Optics

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Optics

• LCHS

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Notation for Mirrors and Lenses

• The object distance is the distance from the
  object to the mirror or lens
• The image distance is the distance from the image
  to the mirror or lens
• The lateral magnification of the mirror or lens
  is the ratio of the image height to the object
  height

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Types of Images

• A real image is formed when light rays pass
  through and diverge from the image point
• A virtual image is formed when light rays do not
  pass through the image point but only appear to
  diverge from that point

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Flat Mirrrors
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Law of Reflection

• The angle of incidence equals the angle of
  reflection.
• This is true for both flat mirrors and curved
  mirrors.

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MIRROR
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Diffuse Reflection
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Locating the Image for Plane Mirrors

1. Draw the image the same distance behind the
   mirror as the object is in front.
2. Draw a connector line from each object to each
   image.
3. If the connector line passes through the mirror,
   the image will be seen.

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These lines are pointed to the only images that
will be seen from each of the original locations
(A-E) NOTE No images will be seen from E
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Lateral Magnification

• Lateral magnification, M, is defined as
• This is the general magnification for any type of
  mirror
• It is also valid for images formed by lenses
• Magnification does not always mean bigger, the
  size can either increase or decrease

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Lateral Magnification of a Flat Mirror

• The lateral magnification of a flat mirror is 1
• This means that h' h for all images

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Reversals in a Flat Mirror

• A flat mirror produces an
  image that has an apparent
  left-right reversal
• For example, if you raise
  your right hand the image
  you see raises
  its left hand
• The reversal is not actually a left-right
  reversal
• The reversal is actually a front-back reversal
• It is caused by the light rays going forward
  toward the mirror and then reflecting back from it

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Summary

• The image is as far behind the mirror as the
  object is in front
• dd do
• The image is unmagnified
• The image height is the same as the object height
• h' h and M 1
• The image is virtual
• The image is upright
• It has the same orientation as the object
• There is a front-back reversal in the image

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• The angle of incidence equals the angle of what?
• a) Dispersion
• b) Refraction
• c) Reflection

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• Specular reflections are images seen after __
  surface(s).
• a) rough
• b) smooth
• c) no

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• Can you see a reflection of yourself in a diffuse
  reflection?
• a) yes
• b) no

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• Where do you draw the connector lines?
• a) from the lens to object
• b) from image to lens
• c) from object to each image

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• What happens if the connector line passes through
  the mirror?
• a) image is invisible
• b) image is seen

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• Light doesnt pass through __ images.
• a) virtual
• b) real
• c) large
• d) small

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SphericalMirrors
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Spherical Mirrors

• A spherical mirror has the shape of a segment of
  a sphere
• The mirror focuses incoming parallel rays to a
  point
• A concave spherical mirror has the light
  reflected from the inner, or concave, side of the
  curve
• A convex spherical mirror has the light reflected
  from the outer, or convex, side of the curve

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Concave and Convex Mirrors
Concave and convex mirrors are curved mirrors
similar to portions of a sphere.
light rays
light rays
Concave mirrors reflect light from their inner
surface, like the inside of a spoon.
Convex mirrors reflect light from their outer
surface, like the outside of a spoon.
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Concave Mirrors
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Light from Infinite Distance
Focuses at the focal point

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Two Rules for Concave Mirrors

• Any incident ray traveling parallel to the
  principal axis on the way to the mirror will pass
  through the focal point upon reflection

• Any incident ray passing through the focal point
  on the way to the mirror will travel parallel to
  the principal axis upon reflection

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Virtual Image
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Convex Mirrors

• A convex mirror is sometimes called a diverging
  mirror
• The light reflects from the outer, convex side
• The rays from any point on the object diverge
  after reflection as though they were coming from
  some point behind the mirror
• The image is virtual because the reflected rays
  only appear to originate at the image point

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Will an image ever focus at a single point with a
convex mirror?
Therefore, the images you see are virtual!
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Image Formed by a Convex Mirror

• In general, the image formed by a convex mirror
  is upright, virtual, and smaller than the object

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Notes on Images

• With a concave mirror, the image may be either
  real or virtual. When the object is
• outside the focal point, the image is real
• at the focal point, the image is infinitely far
  away
• inside the focal point, the image is virtual
• With a convex mirror, the image is always virtual
  and upright
• As the object distance decreases, the virtual
  image increases in size

