S-95

1
S-95

• Explain how a curved mirror, and a curved lens
  are different. Think in terms of image formation
  and in terms of what light photons do.

2
Geometric Optics

• AP Physics
• Chapter 23

3
Geometric Optics

• 23.1 The Ray Model of Light

4
23.1 The Ray Model of Light

• Light travels in a straight line in most cases
  (away from very large gravitational fields)
• Ray Model Light
• travels in
• straight line
• pathways called
• rays
• represents a narrow
  beam
• of light

23.1
5
23.1 The Ray Model of Light

• We see an object when rays of light come from the
  object to our eyes

23.1
6
Geometric Optics

• 23.2 Reflection Image Formation by a Plane Mirror

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23.2 Reflection

• When light strikes an object it is
• Reflected bounces off
• Refracted transmitted through
• Absorbed converted to a different form of
• energy
• Law of Reflection

23.2
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23.2 Reflection

• Diffuse Reflection on a rough surface
• Rays dont form an pattern
• We see color
• Specular Reflection
  
• smooth surface
• Patterns form images

23.2
9
S-101

• Draw a ray diagram for a cat standing in front of
  a mirror. Use geometry to figure out
  the shortest possible mirror that
  will allow the
  cat to see his entire height.

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23.2 Reflection

• How are images formed
• Your eye sees the
• intersection of rays
• from an object

Applet
23.2
11
23.2 Reflection

• Object Distance from mirror to the object
• Image Distance from mirror to the image
• Virtual Image imaginary intersection of light
  rays
• Real Image actual intersection of light

23.2
12
S-94

• Two mirrors are placed facing each other. Use a
  point between the dots, and ray diagrams,
  determine the image distance in the second
  mirror. That is the image of the image in the
  first mirror.

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Geometric Optics

• 23.3 Formation of Images by Spherical Mirrors

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23.3 Formation of Images by Spherical Mirrors

• Spherical Mirrors form a section of a sphere
• Convex reflection on
  outer
• surface of sphere
• Concave
• reflection on
• inner surface
• of sphere

23.3
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23.3 Formation of Images by Spherical Mirrors

• Terms
• Principal Axis straight line normal to the
  center of the curve
• Focus point where parallel rays intersect
• Vertex center of the mirror
• Focal Length distance from vertex to focus
• Images from distant objects are produced at the
  focal point

23.3
16
S-96

• Sketch the path of a ray of light
  coming from an object in front a
  curved mirror to the eyes of an
  observer.

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23.3 Formation of Images by Spherical Mirrors

• The focal point is actually an approximation
• The greater the curve of a mirror, the worse is
  the approximation
• Called
• Spherical
• Aberration
• Examples of Visual
• Aberrations

23.3
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23.3 Formation of Images by Spherical Mirrors

• All rays follow the law of
• reflection
• Two Rules
• A ray parallel to the principle axis reflects
  through the focal point
• A ray through the focal point reflects parallel
• Examples of Diagrams Concave Mirrors
• Real Images
• Virtual Image

23.3
19
S-98

• Sketch a ray diagram for an object that is 10 cm
  from a concave mirror with a focal length of 12
  cm. The object is 2 cm tall. Use a ruler.

20
S-99

• Sketch a ray diagram for an object that is 5 cm
  from a concave mirror with a focal length of 3
  cm. The object is 2.5 cm tall. Use a ruler.

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23.3 Formation of Images by Spherical Mirrors

• Convex Mirrors only form virtual images
• Rules
• Rays parallel to the principle axis reflect away
  from the focal point
• Rays headed for the focal point reflect parallel

23.3
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23.3 Formation of Images by Spherical Mirrors

• Curved Mirror Equations
• ho-object height
• hi-image height
• do-object distance
• di-image distance
• The Mirror Equation
• Magnification

23.3
23
23.3 Formation of Images by Spherical Mirrors

• Sign Conventions
• Image Height
• upright (virtual)
• - inverted (real)
• Image and Object Distance
• front of mirror
• - behind mirror
• Magnification
• upright image
• - inverted image

23.3
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23.3 Formation of Images by Spherical Mirrors

• Sign Conventions
• Focal Length
• concave mirror
• - convex mirror

23.3
25
S-101

• A 14 cm tall man, who apparently had a rough
  evening, stands 25 cm from a curved mirror with a
  focal length of 20 cm.
• What is the location of his image?
• What is the height of the image?
• What is the magnification of the image?

26
S-102

• A 20 cm arrow is placed 25 cm from a concave
  mirror with a focal length of 15 cm.
• What is the position of the image?
• What is the height of the image?
• What is the magnification?
• Is the image real or virtual?
• Is it inverted or right side up?
• Is it enlarged or reduced?

