ?2 33o

4
Apparent Depth 1. Due to the refraction of
light, objects appear to be closer than they
actually are when submerged in ___________ (that
is if your eye is in air). This is due to the
bending of light which makes it appear that the
light comes form a different direction than it is
in reality. 2. Apparent depths can be calculated
by the equation d1 n1 d2 n2 (or
use a factor label approach) d1 apparent depth
and n1 is measured from the medium in which the
object rests. d2 actual depth and n2 is
measured in the other medium which the light
propagates. Example Janet Evans, a swimmer, is
treading water at the surface of a 3.00 m deep
pool. She sees a coin on the bottom slightly at
an angle below, how deep does the coin appear to
be? 2.25 m
water
1.00029 1.333
? m 3.00 m
Homework 1a. What is the index of refraction?
b. What units are used to indicate index of
refraction. c. Is the index of refraction always
less than or greater than 1? Why? 2. What does
optical density measure? 3a. When a light beam
travels from a medium of high optical density to
low optical density, does it bend toward
or away from the normal? b. Draw a picture to
indicate this. 4a. Do objects submerged in water
appear to be deeper or closer to the surface of
the water than they really are? b. If
an object has an apparent depth of 10.0 m in
water from an observer above the surface of the
water, what is the actual depth of the
object? 5. A ray enters a liquid from air at an
incident angle of 40.0º to the normal and is
refracted an angle of 24.0º. What is the
index of refraction of the liquid? 6. The index
of refraction of water is 1.333, calculate the
speed of light in water. (remember to use the
equation for the index of refraction)

• Day-Night Car Mirrors
• Rear-view car mirrors can be adjusted to make
• ______ amounts of light strike our eyes
  from
• objects behind us or can be adjusted to
  allow
• __________ amounts of light to strike our
  eyes
• from bright car headlights behind us.
• In the day time position, light _______________
• by glass, is observed by our eyes.
• In the night time position, light
  _________________
• by glass is observed by our eyes. This
  allows only about 4 of the incident light to
  reach our eyes.

large
small
refracted
reflected
5

• Mirages
• When the air is warm near the grounds surface,
  but cooler above the surface,
• _________________ of light will occur (light
  travels ___________ in warm air than cold
• air). The bending of light from distant objects
  can produce images that appear to be
• reflections from a puddle of water. These are
  called ____________.
• Critical Angle and Total Internal Reflection
• 1. As light travels from a medium of
  ____________ optical density (slow speed) into a
  medium of lesser optical density (more speed),
  light bends ________ from the normal.
• 2. Here, we can notice that the angle of
  incidence will be _______ than the angle of
  refraction.
• 3. As we ______________ the angle of incidence
  we reach a point where the angle of refraction is
  90º.
• 4. At this point, the refracted light travels
  along the ____________________. This incident
  angle is referred to as the ___________ angle.
• 5a. At angles greater than the critical angle
  ___ light enters the second medium, but is
  entirely reflected back into the original medium.
• The reflection of all incident light back into
  the medium from which it came is called
  ___________ ___________ _____________.
• 6. Total internal reflection will only happen
  when light travels from a high optical density to
  a _________ optical density due to the angle of
  incidence always being ____________ than the
  angle of refraction in this situation.

refraction
faster
mirages
high
away
less
increase
boundary
critical
no
total internal reflection
low
smaller
6
The critical angle can be calculated using
Snells Law n1 sin ?1 n2 sin ?2 sin ?1 (n2
/ n1)sin ?2 (?2 90º sin90º 1) sin ?1
n2 / n1 The critical angle is an incident angle
so ?1 ?c Therefore sin ?c n2/n1 when
(n1 gt n2)

• Examples
• A beam of light is propagating through diamond (
  n 2.42) and strikes a diamond-air interface at
  an angle of 28º.
• Will the beam enter into the air
  b. If water rather than air surrounds the
• or will the beam be totally reflected
  diamond, will the ray be totally internally
• back into the diamond? reflected back
  into the diamond or enter the water?