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Mirror Sign Convention
f focal length di image distance do object
distance
1
1
1


f
do
di
for real image - for virtual image
di
for concave mirrors - for convex mirrors
f
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Magnification
By definition,
m magnification hi image height (negative
means inverted) ho object height AND m hi
/ ho -di / do
Magnification is simply the ratio of image height
to object height. A positive magnification means
an upright image.
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Casey decides to join in the fun and she finds a
convex mirror to stand in front of. She sees her
image reflected 7 feet behind the mirror which
has a focal length of 11 feet. Her image is 1
foot tall. Where is she standing and how tall is
she?
do
19.25 feet
ho
2.75 feet
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Mirror Equation Sample Problem
Suppose AllStar, who is 3 and a half feet tall,
stands 27 feet in front of a concave mirror with
a radius of curvature of 20 feet. Where will his
image be reflected
di
15.88 feet
What will its size be?
hi
-2.06 feet
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Determine the image distance for a 5.00-cm tall
object placed 10.0 cm from a concave mirror
having a focal length of 15.0 cm. Use 1 / f 1 /
do 1 / di where f 15 cm and do 10.0 cm di
-30.0 cm
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Determine the image height for a 5.00-cm tall
object placed 10.0 cm from a concave mirror
having a focal length of 15.0 cm. (di -30.0
cm) Then use hi / ho -di / do where ho 5 cm,
do 45 cm, and di -30.0 cm hi 15.0 cm
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A 4.00-cm tall light bulb is placed a distance of
45.7 cm from a concave mirror having a focal
length of 15.2 cm. Determine the image distance.
1/f 1/do 1/di 1/(15.2 cm) 1/(45.7 cm)
1/di 0.0658 cm-1 0.0219 cm-1 1/di 0.0439 cm-1
1/di 22.8 cm di
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A 4.00-cm tall light bulb is placed a distance of
45.7 cm from a concave mirror having a focal
length of 15.2 cm. Determine the image size.
hi/ho - di/do hi /(4.0 cm) - (22.8 cm)/(45.7
cm) hi - (4.0 cm) (22.8 cm)/(45.7 cm) hi
-1.99 cm
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Refraction
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Light Beam
AIR
WATER
AIR
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http//cougar.slvhs.slv.k12.ca.us/pboomer/physics
lectures/secondsemester/light/refraction/refractio
n.html
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Snells Law
?i
ni
nr
?r
Snells law states that a ray of light bends in
such a way that the ratio of the sine of the
angle of incidence to the sine of the angle of
refraction is constant. Mathematically, ni sin?
i nr sin?r Here ni is the index of refraction
in the original medium and nr is the index in the
medium the light enters. ? i and ?r are the
angles of incidence and refraction, respectively.
Willebrord Snell
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Index of Refraction, n
The index of refraction of a substance is the
ratio of the speed in light in a vacuum to the
speed of light in that substance
Medium Vacuum Air (STP) Water (20º
C) Ethanol Glass Diamond
n 1 1.00029 1.33 1.36 1.5 2.42
n Index of Refraction c Speed of light in
vacuum v Speed of light in medium
Note that a large index of refraction corresponds
to a relatively slow light speed in that medium.
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Index of Refraction Equations

• n c/v speed of light in a vacuum
• speed of light in medium

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Index of Refraction Equations

• n c/v speed of light in a vacuum
• speed of light in medium
• n sin i/sin r

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Index of Refraction Equations

• n c/v speed of light in a vacuum
• speed of light in medium
• n sin i/sin r
• sin ?A / sin ?B nB / nA

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Index of Refraction Problem

• A diamond (n 2.42) is in water (n 1.33) and a
  ray of light shines on it making an angle of
  incidence of 55o. What is the angle of
  refraction inside the diamond?
• sin ?A / sin ?B nB / nA
• sin 55o / sin ?B 2.42/1.33
• ?B 27o

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Total Internal Reflection...

• is the total reflection of light traveling in a
  medium when it strikes a surface of a less dense
  medium above the critical angle
• Critical Angle Animation

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Refraction
Critical Angle
AIR
WATER
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Total Internal Reflection
Light Source
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A diver basks in the reflection of the Northern
Lights underwater by George Karbus
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Index of Refraction Problem

• What is the speed of light in water, which has an
  index of refraction of 1.33?
• n c/v ? v c/n
• v (2.998 x 108 m/s) / 1.33
• V 2.25 x 108 m/s

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Index of Refraction Problem

• A ray of light enters a piece of crown glass at
  an angle of 57o and is refracted to 31o inside
  the glass. What is the index of refraction?
• n sin i/sin r
• sin 57o / sin 31o
• 1.63

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Air Water Interface

• sin ? n2/n1
• Air nair 1 and Water n2 1.33
• sin ? 1.00/1.33 0.750
• sin ? 0.750
• ? sin-1 0.750
• ? 49o

