PHYSICS Mr. BALDWIN GEOMETRIC OPTICS23-Jun-15

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PHYSICS Mr. BALDWINGEOMETRIC OPTICS 23-Jun-15

• AIM What does a spoon or pencil look like in a
  clear glass of water?
• DO NOW
• If an object is located on the reflective side of
  a mirror, is its distance positive or negative?
• If an image is located on the reflective side of
  a mirror, is its distance positive or negative?
• If the focal point of a mirror is located on the
  reflective side of a mirror, is its distance
  positive or negative?

BALDWIN
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Refraction Snells Law
Light changes direction (bends) when crossing a
boundary from one medium to another. This is
called Refraction. The angle the outgoing ray
makes with the normal is called the angle of
refraction.
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Refraction Snells Law
Refraction is what makes objects half-submerged
in water look odd. http//interactagram.com/physic
s/optics/refraction/
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Index of Refraction
Light slows when traveling through a medium. The
index of refraction, n, of the medium is the
ratio of the speed of light in vacuum to the
speed of light in the medium
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PHYSICS Mr. BALDWINGEOMETRIC OPTICS 23-Jun-15

• AIM What is Snells Law? (How do we determine
  how much a light ray bends when it enters a
  medium?)
• DO NOW
• A ray of light enters into a piece of plexiglas.
  The refractive index of plexiglas is 1.51. What
  is the speed of light when it enters the
  plexiglas? Take the speed of light to be 3.0 x
  108 m/s.
• Homework Refraction Handout

BALDWIN
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Refraction Snells Law
The angle of refraction depends on the indices of
refraction, and is given by Snells law
Using Snells law, what is the refracted angle?
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Snells Law

• When a ray of light crosses from one material to
  another, the amount it bends depends on the
  difference in index of refraction between the two
  materials.

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PHYSICS Mr. BALDWINGEOMETRIC OPTICS 23-Jun-15

• AIM How does light travel in a fiber optic
  cable? (An application of Snells Law)
• DO NOW (Quiz)
• A ray of light enters into a diamond at 30
  degrees. The refractive index of diamond is 2.42.
  What is the speed of light when it enters the
  diamond and what is the refracted angle? Take the
  speed of light to be 3.0 x 108 m/s.
• Homework None

BALDWIN
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Total Internal Reflection Fiber Optics
If light passes from one medium into another
medium with a smaller index of refraction, IS the
angle of refraction larger or smaller?
LARGER There is an angle of incidence that will
make the angle of refraction equals 90 this
angle is called the critical angle. Thus, derive
an expression for the critical angle using
Snells Law.
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Total Internal Reflection
If the angle of incidence is larger than this
(critical angle), no transmission occurs. The
light is trapped. This is called total internal
reflection. Based on the diagram, which letter
represents TIR?
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Challenge.

• Fused silica has a refractive index of 1.46.
  Calculate its critical angle.
• The critical angle for diamond is 24o. Determine
  the refractive index of diamond.
• Find the subsequent paths of rays of light
  incident internally on the surface of fused
  silica at angles of incidence of
• (a) 35o
• (b) 65o

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Describe an application of total internal
reflection used in the communications industry.
Application of Total Internal Reflection Fiber
Optics
Total internal reflection is also the principle
behind fiber optics. 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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Total Internal Reflection Binoculars
Binoculars often use total internal reflection
this gives true 100 reflection, which even the
best mirror cannot do.
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WORKSHEET No.2

• 1. Calculate the absolute refractive index for a
  clear plastic material, if the velocity of light
  in the plastic is 2.5 x 108 ms-1. (1.2)
• 2. A ray of light in air is incident at an angle
  of 40.8o on the surface of the same plastic
  material used in Q.1. Determine the angle of
  refraction in the plastic. (33o)
• 3. A ray of light passes from kerosene to glass.
  The angle of incidence of the light is 45.2o and
  the relative refractive index from kerosene to
  glass is 1.08. Calculate the angle of refraction
  in the glass. (41o)
• 4. Using relevant information from Q.3, calculate
  the absolute index of refraction of kerosene if
  the absolute index of refraction of glass is 1.5.
  (1.39)
• 5. A ray of light passes from air into a glass
  prism at an angle of incidence of 35o. If the
  angle of refraction in the glass is 23.7o, what
  is the speed of the light in the glass? (2.1 x
  108 ms-1)

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• 6. The absolute refractive index of water is 4/3
  and that of glass is 3/2. Find the relative
  refractive index for light traveling from water
  to glass.
• 7. The critical angle for diamond is 24o.
  Determine the refractive index of diamond.
• 8. Fused silica has a refractive index of 1.46.
  Calculate its critical angle. (43.2o) Find the
  subsequent paths of rays of light incident
  internally on the surface of fused silica at
  angles of incidence of
• (a) 35o
• (b) 65o
• 9. Describe an application of total internal
  reflection used in the communications industry.
• 10. For yellow light, the refractive index of
  glass is 1.6 and the refractive index of water is
  1.2. Which of the following statements is
  correct?
• (a) The wavelength of yellow light in glass is
  longer than the wavelength of yellow light in
  water.
• (b) For the same angle of incidence, yellow light
  is refracted more by water than glass.
• (c) Total internal reflection cannot occur when
  yellow light travels from water to glass.
• (d) Light travels faster in glass than in water.

