Waves

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Waves

• Optics

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Wave Behavior 3 Diffraction

• Diffraction is the bending of a wave AROUND a
  barrier
• Diffracted waves can interfere and cause
  diffraction patterns

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Double Slit Diffraction

• n? d sinT
• n bright band number
• ? wavelength (m)
• d space between slits (m)
• T angle defined by central band, slit, and band n

• This also works for diffraction gratings
  consisting of many, many slits that allow the
  light to pass through. Each slit acts as a
  separate light source

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Single Slit Diffraction

• n ? s sin T
• n dark band number
• ? wavelength (m)
• s slit width (m)
• T angle defined by central band, slit, and dark
  band

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10 11

• 3. Light of wavelength 360 nm is passed through a
  diffraction grating that has 10,000 slits per cm.
  If the screen is 2.0 m from the grating, how far
  from the central bright band is the first order
  bright band?
• 4. Light of wavelength 560 nm is passed through
  two slits. It is found that, on a screen 1.0 m
  from the slits, a bright spot is formed at x 0,
  and another is formed at x 0.03 m. What is the
  spacing between the slits?

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Reflection

• Reflected sound can be heard as an echo
• Light waves can be drawn as rays to diagram
  light reflected off mirrors

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Mirrors

• Mirrors can be
• Plane (flat)
• Spherical
• Convex reflective side curves outward
• Concave reflective side curves inward

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Mirrors and Ray Tracing

• Ray tracing is a method of constructing an image
  using the model of light as a ray
• We use ray tracing to construct optical images
  produced by mirrors and lenses
• Ray tracing lets us describe what happens to the
  light as it interacts with a medium

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Reflection and Plane Mirrors

• Law of Reflection

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Problem 3

• A light ray reflects from a plane mirror with an
  angle of incidence of 37. If the mirror is
  rotated by an angle of 5, through what angle is
  the reflected ray rotated?

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Problem 4

• Standing 2.0 m in front of a small vertical
  mirror, you see the reflection of your belt
  buckle, which is 0.70 m below your eyes.
• What is the vertical location of the mirror
  relative to the level of your eyes?
• If you move backward until you are 6.0 m from the
  mirror, will you still see the buckle, or will
  you see a point on your body that is above or
  below the buckle? Explain.

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Solution
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Optical Images

• Nature
• Real (converging rays)
• Virtual (diverging rays)
• Orientation
• Upright
• Inverted
• Size
• True
• Enlarged
• Reduced

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Ray Tracing Plane Mirrors

• Use at least two rays to construct the image

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Spherical Mirrors

• Concave

• Convex

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Parts of a Spherical Concave Mirror

• The focal length is half the radius of curvature
• R 2f
• The focal length is positive for a concave mirror
  because it is on the shiny side
• Rays parallel to the optical axis all pas through
  the focus

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Ray Tracing for Concave Mirrors

• You must draw at least TWO of the three principal
  rays to construct an image
• The p-ray parallel to the principal axis, then
  reflects through the focus
• The f-ray travels through the focus then
  reflects back parallel to the principal axis
• The c-ray travels through the center, then
  reflects back through the center

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Concave Mirrors

• Diagram the following images
• Object outside the center of curvature
• Object at the center of curvature
• Object between center of curvature and focus
• Object at the focal point
• Object inside the focus

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Mirror Equation 1 Mirror Equation 2

• 1/si 1/s0 1/f
• si image distance
• s0 object distance
• f focal length

• M hi/h0 -si/s0
• si image distance
• s0 object distance
• hi image height
• h0 object height
• M magnification

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Sign Conventions

• Focal length (f)
• Positive for concave mirrors
• Negative for convex mirrors
• Magnification (M)
• Positive for upright images
• Negative for inverted images
• Enlarged M gt 1
• Reduced M lt 1
• Image Distance
• si is positive for real images
• si is negative for virtual images

• Practice A spherical concave mirror, focal
  length 20 cm, has a 5-cm high object placed 30 cm
  from it
• Draw a ray diagram and construct the image
• Use mirror equations to calculate the position,
  magnification, and size of the image
• Name the image

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Parts of a Spherical Convex Mirror

• The focal length is half the radius of curvature
  and both are on the dark side of the mirror
• The focal length is negative

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Ray Tracing

• Construct the image for an object located outside
  a spherical convex mirror
• Name the image

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Practice 5

• A spherical concave mirror, focal length 10 cm,
  has a 2-cm high object placed 5 cm from it
• Draw a ray diagram and construct the image
• Use the mirror equations to calculate position,
  magnification, and size of image
• Name the image

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Spherical Mirrors

• Concave

• Convex

• Image is real when object is outside focus
• Image is virtual when object is inside focus
• Focal length is positive

• Image is ALWAYS virtual
• Focal length is negative

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Wave Behavior 2 Refraction

• Refraction occurs when a wave is transmitted from
  one medium to another
• Refracted waves may change speed and wavelength
• Refraction is almost always accompanied by some
  reflection
• Refracted waves do NOT change frequency

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Refraction of Light

• Refraction causes a change in speed of light as
  it moves from one medium to another
• Refraction can cause bending of the light ray at
  the interface between media
• Index of Refraction (n)
• n speed of light in vacuum / speed of light in
  medium
• n c/v

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Snells Law

• n1sinT1 n2sinT2

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Snells Law

• When the index of refraction increases, light
  bends TOWARD the normal
• When the index of refraction decreases, light
  bends AWAY FROM the normal

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Problem 6!

• Light enters an oil from the air at an angle of
  50 with the normal, and the refracted beam makes
  an angle of 33 with the normal
• Draw the situation
• Calculate the index of refraction of the oil
• Calculate the speed of light in the oil

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Prism Problems (7)

• Light enters a prism as shown, and passes through
  the prism
• a. Complete the path of light through the prism
  and show the angle it will make when it leaves
  the prism
• b. If the refractive index of the glass is 1.55,
  calculate the angle of refraction when it leaves
  the prism
• c. How would the answer to (b) change if the
  prism were immersed in water?

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Prism Problems (8)

• Light enters a prism made of air from glass
• Complete the path of the light through the prism,
  and show the angle it will make when it leaves
  the prism
• If the refractive index of the glass is 1.55,
  calculate the angle of refraction when it leaves
  the prism

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Critical Angle of Incidence

• The smallest angle of incidence for which light
  cannot leave a medium is called the critical
  angle of incidence
• If light passes into a medium with a greater
  refractive index than the original medium, it
  bends away from the normal and the angle of
  refraction is greater than the angle of incidence
• If the angle of refraction is 90, the light
  cannot leave the medium and no refraction occurs
• We call this TOTAL INTERNAL REFLECTION

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Total Internal Reflection

• Calculating the Critical Angle

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Practice No. 9

• What is the critical angle of incidence for a
  gemstone with refractive index 2.45 if it is in
  air?
• If you immerse it in water (refractive index
  1.33), what does this do to the critical angle of
  incidence?

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Lenses Refract Light

• Converging (Convex)

• Diverging (Concave)

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Lens Ray Tracing

• Ray tracing is used for lenses also. Use the
  same principal rays used with mirrors. You must
  draw TWO of the three
• the p-ray parallel to the principal axis,
  refracts through the focus
• the f-ray travels through the focus, then
  refracts parallel to the principal axis
• the c-ray travels through the center and
  continues without bending
• Use the same equations we used for mirrors

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Converging Lenses
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Construct the following images

• Object located outside 2F for a converging lens
• Object located at 2F
• Object located between F and 2F
• Object at the focus
• Object inside the focus

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Diverging Lenses

• Construct an image for an object located in front
  of a diverging lens