Transcript Slide 1

By Mike Maloney
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Light as a Ray
Light very often travels in straight
lines. We represent light using rays,
which are straight lines emanating
from an object. This is an
idealization, but is very useful for
geometric optics.
© 2003 Mike Maloney
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Light as a Ray
When the source of light is very far
away (like the sun) we can assume
that the rays are all coming in parallel
to each other.
In other cases, they radiate out from
the source in all direction.
© 2003 Mike Maloney
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Reflection
• We know that when a wave meets a
boundary (change in medium), part of
it gets reflected.
• The same is true for light waves … if
they didn’t we wouldn’t really see
anything at all.
• When a light wave meets a boundary
with something that is opaque, it is
reflected.
© 2003 Mike Maloney
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Reflection
Law of reflection: the angle of
reflection (that the ray makes with the
normal to a surface) equals the angle
of incidence.
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Reflection
• The law states that the angle that a
light ray is reflected is equal to the
angle it hits the surface at (aka angle
of incidence.
• Or in laymen's terms, the angle the
light leaves the surface at is the same
as the angle that it hits the surface at.
© 2003 Mike Maloney
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Reflection
• If all opaque objects reflect light, how
come I can’t see my image in the wall or
your shirt, but I can in a mirror?
• Because all surfaces are not flat, even the
ones that look like they are.
• Regular (Specular) Reflection, is the kind
that you see when you look in a mirror.
• All the light rays reflect parallel to each
other, so the reflected image looks the
same, just flipped left to right.
• Diffuse Reflection is what happens when
the surface is not flat. The reflected light
rays do not end up parallel to each other.
© 2003 Mike Maloney
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Diffuse Reflection
When light reflects from a rough
surface, the law of reflection still
holds, but the angle of incidence
varies. This is called diffuse reflection.
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Diffuse Reflection
With diffuse reflection, your eye sees
reflected light at all angles. With
specular reflection (from a mirror),
your eye must be in the correct
position.
Diffuse Reflection
© 2003 Mike Maloney
Specular Reflection
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Perception and Reflection
What you see when you look into a
plane (flat) mirror is an image, which
appears to be behind the mirror.
© 2003 Mike Maloney
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Refraction
• Have you ever looked at your
legs in a pool …or looked at a
pencil in a glass of water?
• You may notice that they seem
to bend.
• This phenomenon is called
REFRACTION.
• Can you guess why it might
happen?
HINT: remember light is a wave
…
© 2003 Mike Maloney
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Refraction
• When light passes from one medium to
another at an angle it seems to bend.
• This is due to the fact that it slows down or
speeds up when it changes mediums.
• n (index of refraction) is an experimental
number used to compare different
materials to each other based on how
much they slow down light.
• n = (speed of light in vacuum) /
(speed of light in medium)
Why is this true?
• n = c / v = o / 
• n is always bigger than 1.
Why is this true?
© 2003 Mike Maloney
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Some indices of Refraction
What happens to the wavelength of light when it
enters a new medium?
BACK
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Less Dense to More Dense
• When light travels from a less dense to a more
dense medium and does not hit is straight on, it
slows down and bends towards the center.
© 2003 Mike Maloney
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More Dense to Less Dense
• And what do you think happens when you go from
more dense to less dense?
• Right it speeds up and bends away from the
middle.
© 2003 Mike Maloney
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Refraction
Light changes direction when crossing a
boundary from one medium to another.
This is called refraction, and the angle the
outgoing ray makes with the normal is
called the angle of refraction.
© 2003 Mike Maloney
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Refraction
• Different materials bend light at
different amounts
• n (index of refraction) can also be
used to compare different materials
to each other based on how much
they bend light.
© 2003 Mike Maloney
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Snell’s Law
• 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 a constant, and this
constant is the index of refraction.
• OR,
Sin Θi
n=
Sin Θr
n = index of refraction
Θi = angle of incidence (incoming angle)
Θr = angle of refraction (outgoing/bent angle)
** NOTE this equation is only good when the light
is incident in air or a vacuum.