a. sin ?c n2 / n1 ?c sin-1 ( n2 / n1) ?c
sin-1(1.00029 / 2.42) ?c 24.4o It will be
totally internally reflected
a. sin ?c n2 / n1 ?c sin-1 ( n2 / n1) ?c
sin-1(1.333 / 2.42) ?c 33.4o No it will enter
the water
7

• Questions and Problems
• 1. What is a mirage and how is it formed on dry
  pavement?
• 2. When shining a beam of light toward a media
  barrier from the air into water
• a. How do the angles of incidence and
  refraction compare? (Show a diagram of this)
• b. Can a critical angle be obtained? c. Is
  any light reflected from the surface?
• 3. When shining a beam of light from water into
  air
• a. How do the angles of incidence and
  refraction compare? (Show a diagram of this)
• b. How does the light behave at angles greater
  and less than the critical angle?
• 4a. A ray of light is incident upon a sheet of
  crown glass from the air at an angle of 0º to the
  normal,
• what is the angle of refraction? (Show
  a picture of this)
• b. A ray of light is incident upon a sheet of
  crown glass from the air at an angle of 30º to
  the normal,
• what is the angle of refraction? (Show a picture
  of this)
• c. A ray of light travels at an angle of 37º
  from crown glass into the air. What is the angle
  of refraction?
• (Show a picture of this)
• d. What is the critical angle of light traveling
  from crown glass into the air?
• 5. What is the critical angle of light traveling
  from crystalline quartz into air?
• When a car rear-view mirror is adjusted for night
  driving, does the driver observe reflected or
• refracted light from the car behind?

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Refraction of Light II Applications of Total
Internal Reflection (pg. 541-546) 1. Fiber
Optic small glass fibers which pipe light from
one area to another in order to pass video,
telephone, or computer ___________. a. Light
inside of a fiber optic cable bounces around at
angles ___________ than the critical angle.
Since all of the light is reflected, the signal
can be carried 100s of miles without diminishing
in ___________. (pg. 546) b. Fiber optic
cables are also used in medicine. A fiber optic
cable can be sent through the esophagus to look
for stomach __________ or abnormalities. It is
also used in arthroscopic surgery. Here, the
surgeon places a small surgical instrument on a
_________ optic. This way the surgeon can make a
tiny incision and insure minimal damage to
surrounding tissue. 2. Used in binoculars and
telescopes (pg. 544) Glass ____________
can be used to turn beams of light 90º or 180º .
The critical angle for a glass-air interface is
_____. At an angle greater than 42º, the light
is totally internally _____________. 3. It is
the reason that diamonds _____________. (pg.
545). a. When a light ray enters diamond from
the air, the light is _____________ into the
diamond. b. In the figure light strikes
the bottom facet at an angle greater than the
critical angle. Therefore the light is totally
___________________ reflected. c. This light
will eventually emerge from the top of the
diamond and be seen as a ____________.
information
greater
intensity
ulcers
fiber
prisms
42o
reflected
sparkle
refracted
internally
sparkle
9

• Dispersion of Light Prisms and Rainbows (pg.
  541-543)
• 1. Prisms- can separate light into its component
  _______ ( ).
• a. The figure shows light entering a prism being
  bent toward the normal.
• b. As the light exits the prism, it bends
  __________ from the normal.
• c. The visible light separates into all colors
  because each ______________ (color) of
• visible light has a different value of index
  of refraction ( ). See table below.
• d. Notice that the color red has a __________
  index of refraction than violet.
• e. Since, the degree of refraction will be
  greater when ___ values are greater, violet will
• be refracted more than red.
• (The order from least bending to most bending
  would be ______________).
• Approximate Wavelength
  Crown Flint
• Color in Vacuum (nm)
  Glass Glass Diamond
• Red 660
  1.520 1.662
  2.410
• Yellow 580
  1.523 1.667
  2.417
• Blue 470
  1.531 1.684
  2.444
• Violet 410
  1.538 1.698
  2.458
• 2. Rainbows occur after rainstorms when a
  _____ sun is at your back.
• When a sunlight ray emerges from a raindrop it is
  __________ into its
• component colors.

