Why is the sky blue?

1

• Why is the sky blue?
• How do rainbows work?

2
Chapter 14

• Refraction Of Light

3
Specular Reflection

• Specular reflection is reflection from a smooth
  surface
• The reflected rays are parallel to each other
• All reflection in this text is assumed to be
  specular

4
Diffuse Reflection

• Diffuse reflection is reflection from a rough
  surface
• The reflected rays travel in a variety of
  directions
• Diffuse reflection makes the road easy to see at
  night

5
Refraction of Light, cont

• The incident ray, the reflected ray, the
  refracted ray, and the normal all lie on the same
  plane
• The angle of refraction, ?2, depends on the
  properties of the medium

6
Following the Reflected and Refracted Rays

• Ray ? is the incident ray
• Ray ? is the reflected ray
• Ray ? is refracted into the lucite
• Ray ? is internally reflected in the lucite
• Ray ? is refracted as it enters the air from the
  lucite

7
Why is Light Bent or Refracted?

• Light is refracted because the speed of light
  varies in different media
• nair 1.00
• nglass 1.458 -1.66
• ndiamond 2.419
• The speed of light varies in different media
  because of varying time lags in absorption and
  re-emission of light due to electronic structure

8
The Index of Refraction

• The index of refraction, n, of a medium can be
  defined
• For a vacuum, n 1
• For other media, n gt 1
• n is a unitless ratio
• When ngt1, light slows down to maintain frequency

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Indices of Refraction for Various Substances
Chapter 14
10
Refraction
Chapter 14
11
Image Position for Objects in Different Media
Chapter 14
12
Snells Law of Refraction

• Discovered experimentally
• n1 sin ?1 n2 sin ?2
• ?1 is the angle of incidence
• 30.0 in this diagram
• ?2 is the angle of refraction

13
Refraction in a Prism

• The amount the ray is bent away from its original
  direction is called the angle of deviation, d
• Since all the colors have different angles of
  deviation, they will spread out into a spectrum
• Violet deviates the most
• Red deviates the least

14
Fig. 22.16, p.697
15
Variation of Index of Refraction with Wavelength

• The index of refraction for a material usually
  decreases with increasing wavelength
• Violet light refracts more than red light when
  passing from air into a material
• This phenomena is also known as dispersion

16
Observing the Rainbow
17
Thin Lenses

• A thin lens consists of a piece of glass or
  plastic, ground so that each of its two
  refracting surfaces is a segment of either a
  sphere or a plane
• Lenses are commonly used to form images by
  refraction in optical instruments

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Thin Lens Shapes

• These are examples of converging lenses
• They have positive focal lengths
• They are thickest in the middle

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More Thin Lens Shapes

• These are examples of diverging lenses
• They have negative focal lengths
• They are thickest at the edges

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Focal Length of Lenses

• The focal length, ƒ, is the image distance that
  corresponds to an infinite object distance
• This is the same as for mirrors
• A thin lens has two focal points, corresponding
  to parallel rays from the left and from the right
• A thin lens is one in which the distance between
  the surface of the lens and the center of the
  lens is negligible

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Focal Length of a Converging Lens

• The parallel rays pass through the lens and
  converge at the focal point
• The parallel rays can come from the left or right
  of the lens

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Focal Length of a Diverging Lens

• The parallel rays diverge after passing through
  the diverging lens
• The focal point is the point where the rays
  appear to have originated

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Farsighted and Nearsighted
Chapter 14
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Lens Equations

• The equations can be used for both converging and
  diverging lenses
• A converging lens has a positive focal length
• A diverging lens has a negative focal length

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Lens Equations

• The geometric derivation of the equations is very
  similar to that of mirrors

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Lens Imaging
Lens Type Object Beyond Focal Point Object At Focal Point Object Between Focal Point And Lens
Converging (convex) Real Inverted Reduced Image No Image Formed Erect Virtual Magnified Image
Diverging (concave) Virtual Erect Reduced Image Virtual Erect Reduced Image Virtual Erect Reduced Image
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Sign Conventions for Thin Lenses
Quantity Positive When Negative When
Object location (p) Object is in front of the lens Object is in back of the lens
Image location (q) Image is in back of the lens (real image) Image is in front of the lens (virtual image)
Image height (h) Image is upright Image is inverted
Magnification Image is upright Image is inverted
Focal length (f) Converging lens Diverging lens
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Ray Diagram for Converging Lens, p gt f

• The image is real
• The image is inverted

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Ray Diagram for Converging Lens, p lt f