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PHYSICS Mr. BALDWINGEOMETRIC OPTICS 23 June
2015

• AIM How are images formed by plane mirrors?
• DO NOW
• How far inside a plane (flat) mirror do you
  appear to be when you are standing in front of
  one?
• How large is your image?
•  Is there anything else about your image you
  observe?
• HOME WORK Handout

BALDWIN
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How is an image in a mirror produced?
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The Ray Model of Light
Light very often travels in straight lines. We
represent light using rays, which are straight
lines emanating from an object.
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Recall What is The Law of Reflection?
Q How are the angles measured again?
A The angles of incidence/reflection are the
angles that are measured from the normal to the
incident/reflected ray.
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Reflection Image Formation by a Plane Mirror
Q What you see when you look into a plane (flat)
mirror? Describe the image (its dimensions, its
location)?
the image appears to be behind the mirror.
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• DRAWING A RAY DIAGRAM FOR A PLANE MIRROR
• For an object standing in front of a plane
  mirror, we can locate the image by extending
  (extrapolating) two of the rays coming from the
  top of the object and finding their point of
  intersection.
• .

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• Thus we have found the position of the image, its
  magnification, and its orientation (whether it is
  inverted or upright).
• What can be said about the characteristic of an
  image formed by a plane mirror? (Describe the
  image?)
• Object/Image distances?
• The distance of the object from the mirror equals
  the distance of the image from the mirror.
• Image height? (magnification?)
• The image is the same height as the object, so
  the magnification 1.
• Orientation?
• The image is upright.

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• How can an image lie behind a mirror hanging on a
  wall, when no light can reach that point?
• Does light actually pass through the position
  where the image is located?
• The light never gets behind the mirror at all, it
  just appears to come from points behind the
  mirror as it is reflected.
• Since the light never
• actually passes
• through the point
• where the image is
• located, the image is
• called virtual.

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VIRTUAL IMAGES
This is called a virtual image, as the light ray
does not go through it (image). Note The
distance of the image from the mirror is equal to
the distance of the object from the mirror.
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 DESCRIBING THE PROPERTIES OF AN IMAGE   USE
SALT! S Size of image (larger, smaller,
same) A Attitude of image (way image is
oriented (inverted, upright?) L Location of
image T Type of Image (real or virtual)
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PHYSICS Mr. BALDWINGEOMETRIC OPTICS 23 June
2015

• AIM How do we construct a ray diagram for a
  spherical mirror?
• DO NOW
• Describe the image formed by the security mirrors
  in your neighborhood bodegas, elevators, ATMs or
  in any department stores. What are their purpose?
• What is S.A.L.T.?
• HOME WORK none

BALDWIN
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Spherical Mirrors
Spherical mirrors are shaped like sections of a
sphere, and may be either reflective on the
outside (convex) or reflective on the inside
(concave).
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Spherical Mirrors
Parallel rays striking a spherical concave mirror
all converge at exactly the same point called the
focal point. The distance from mirror to focus is
called the focal length f
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Spherical Mirrors
Using geometry, we find that the radius of
curvature is twice the focal length
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Images formed by Spherical Mirrors

• We use ray diagrams to determine where an image
  will be. For mirrors, we use THREE key rays, all
  of which begin on the TOP of the object
• A ray parallel to the axis
• A ray after reflection it passes through the
  focal point
• A ray through the radius of curvature

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DRAWING A RAY DIAGRAM
Mirror
Ray 1
Object
Ray 2
Ray 3
Image
Principal Axis
Radius of Curvature
Focal Point
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Question?...How would do you describe (SALT) the
image?

• Size Smaller, larger or equal?
• Smaller than object.
• Attitude Erect or Inverted?
• Inverted
• Location In front of or behind the mirror?
• In front the mirror
• Type Real or Virtual?
• Real

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Characteristics of Images Formed by Concave
(Converging) Mirrors
If an object is inside the focal point, its image
will be upright, larger, and virtual.
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Formation of Images by Spherical Mirrors
The Mirror Equation an equation that relates the
object distance, image distance, and focal length
of the mirror
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Formation of Images by Spherical Mirrors
We can also find the magnification (ratio of
image distance/height to object distance/height).
Note The negative sign indicates that the image
is inverted.
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PHYSICS Mr. BALDWINGEOMETRIC OPTICS 10
January 2013

• AIM How do we construct a ray diagram for a
  Convex Mirror?
• DO NOW
• Draw the ray diagram and describe the
  characteristics of an image formed by a concave
  mirror if the object is placed between the radius
  of curvature focal point?
• HOME WORK Prepare for Test next week Friday

BALDWIN
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Characteristics of Images Formed by Spherical
Mirrors

• If the object is between the center of curvature
  and the focal point, its image is
• Larger, inverted, and real.
• If an object is outside the center of curvature
  of a concave mirror, its image is
• Smaller, inverted, and real.