ROYGBIV
colors
away
wavelength
n
smaller
n
ROYGBIV
low
separated
more
1
altitudes
least
lower
violet
10

• Questions
• How are fiber optics used?
• 2. Why do diamonds sparkle?
• 3a. How does refraction of visible light depend
  upon the wavelength of light in crown glass?
• b. How can this be applied to the dispersion
  of visible light in a prism?
• 4. How is total internal reflection utilized in
  binoculars?
• 5a. What conditions are necessary to view a
  rainbow?
• b. How does a raindrop act similar to a prism?
• c. Since each drop separates all colors of
  light, why do we need to observe raindrops
• located at different altitudes?
• d. Why will a rainbow from an airplane appear
  to be a complete circle?

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• Lenses
• 2 Types of Lenses See figure 28.42 pg. 546
• Converging Lens will cause light rays ___ to
  principal axis to converge through
• a focal point.
• 2. Diverging Lens will cause light rays ____ to
  principal axis to diverge away from
• a focal point.
• Constructing images from ray diagrams for lenses
  is very similar to mirrors except
• that the light travels through the lens. See
  pg. 468-470 of old book
• Converging Lens (3 Light rays for determining
  images)
• Ray 1 The incident ray ___ to the principal
  axis refracts through ___.
• Ray 2 The incident ray passes through ___ and
  refracts ___ to the principal axis.
• Ray 3 The incident ray through ___ is a
  straight line.

F2

F1

V
image
12
6 Useful object positions for determining images
for converging lenses (Note object distance (
) and image distance ( ) at each
position.) Position 1 Object lies at a
distance infinitely far from the lens relative to
the size of the lens. Image is ________ and
appears as a ________ of light at F2. Case
1 do 8 (di f2 ) (real
image) Position 2 Object lies outside
of 2f1 (but not infinitely far away). The image
is ______, _________ and has a magnification
_____________ -1 and 0. (camera lenses operate
in this fashion) Case 2 8 gt do gt 2f1 (2f2 gt
di gt f2 ) (real image)
do
di
real
point
real inverted
between
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Position 3 Object lies on 2F1 The image is
______, _________ and has a magnification of
____. Case 3 do 2f1 (di 2f2 )
(real image) Position 4 Object lies
between 2F1 and F1. Image is _____, ___________
and has a magnification ________ than -1. (See
figure below) (slide projectors utilize this
location) Case 4 2f1 gt do gt f1 (8 gt di gt 2f2
) (real image)
Real inverted -1
Real inverted
less
14

• Position 5 Object lies on F1 .
• ____ image is formed. All light rays leave ___ to
  each other.
• Case 5 do f1
• (di 8) (no image)

No

Position 6 Object lies between F1 and V. The
refracted rays do not converge but seem to
diverge from a point on the same side of the
lens as the object (opposite side as your eye).
This creates a ___________ image. The image is
_________ with a magnification ____________than
1.
virtual
greater
upright
Case 6 do lt f1 (di lt 0) (virtual image)
Magnifying glasses utilize this distance
15

• Diverging Lenses
• Any incident light ray ___ to the principal axis
  will be refracted away from ____.
• Any incident light ray directed toward F2 is
  refracted ____ to the principal axis.
• Any ray directed at V will continue in a ________
  line.

F1

straight
8
Position 1 Object an ____ distance away.
Image is a ______ at F1. Case 1
do 8 (di f1)
8
Position 2 Object inside of __ Image is
________, _________ and _______ Case 2 do lt
8 M is between ___ and 1.
point
virtual upright reduced
0