• The image is virtual
• The image is upright

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Ray Diagram for Diverging Lens

• The image is virtual
• The image is upright

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Ray Diagrams for Thin Lenses

• Ray diagrams are essential for understanding the
  overall image formation
• Three rays are drawn
• The first ray is drawn parallel to the first
  principle axis and then passes through (or
  appears to come from) one of the focal lengths
• The second ray is drawn through the center of the
  lens and continues in a straight line
• The third ray is drawn from the other focal
  point and emerges from the lens parallel to the
  principle axis
• There are an infinite number of rays, these are
  convenient

32
The Rainbow

• A ray of light strikes a drop of water in the
  atmosphere
• It undergoes both reflection and refraction
• First refraction at the front of the drop
• Violet light will deviate the most
• Red light will deviate the least

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Prism Spectrometer

• A prism spectrometer uses a prism to cause the
  wavelengths to separate
• The instrument is commonly used to study
  wavelengths emitted by a light source

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Total Internal Reflection

• Total internal reflection can occur when light
  attempts to move from a medium with a high index
  of refraction to one with a lower index of
  refraction
• Ray 5 shows internal reflection

When the incident angle is equal to the critical
angle, total internal reflection occurs
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Critical Angle

• A particular angle of incidence will result in an
  angle of refraction of 90
• This angle of incidence is called the critical
  angle
• n1sin?cn2sin90
• Therefore
• sin?c n2
• n1

Calculate the critical angle for a Plastic light
guide, n1.49
36
Fiber Optics

• An application of internal reflection
• Plastic or glass rods are used to pipe light
  from one place to another
• Applications include
• medical use of fiber optic cables for diagnosis
  and correction of medical problems
• Telecommunications
• Internet
• Dash board lighting

37
Fig. 22.29, p.705
38
Huygens Principle

• Huygen assumed that light is a form of wave
  motion rather than a stream of particles
• Huygens Principle is a geometric construction
  for determining the position of a new wave at
  some point based on the knowledge of the wave
  front that preceded it

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Huygens Principle, cont

• All points on a given wave front are taken as
  point sources for the production of spherical
  secondary waves, called wavelets, which propagate
  in the forward direction with speeds
  characteristic of waves in that medium
• After some time has elapsed, the new position of
  the wave front is the surface tangent to the
  wavelets

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Huygens Construction for a Plane Wave

• At t 0, the wave front is indicated by the
  plane AA
• The points are representative sources for the
  wavelets
• After the wavelets have moved a distance c?t, a
  new plane BB can be drawn tangent to the
  wavefronts

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Huygens Construction for a Spherical Wave

• The inner arc represents part of the spherical
  wave
• The points are representative points where
  wavelets are propagated
• The new wavefront is tangent at each point to the
  wavelet

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Using Spectra to Identify Gases

• All hot, low pressure gases emit their own
  characteristic spectra
• The particular wavelengths emitted by a gas serve
  as fingerprints of that gas
• Some uses of spectral analysis
• Identification of molecules
• Identification of elements in distant stars
• Identification of minerals

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Dispersion

• The index of refraction in anything except a
  vacuum depends on the wavelength of the light
• This dependence of n on ? is called dispersion
• Snells Law indicates that the angle of
  refraction when light enters a material depends
  on the wavelength of the light

44
Huygens Principle and the Law of Reflection

• The Law of Reflection can be derived from
  Huygens Principle
• AA is a wave front of incident light
• The reflected wave front is CD

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Huygens Principle and the Law of Reflection, cont

• Triangle ADC is congruent to triangle AAC
• ?1 ?1
• This is the Law of Reflection

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Huygens Principle and the Law of Refraction

• In time ?t, ray 1 moves from A to B and ray 2
  moves from A to C
• From triangles AAC and ACB, all the ratios in
  the Law of Refraction can be found
• n1 sin ?1 n2 sin ?2

47
Refraction of Light

• When a ray of light traveling through a
  transparent medium encounters a boundary leading
  into another transparent medium, part of the ray
  is reflected and part of the ray enters the
  second medium
• The ray that enters the second medium is bent at
  the boundary
• This bending of the ray is called refraction

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Critical Angle, cont

• For angles of incidence greater than the critical
  angle, the beam is entirely reflected at the
  boundary
• This ray obeys the Law of Reflection at the
  boundary
• Total internal reflection occurs only when light
  attempts to move from a medium of higher index of
  refraction to a medium of lower index of
  refraction

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Fig. 22.12, p.694