Speed of light

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Speed of light
In a vacuum, light travels at a speed of 3 x 108
m/s. In any other medium, such as air, water,
glass, etc., light travels slower.
Material Speed
vacuum c
air (STP) 99.97 c
water 75.1 c
aqueous humor and vitreous humor of human eye 74.85 c
cornea of human eye 72.68 c
crystalline lens of human eye 71.11 - 72.15 c
glass 66 c
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Model of a car
If a car travels from pavement to gravel, it
slows down. Suppose that it is incident on the
pavement/gravel interface at an angle. One tire
slows down before the other tire hits the gravel.
As a result, the axle rotates.
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Plane wave incident on glass
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Bending of light at an interface of two mediums
If slowing down (v2 lt v1), the ray bends toward
the normal.
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Bending of light at an interface of two mediums
If speeding up (v2 gt v1), the ray bends away from
the normal.
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Wavelength
The medium affects the wavelength of the wave,
but not the frequency. The slower the medium, the
shorter wavelength.
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Refraction
Refraction is the bending of light toward the
normal or away from the normal as a result of
speeding up or slowing down as the light travels
from one medium to another medium.
The ratio of the speed of light in vacuum to the
speed of light in the medium is called the index
of refraction, n.
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Poll

• In which material does light travel slowest?
• vacuum
• air (at STP)
• water
• glass

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Poll

• Suppose that light of wavelength 600 nm in vacuum
  is incident on the following materials. In which
  material will the wavelength be shortest?
• vacuum
• air (at STP)
• water
• glass

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Snells Law
Angle of refraction is given by Snells Law.
The larger the difference in n, the larger the
difference in angles.
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Low index to high index
If light travels from a medium of low index to
high index, it bends toward the normal.
If light travels from a medium of high index to
low index, it bends toward the normal.
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Example
Laser light in air strikes a flat surface of
glass at the angle shown. On the other side of
the glass is water. At what angle does it travel
through the water?
30?
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If a ray strikes the surface of a cut sapphire
from within at an incident angle of 30, it
passes into the air at an angle q2 62.3. All
angles are measured from the normal.
62.3
30
Show in Slide Show view to have question appear
in two parts.
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Above are four rays of light from the same
monochromatic laser source. Each ray passes from
one medium to another. Water is always one of the
two media the other media (A, B, C, and D) may
be different. Which of the following correctly
compares the index of refraction of the media?
A. nB nD gt nC gt nA B. nC gt nD
nB gt nA C. nD gt nB nC gt nA
D. nA gt nC gt nB nD E. nB nC nD gt nA
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qr 60?
qi 30?
The diagram shows a ray passing from the blue
medium into the pink medium. If the incident
angle qi is doubled, the refracted angle qr will
be ______________.
A. doubled B. less than
doubled C. more than doubled D.
none of the above
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Total internal reflection
n1 gt n2
increase n1 until the refracted angle90?
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Critical Angle
the incident angle is called the critical angle
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Example
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Total Internal Reflection (Example)
Can light passing from crown glass into air be
totally internally reflected? If so, what is
the critical angle?
n11.52
n21
YES!!! since n1gtn2
Crown Glass
Air
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Poll
If light from air is incident on glass,

1. it can not refract at the critical angle.
2. it may refract at the critical angle and not be
   transmitted through the glass.

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Dispersion
The index of refraction n depends on the
frequency (i.e. color) of the light. As a result,
different colors bend different amounts as they
pass through glass or water, for example. If
white light is incident on glass or water, then
the different frequencies bend different amounts
and the white light separates into its component
colors. this effect is called dispersion.
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Poll
Which will have a greater angle of refraction,
red or violet light?

1. red
2. violet
3. neither, they bend the same amount

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Converging Lens
All rays parallel to principal axis pass through
focal point F.
Double Convex
F
P.A.
nlens gt noutside
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Converging Lens
F
P.A.
Object
F
1) Rays parallel to principal axis pass through
focal point.
2) Rays through center of lens are not refracted.
3) Rays through F emerge parallel to principal
axis.
Image is real, inverted and enlarged (in this
case).
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3 Cases
Past 2F
This could be used in a camera. Big object on
small film
Inverted Reduced Real
Between F 2F
Inverted Enlarged Real
This could be used as a projector. Small slide on
big screen
Upright Enlarged Virtual
Inside F
This is a magnifying glass
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Lens Equation
In Front of Lens
Behind Lens
do
F
Image
P.A.
Object
F
di

• so distance object is from lens
• Positive object in front of lens (this is
  usually the case)
• Negative object behind lens

• si distance image is from lens
• Positive real image (behind lens)
• Negative virtual image (in front of lens)

• f focal length lens
• Positive converging lens
• Negative diverging lens

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Example
A 2.0 cm high object is placed 5 cm in front of a
10 cm focal length lens. Where is the object
located? Is it real or virtual? Find the height
of the image.
Image
F
P.A.
Object
F
The image is upright, virtual, and enlarged!
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Example
A 4.0 cm high object is placed 18 cm in front of
a 8 cm focal length lens. Where is the object
located? Is it real or virtual? Find the height
of the image.
F
Object
F