22.5 Dispersion

1
22.5 Dispersion

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

2
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

3
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

4
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

5
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

6
Example
Flint glass prism
n21
Find the angle each ray makes with the
horizontal.
30?
n11.66 (red)
q130?
60?
n11.70 (violet)

• n1sinq1 n2sinq2
• Red
• q2sin-1(1.66/1.00sin30?)56.1?
• Result 56.1?-30.0?26.1?
• Violet
• q2sin-1(1.70/1.00sin30?)58.2?
• Result 58.2?-30.0?28.2?

7
22.6 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

8
The Rainbow, cont.

• 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 violet
  ray is 40
• The angle between the white light and the red ray
  is 42

9
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

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22. 7.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

11
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

12
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, which is the tangent
  to the wavefronts

13
Huygens Construction for a Spherical Wave

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

14
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

15
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

• sinq1v1t/d (yellow triangle)
• sinq2v2t/d (green triangle)

The geometrical derivation of the law of
refraction (Snells law).
17
Huygens Principle and the Law of Refraction,
cont.
Air

• Every point on a wave front can be considered to
  be a source of secondary waves. The figure
  explains the refraction at an interface between
  media with different optical densities.

Medium 1
18
Huygens Principle and the Law of Refraction,
cont.
n1sinq1n2sinq2
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22.8 Total Internal Reflection and Fiber Optics

• Total internal reflection. When light enters a
  less optically dense medium, it is refracted away
  from the normal. At a critical angle ?c, the
  light is reflected along the interface. At angles
  greater than ?c, there is total internal
  reflection.

20
Total Internal Reflection

• Rays of laser light enter the water in the
  fishbowl from above they are reflected at the
  bottom by mirrors tilted at slightly different
  angles, and one ray undergoes total internal
  reflection at the air-water interface.

Total internal reflection
21
Critical Angle

• n1sin?1 n2sin?2
• If q290?
• sin?21 ? q1qc
•  

Critical angle
sin?cn2/n1 (for n1gtn2)
For ray 4, q2 is 90? ? Total internal reflection
starts
22
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 (ray 5 in the previous picture)
• 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

23
Fiber Optics
Fiber-optic cable

• Internal reflection is the basis of fiber optics.

Very important for modern data transfer and
communication systems ? phones!  
Total internal reflection
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Optical fiber communication system
Decoder
Electrical/optical converter
Electric signal
Optical/electrical converter
Fiber
Encoder
Repeater
Digital encoding scheme for optical
communications
One
Zero
High-power pulse ? one Low-power pulse ? zero
High-power pulse ? One
25
Step-index Fiber
Step in the refractive index
In
Disadvantage Pulse broadening
Intensity
Out
Time
26
Graded-index fiber
Pulse broadening is not so severe
Refractive index vary parabolically across the
cross-section
Intensity remains almost constant
In
Out
Time
27
Graded-index Fiber, cont.

• In the graded-index fiber, light rays that
  traverse longer path lengths through the outer
  periphery of the core travel faster in this lower
  index material ? all rays arrive at the same time
  at the output ? almost no pulse broadening!

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Fibers, Summary

• Step-index optical fibers are used for cheap
  short-range applications
• Graded-index fibers are used for long-range
  high-quality data transfer