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Critical Angle Sample Problem
Calculate the critical angle for the diamond (n
2.42) -air (n 1) boundary.
?c sin-1 (nr / ni) sin-1 (1 / 2.42)
24.4? Any light shone on this boundary beyond
this angle will be reflected back into the
diamond.
air
diamond
?c
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Lenses
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Focal Length and Focal Point of a Thin Lens

• A converging lens has a positive focal length
• Therefore, it is sometimes called a positive lens
• A diverging lens has a negative focal length
• It is sometimes called a negative lens

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Converging or Convex Lens
C
F
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Converging or Convex Lens
C
F
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Converging or Convex Lens
C
F
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Converging or Convex Lens
C
F
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Converging or Convex Lens
C
F
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Converging or Convex Lens
C
F
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Converging or Convex Lens
C
F
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Converging or Convex Lens
C
F
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Converging or Convex Lens
C
F
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Converging or Convex Lens
C
F
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Lens Sign Convention
f focal length di image distance do object
distance
1
1
1


f
do
di
for real image - for virtual image
di
for convex lenses - for concave lenses
f
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Lens / Mirror Sign Convention
The general rule for lenses and mirrors is this
for real image - for virtual image
di
and if the lens or mirror has the ability to
converge light, f is positive. Otherwise, f
must be treated as negative for the mirror/lens
equation to work correctly.
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Lens Equation dogt C

• f 2 cm, C 4 cm, ho 2 cm, do 5cm, di ?
• 1/f 1/do 1/di
• 1/2 1/5 1/di
• 1/di 1/2 - 1/5 0.5 0.2 0.3
• di 3.33 cm
• M hi/ho -di/do ? (-ho x di )/ do hi
• hi (-2 x 3.3)/5
• hi -1.3 cm

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Lens Equation do lt f

• f 2 cm, C 4 cm, ho 2 cm, do 0.5 cm, di
  ?
• 1/f 1/do 1/di
• 1/2 1/1 1/di
• 1/di 1/2 - 1/0.5 0.5 2.0 -1.5
• di -.67 cm
• M hi/ho -di/do ? (-ho x di )/ do hi
• hi (-2 x -.67)/0.5
• hi 8/3 3.67
• M - di / do 1.33

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Lens Sample Problem




F
2F
F
2F
14.24 feet
-5.83 feet
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Diverging or Concave Lens
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Concave Lenses

• Rays traveling parallel to the principal axis of
  a concave lens will refract as if coming from the
  focus.
• Rays traveling directly through the center of
  a concave lens will leave the lens traveling in
  the exact same direction, just as with a convex
  lens.

Rays traveling toward the focus will refract
parallel to the principal axis.
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Concave Lens Diagram
No matter where the object is placed, the image
will be on the same side as the object. The image
is virtual, upright, and smaller than the object
with a concave lens.
object




F
2F
F
2F
image
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Image Summary

• For a converging lens, when the object distance
  is greater than the focal length (p gtƒ)
• The image is real and inverted
• For a converging lens, when the object is between
  the focal point and the lens, (pltƒ)
• The image is virtual and upright
• For a diverging lens, the image is always virtual
  and upright
• This is regardless of where the object is placed

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• For a converging lens, the object real and
  inverted when the object distance is __.
• a) Greater than the focal length
• b) Less than the focal length
• c) Equal to the focal length

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• For a diverging lens, the image is always what?
• a) virtual
• b) upright
• c) real
• d) a and b

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• A converging lens has a __ focal length and a
  diverging lens has a __ focal length.
• a) , -
• c) ,
• b) -,
• d) -,-

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Fiber Optics
Fiber optic lines are strands of glass or
transparent fibers that allows the transmission
of light and digital information over long
distances. They are used for the telephone
system, the cable TV system, the internet,
medical imaging, and mechanical engineering
inspection.
spool of optical fiber
Optical fibers have many advantages over copper
wires. They are less expensive, thinner,
lightweight, and more flexible. They arent
flammable since they use light signals instead of
electric signals. Light signals from one fiber
do not interfere with signals in nearby fibers,
which means clearer TV reception or phone
conversations.
A fiber optic wire
Continued
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Fiber Optics Cont.
Fiber optics are often long strands of very pure
glass. They are very thin, about the size of a
human hair. Hundreds to thousands of them are
arranged in bundles (optical cables) that can
transmit light great distances. There are three
main parts to an optical fiber

• Core- the thin glass center where light travels.
  
• Cladding- optical material (with a lower index
  of refraction than the core) that surrounds the
  core that reflects light back into the core.
• Buffer Coating- plastic coating on the outside
  of an optical fiber to protect it from damage.

