35 6 huygens s principle l.
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35.6 Huygens’s Principle Huygens’s Principle Huygens assumed that light is a form of wave motion rather than a stream of particles

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huygens s principle
Huygens’s Principle
  • Huygens assumed that light is a form of wave motion rather than a stream of particles
  • Huygens’s 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
huygens s principle cont
Huygens’s 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 outward through a medium with speeds characteristic of waves in that medium
  • After some time has passed, the new position of the wave front is the surface tangent to the wavelets
huygens s construction for a plane wave
Huygens’s 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
huygens s construction for a spherical wave
Huygens’s 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
huygens s principle and the law of reflection
Huygens’s Principle and the Law of Reflection
  • The law of reflection can be derived from Huygens’s principle
  • AB is a wave front of incident light
    • The wave at A sends out a wavelet centered on A toward D
    • The wave at B sends out a wavelet centered on B toward C
  • AD = BC = c∆t
huygens s principle and the law of reflection cont
Huygens’s Principle and the Law of Reflection, cont.
  • Triangle ABCis congruent to triangle ADC
  • cos g = BC / AC
  • cos g’ = AD / AC
  • Therefore, cos g = cos g ’ and g = g ’
  • This gives 1 = 1’
  • This is the law of reflection
huygens s principle and the law of refraction
Huygens’s Principle and the Law of Refraction
  • Ray 1 strikes the surface and at a time interval ∆t later, ray 2 strikes the surface
    • During this time interval, the wave at A sends out a wavelet, centered at A, toward D
    • The wave at B sends out a wavelet, centered at B, toward C
huygens s principle and the law of refraction cont
Huygens’s Principle and the Law of Refraction, cont.
  • The two wavelets travel in different media, therefore their radii are different
  • From triangles ABC and ADC, we find
huygens s principle and the law of refraction final
Huygens’s Principle and the Law of Refraction, final
  • The preceding equation can be simplified to
  • This is Snell’s law of refraction
35 7 dispersion and prisms
35.7 Dispersion and Prisms
  • For a given material, the index of refraction varies with the wavelength of the light passing through the material
  • This dependence of nonis calleddispersion
  • Snell’s law indicates light of different wavelengths is bent at different angles when incident on a refracting material
variation of index of refraction with wavelength
Variation of Index of Refraction with Wavelength
  • The index of refraction for a material generally decreases with increasing wavelength
  • Violet light bends more than red light when passing into a refracting material
angle of deviation
Angle of Deviation
  • The ray emerges refracted from its original direction of travel by an angle δ, called the angle of deviation
  • The angle of deviation depends on the wavelength
refraction in a prism
Refraction in a Prism
  • Since all the colors have different angles of deviation, white light will spread out into a spectrum
    • Violet deviates the most
    • Red deviates the least
    • The remaining colors are in between
example 35 5 measuring n from a prism
Example 35.5 Measuring n from a Prism
  • The minimum angle of deviation(δmin) for a prism occurs when the incident angle 1is such that the refracted ray inside the prism makes the same angle with the normal to the two prism faces.
  • Obtain an expression for the index of refraction of the prism material.
example 35 5 measuring n from a prism cont
Example 35.5 Measuring n from a Prism, cont.
  • From the geometry:
  • From Snell’s Law (with n = 1 for air):
the rainbow
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
the rainbow 2
The Rainbow, 2
  • At the back surface the light is reflected
  • It is refracted again as it returns to the front surface and moves into the air
  • The rays leave the drop at various angles
    • The angle between the white light and the most intense violet ray is 40°
    • The angle between the white light and the most intense red ray is 42°
slide19

Active Figure 35.23

(SLIDESHOW MODE ONLY)

observing the rainbow
Observing the Rainbow
  • If a raindrop high in the sky is observed, the red ray is seen
  • A drop lower in the sky would direct violet light to the observer
  • The other colors of the spectra lie in between the red and the violet
double rainbow
Double Rainbow
  • The secondary rainbow is fainter than the primary
  • The secondary rainbow arises from light that makes two reflections from the interior surface before exiting the raindrop
  • Higher-order rainbows are possible, but their intensity is low
35 8 total internal reflection
35.8 Total Internal Reflection
  • A phenomenon called total internal reflection can occur when light is directed from a medium having a given index of refraction toward one having a lowerindex of refraction
possible beam directions
Possible Beam Directions
  • Possible directions of the beam are indicated by rays numbered 1 through 5
  • The refracted rays are bent away from the normal since n1 > n2
critical angle
Critical Angle
  • There is a particular angle of incidence that will result in an angle of refraction of 90°
    • This angle of incidence is called the critical angle,C

(35.10)

slide25

Active Figure 35.26

(SLIDESHOW MODE ONLY)

critical angle cont
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 is directed from a medium of a given index of refraction toward a medium of lower index of refraction
example 35 6 find critical angle c
Example 35.6 Find Critical Angle C
  • Find C for an Air-Water boundary.

n1 = 1.00 and n2 = 1.33

example 35 7 a view from the fish s eye
Example 35.7 A view from the Fish’s Eye
  • A fish in a still pond looks upward toward the water’s surface. What does it see?
  • Using the result from Example 35.6
    • At an angle less than C (48.8°) the fish can see out of the water
    • At 48.8° the light has to skim along the water’s surface before been refracted, so the fish can see the whole shore of the pond.
    • At an angle greater than C (48.8°) the fish sees a reflection of the bottom of the pond.
fiber optics
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
fiber optics cont
Fiber Optics, cont.
  • A flexible light pipe is called an optical fiber
  • A bundle of parallel fibers (shown) can be used to construct an optical transmission line
construction of an optical fiber
Construction of an Optical Fiber
  • The transparent core is surrounded by cladding
    • The cladding has a lower n than the core
    • This allows the light in the core to experience total internal reflection
  • The combination is surrounded by the jacket
slide32

Material for the Midterm

  • Examples to Read!!!
    • NONE
  • Homework to be solved in Class!!!
    • Question: 19
    • Problems: 31, 36