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Characteristics of Images Formed by Convex
(Diverging) Mirrors

• For a convex mirror, the image of an object
  placed anywhere in front the mirror is ALWAYS
• Virtual
• Upright
• Smaller

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DRAWING A RAY DIAGRAM
Ray 1
Ray 2
Object
Ray 3
Principal Axis
Radius of Curvature
Focal Point
Mirror
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Review Characteristics of Images Formed by
Spherical Mirrors
Sign conventions if the object distance, image
distance, or focal length is on the reflective
side of the mirror, its distance is positive, and
negative otherwise. Magnification is positive
if image is upright, negative otherwise.
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PHYSICS Mr. BALDWINGEOMETRIC OPTICS Review

1. What is the distance from the focal point to
   mirror along the principal axis called?
2. Twice the distance from the focal point to mirror
   along the principal axis is called?
3. What is another name for a concave mirror?
4. What is another name for a convex mirror?
5. How do we construct a ray diagram?
6. What type of images are formed by a plane mirror?

BALDWIN
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PHYSICS Mr. BALDWINGEOMETRIC OPTICS 23 June
2015

• AIM How are images produced by thin lenses?
• DO NOW Quick Review
• What is the distance from the focal point to
  mirror along the principal axis called?
• Twice the distance from the focal point to mirror
  along the principal axis is called?
• What is another name for a concave mirror?
• What is another name for a convex mirror?
• How do we construct a ray diagram?
• What type of images are formed by a plane mirror?

BALDWIN
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Thin Lenses Ray Tracing

• Thin lenses are made of transparent materials
  whose thickness is small compared to their radius
  of curvature.
• They may be either
• converging
• diverging.

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CONVEX LENS
Parallel rays are brought to a focus by a CONVEX
(converging) lens (one that is thicker in the
center than it is at the edges).
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CONCAVE LENS
A CONCAVE (diverging) lens (thicker at the edges
than in the center) make parallel rays of light
diverge the focal point is that point where the
diverging rays would converge if extrapolated.
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Thin Lenses Ray Tracing

• Ray tracing for thin lenses is similar to that
  for
• mirrors. We have three key rays
• One ray travels parallel to the principal axis
• A second ray passes through the focal point.
• A third ray goes through the center of the lens
  and is undeflected.

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CONVEX LENS
For a CONVERCING LENS, we can use three rays the
IMAGE characteristics (real, virtual, upright,
inverted, larger, smaller) are determined by the
OBJECTS location.
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How would you describe the previous image?

• S.A.L.T.
• IMAGE is real, inverted, smaller and on the
  opposite side of the lens.

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DRAWING A RAY DIAGRAM
Ray 1
Ray 3
Object
Ray 2
Principal Axis
Image
Focal Point
Focal Point
Concave Lens
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CONCAVE LENS
Now, how would you describe the image formed by a
concave lens? For a DIVERGING LENS, we can use
the same three rays the image is ALWAYS Upright
Virtual Smaller and On same side of lens as
object.
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PHYSICS Mr. BALDWINGEOMETRIC OPTICS 23 June
2015

• AIM How do we determine the characteristics of
  an image produced by a thin lens?
• (How do we use the lens equation?)
• DO NOW (In complete sentences)
• Define the focal length of a lens.
• What happens to parallel rays of light as it
  passes through a concave lens?
• What happens to parallel rays of light as it
  passes through a convex lens?
• Which lens focal length is negative and why?
• HOME WORK Handout

BALDWIN
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The Thin Lens Equation
The thin lens equation is the same as the mirror
equation
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Magnification
The magnification is the ratio of the image
distance (size) to the object distance (size)
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Power of Thin Lenses
The power of a lens is the inverse of its focal
length.
Lens power is measured in diopters, D. 1 D 1 m-1
The power of a lens is positive if it is
converging and negative if it is diverging.
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The sign conventions are slightly different

• The focal length is positive for converging
  lenses and negative for diverging lenses.
• The object distance is positive when the object
  is on the same side as the light entering the
  lens (not an issue except in compound systems)
  otherwise it is negative.
• The image distance is positive if the image is
  on the opposite side from the light entering the
  lens otherwise it is negative.
• The height of the image is positive if the image
  is upright and negative otherwise.

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Sign Convention for Spherical Mirrors Lenses
Quantity Conditions Sign
Focal Length, f Concave mirror Convex mirror Convex lens Concave lens
Object distance, do Always
Image distance, di Image real Image virtual
Magnification, m Image upright Image inverted