© 2003 Mike Maloney
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Snell’s Law
• nr / ni = sin Θi / sin Θr
Or by playing with the math
• n1 sinΘ1 = n2 sinΘ2
• In this equation n1 and
n2 are the index of
refractions of each
material, and Θ1 and Θ2
are the corresponding
angles.
• Θ is always measured
from the normal line.
• Let’s try an example.
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Why are you short in water?
Refraction is what makes objects
half-submerged in water look odd.
© 2003 Mike Maloney
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Total Internal Reflection
• What would happen if when light
went from a more dense medium to a
less dense medium and the angle of
refraction was greater than 90°?
n = 1.0
n = 1.33
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Total Internal Reflection
• What would happen if when light
went from a more dense medium to a
less dense medium and the angle of
refraction was greater than 90°?
• You would get something called total
internal reflection. The light would be
refracted so much that the ray never
makes it outside of the medium, and
no transmission would occur.
• The light would all reflect at the same
incident angle.
© 2003 Mike Maloney
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Total Internal Reflection
• As the incident angle increases, the
refracted angle gets closer to 90°. The
minimum angle that causes total internal
reflection (Θr = 90°) between two materials
is known as the critical angle (θc).
© 2003 Mike Maloney
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Critical Angle ΘC
• It is found using Snell’s law and
setting the angle of refraction to 90°
and solving for the angle of
incidence.
• n1 sinΘc = n2 sin(90°)
• If ΘC is bigger than 90°, no
transmission occurs, only reflection.
© 2003 Mike Maloney
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Finding the Critical Angle ΘC
• Lets find the critical angle for light
moving from water to air.
• nwater = 1.33, nair = 1.00
•
•
•
•
•
n1sinΘ1 = n2 sin(90°)
1.33*sinΘ1 = 1*sin(90)
sinΘ1 = 1/1.33 = .75
Θ1 = sin-1(0.75)
Θ1 = 48.6 deg
© 2003 Mike Maloney
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Summary of Equations
i  r
• Reflection
• Refraction
c 0 sin i
n 

v  sin  r
n1 sin 1 n2 sin2
n2
sin  c 
n1
© 2003 Mike Maloney
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Some Effects Of Refraction
•
•
•
•
•
Mirages
Prisms
Rainbows
Lenses
Fiber-optics
© 2003 Mike Maloney
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Mirages
• The high temperature
near the ground
changes the index of
refraction of the air
near the ground.
• This makes the light
curve or refract.
• If it is hot enough, the
light coming down can
curve back up into your
eyes and you see a
“fake” reflection.
© 2003 Mike Maloney
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Prisms
• Different wavelengths of
light have slightly
different indices of
refraction.
• When white light moves
through a prism all the
colors get refracted
twice, each by a slightly
different amount.
• When they emerge they
are no longer on top of
each other, but are now
separated (dispersed).
© 2003 Mike Maloney
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Rainbows
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Rainbows Explained
• Different colors of light get
diffracted different amounts when
they travel through water.
• This causes a spectrum of light to
appear in the sky when the Sun
shines onto droplets of moisture in
the Earth's atmosphere.
• White light enters and refracts,
reflects off the back and refracts
again as it comes out. The various
colors have been refracted
different amounts and are no
longer on top of each other.
• What you see is a pattern of
different refracted colors from
different drops (red from one drop,
green from another, blue from
another) in the shape of a bow that
reach your eyes.
• Everyone sees a different rainbow.
© 2003 Mike Maloney
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Lenses
• A lens can be used to
focus light.
• Depending on where on
the lens the light hits, it
has different incoming
angle, and therefore leaves
at a different refracted
angle.
• If the lens is shaped right,
all the waves focus on a
point called the focal point.
• What is the purpose of
your eyeglasses?
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Fiber Optics/TV Rock
Light will be transmitted along the fiber
even if it is not straight. An image can
be formed using multiple small fibers.
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