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Geometric Optics

• 23.4 Index of Refraction

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23.4 Index of Refraction

• Index of Refraction the ratio of the speed of
  light in a vacuum to the speed in a given
  material

Material Index Material Index
Vacuum 1.00000 NaCl 1.54
Air at STP 1.00029 Polystyrene 1.57
Water 1.33 Flint Glass 1.65
Quartz 1.46 Sapphire 1.77
Crown Glass 1.53 Diamond 2.417
23.4
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23.4 Index of Refraction

• Value can never be less than 1

Material Index Material Index
Vacuum 1.00000 NaCl 1.54
Air at STP 1.00029 Polystyrene 1.57
Water 1.33 Flint Glass 1.65
Quartz 1.46 Sapphire 1.77
Crown Glass 1.53 Diamond 2.417
23.4
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Geometric Optics

• 23.5 Refraction Snells Law

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23.5 Refraction Snells Law

• Refraction when a ray of light changes
  direction as it changes media
• The change in angle depends on the change in
  velocity of light (or the index of refraction of
  the two media)

23.5
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23.5 Refraction Snells Law

• Snells Law relates the index of refractions
  and the angles
• Also called the Law of Refraction
• If light speeds up, rays bend away
• from the normal
• If light slows down, rays bend
• toward the normal

23.5
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23.5 Refraction Snells Law

• Refraction occurs when one side of the wave slows
  down before the other

23.5
34
Geometric Optics

• 23.6 Total Internal Reflection Fiber Optics

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23.6 Total Internal Reflection Fiber Optics

• When light travels from a more optically dense
  medium, the ray bends away from the normal
• As the angle increases, the angle of refraction
  eventually reaches 90o.
• This is called the critical
• angle

23.6
36
S-100

• A short, 1.5 m tall moose stands 1.4 m from a
  convex mirror with a focal length of 1.8 m.
• What is the location of the image?
• What is the height of the image?
• Describe the image.
• Repeat all steps for the
  mirror if it was
  concave.

37
S-104

• A ray of light traveling from air into glass
  (n1.68).
• Is there a critical angle? If so, what
  is it?
• What is the angle of refraction if
  the angle of incidence is 37o?

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23.6 Total Internal Reflection Fiber Optics

• Above the critical angle, light reflects
  following the law of reflection
• Used in fiber optics

23.6
39
S-105

1. Light travels at 250,000,000 m/s through a piece
   of glass. What is its index of refraction?
2. A mirror with a focal length of 25 cm
   forms an image that is -12.2 cm from the
   mirror. What is the distance
   of the object?

40
Geometric Optics

• 23.8 The Thin Lens Equation Magnification

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23.8 The Thin Lens Equation Magnification

• Equations are similar to Mirrors, conventions are
  different
• The Thin Lens Equation is
• To Calculate Magnification

23.8
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23.8 The Thin Lens Equation Magnification

• Conventions
• Focal Length
• converging lens
• - diverging lens
• Object Distance
• same side as original light
• - different side (only when more than 1
  lens)

23.8
43
23.8 The Thin Lens Equation Magnification

• Conventions
• Image Distance
• opposite side from light
• - same side as light
• Height
• upright
• - upside down

23.8
44
Geometric Optics

• 23.7 Thin Lenses Ray Tracing

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23.7 Thin Lenses Ray Tracing

• Thin lens very thin compared to its diameter
• Diagrams are similar to mirrors
• Converging rays converge

23.7
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23.7 Thin Lenses Ray Tracing

• Converging Lenses
• A ray parallel to the Principle Axis refracts
  through F
• A ray through F refracts parallel.
• A ray through the optical center, O, does not
  refract

Converging Lens
23.7
47
23.7 Thin Lenses Ray Tracing

• Diverging Lens spreads apart rays of light
• Only produces virtual images
• Rules
• Parallel rays refract
• away from F
• Rays headed toward
• F refract parallel
• Rays through O do not
• refract

23.7
48
S-106

• Shortly before being released into the wild to
  fend for himself, a cute black bunny stands in
  front of a lens with a focal length of -24 cm.
  The bunny stands 32 cm in front of the lens.
• What is the location of the I mage?
• What is the height of the image?
• Describe the image.

49
S-105

• A large refracting telescope is used to look at
  the image of stars in the night sky. The focal
  length of the lens is 450 m.
• What would be the location of the image?
• What would be the magnification?

50
Geometric Optics

• 23.9 Combinations of Lenses

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23.9 Combinations of Lenses

• Many devices used combinations of lenses
• Combination problems are treated as separate
  lenses
• Calculate or draw the image from the first lens

Applet
23.9