Continued
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Fiber Optics (cont.)
Light travels through the core of a fiber optic
by continually reflecting off of the cladding.
Due to total internal reflection, the cladding
does not absorb any of the light, allowing the
light to travel over great distances. Some of
the light signal will degrade over time due to
impurities in the glass.
There are two types of optical fibers

• Single-mode fibers- transmit one signal per
  fiber (used in cable TV and telephones).
• Multi-mode fibers- transmit multiple signals per
  fiber (used in computer networks).

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Mirage Pictures
Mirages
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Inferior Mirages
A person sees a puddle ahead on the hot highway
because the road heats the air above it, while
the air farther above the road stays cool.
Instead of just two layers, hot and cool, there
are really
many layers, each slightly hotter than the layer
above it. The cooler air has a slightly higher
index of refraction than the warm air beneath it.
Rays of light coming toward the road gradually
refract further from the normal, more parallel to
the road. (Imagine the wheels and axle on a
light ray coming from the sky, the left wheel is
always in slightly warmer air than the right
wheel, so the left wheel continually moves
faster, bending the axle more and more toward the
observer.) When a ray is bent enough, it
surpasses the critical angle and reflects. The
ray continues to refract as it heads toward the
observer. The puddle is really just an inverted
image of the sky above. This is an example of an
inferior mirage, since the cool are is above the
hot air.
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Sunlight after Sunset
Lingering daylight after the sun is below the
horizon is another effect of refraction. Light
travels at a slightly slower speed in Earths
atmosphere than in space. As a result, sunlight
is refracted by the atmosphere. In the morning,
this refraction causes sunlight to reach us
before the sun is actually above the horizon. In
the evening, the
Apparent position of sun
Observer
Actual position of sun
Earth
Atmosphere
sunlight is bent above the horizon after the sun
has actually set. So daylight is extended in the
morning and evening because of the refraction of
light. Note the picture greatly exaggerates this
effect as well as the thickness of the atmosphere.
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Rainbows
A rainbow is a spectrum formed when sunlight is
dispersed by water droplets in the atmosphere.
Sunlight incident on a water droplet is
refracted. Because of dispersion, each color is
refracted at a slightly different angle. At the
back surface of the droplet, the light undergoes
total internal reflection. On the
way out of the droplet, the light is once more
refracted and dispersed. Although each droplet
produces a complete spectrum, an observer will
only see a certain wavelength of light from each
droplet. (The wavelength depends on the relative
positions of the sun, droplet, and observer.)
Because there are millions of droplets in the
sky, a complete spectrum is seen. The droplets
reflecting red light make an angle of 42o with
respect to the direction of the suns rays the
droplets reflecting violet light make an angle of
40o.
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Primary Rainbow
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Secondary Rainbow
Secondary
Primary
Alexanders dark region
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• Dispersion is the ___ of white light into pure
  colors.
• a) combination
• c) absorption
• b) separation
• d) decomposition

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• What color can bend the most?
• a) violet
• c) red
• b) cyan
• d) magenta

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• Which of these can raindrops not do to sunlight?
• a) Refract
• c) Reflect
• b) Absorb
• d) Disperse

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Credits
Snork pics http//www.geocities.com/EnchantedFore
st/Cottage/7352/indosnor.html Snorks icons
http//www.iconarchive.com/icon/cartoon/snorks_by_
pino/ Snork seahorse pic http//members.aol.com/d
iscopanth/private/snork.jpg Mirror, Lens, and Eye
pics http//www.physicsclassroom.com/
Refracting
Telescope pic http//csep10.phys.utk.edu/astr162/
lect/light/refracting.html Reflecting
Telescope pic http//csep10.phys.utk.edu/astr162/
lect/light/reflecting.html Fiber
Optics
http//www.howstuffworks.com/fiber-optic.htm
Willebrord Snell and Christiaan Huygens pics
http//micro.magnet.fsu.edu/optics/timeline/people
/snell.html Chromatic Aberrations
http//www.dpreview.com/learn/Glossary/Optical/Chr
omatic_Aberrations_01.htm

Mirage Diagrams http//www.islandnet
.com/see/weather/elements/mirage1.htm
Sir David Brewster pic http//www.brewstersociet
y.com/brewster_bio.html
Mirage pics
http//www.polarimage.fi/
http//www.greatestplaces.org/mirage/desert1.html
http//www.ac-grenoble.fr/college.ugine
/physique/les20mirages.htmlDiffuse reflection
http//www.glenbrook.k12.il.us/gbssci/phys/Class/r
efln/u13l1d.htmlDiffraction http//hyperphysics.
phy-astr.gsu.edu/hbase/phyopt/grating.html