Reflection and Refraction

1
Chapter 22

• Reflection and Refraction
• of
• Light

2
22.1 The Nature of Light

• 1000 AD
• It was proposed that light consisted of tiny
  particles
• Newton
• Used this particle model to explain reflection
  and refraction
• Huygens
• 1670
• Explained many properties of light by proposing
  light was wave-like

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A Brief History of Light, cont.

• Young
• 1801
• Strong support for wave theory by showing
  interference
• Maxwell
• 1865
• Electromagnetic waves travel at the speed of
  light

4
A Brief History of Light, final

• Planck
• EM radiation is quantized
• Implies particles
• Explained light spectrum emitted by hot objects
  (black body radiation)
• Einstein
• Particle nature of light
• Explained the photoelectric effect

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Dual Nature of Light

• Experiments can be devised that will display
  either the wave nature or the particle nature of
  light
• Nature prevents testing both qualities at the
  same time

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The Nature of Light, final

• Particles of light are called photons
• Each photon has a particular energy
• E h
• h is Plancks constant
• h 6.63 x 10-34 J s
• Encompasses both natures of light
• Interacts like a particle
• Has a given frequency like a wave

7
22.2 Geometrical Optics Using a Ray
Approximation

• Light travels in a straight-line path in a
  homogeneous medium until it encounters a boundary
  between two different media
• The ray approximation is used to represent beams
  of light
• A ray of light is an imaginary line drawn along
  the direction of travel of the light beams

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Wave Fronts and Rays

• (a) Near a point source, the wave fronts (i.e.,
  surfaces of constant phase) are circular in two
  dimensions (? stone in the water) and spherical
  in three dimensions. (b) Far from a point
  source, the wave fronts are approximately linear
  or planar. A line perpendicular to a wave front
  in direction of the waves propagation is called
  a ray.

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Wave Fronts and Rays, cont.
Far field
Near field
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Geometrical Optics

• Plane waves are important in understanding the
  properties of mirrors and lenses.  
• For light waves, the ray concept is particularly
  convenient for showing the path taken by the
  light.
•  
• Geometrical Optics
• We will make frequent use of light rays, and they
  can be regarded essentially as narrow beams of
  light much like those lasers produce.

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22.3 Reflection of Light

• A ray of light, the incident ray, travels in a
  medium
• When it encounters a boundary with a second
  medium, part of the incident ray is reflected
  back into the first medium
• This means it is directed backward into the first
  medium

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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

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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

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Specular and Diffuse Reflection
Diffuse
Specular
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Law of Reflection

• The normal is a line perpendicular to the surface
• It is at the point where the incident ray strikes
  the surface
• The incident ray makes an angle of ?1 with the
  normal
• The reflected ray makes an angle of ?1 with the
  normal

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Law of Reflection, cont.
Incident and reflected ray are in the same plane.

• The angle of reflection is equal to the angle of
  incidence
• ?1?1

?1
?1
17
Refraction of Light

• When a ray of light traveling in a transparent
  medium encounters a boundary leading into a
  second 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

18
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

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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

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22.4 The Law of Refraction

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

The geometrical derivation of the law of
refraction (Snells law).
21
Refraction, cont.

• Speed of lightconstant?
• Yes, but only in ONE medium!

vc (light velocity)
Air
Index of refraction
vc/n Water (optically denser than air)
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Index of refraction

• The index of refraction defines the velocity of
  light in the optically denser medium ? c/n.

Speed of light in vacuum (air)
Index of refraction
Speed of light in a medium (e.g. water)
23
Index of Refraction, cont.

• For a vacuum and air, n 1
• For other media, n gt 1
• n is a unitless ratio

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Frequency Between Media

• As light travels from one medium to another, its
  frequency does not change
• Both the wave speed and the wavelength do change
• The wavefronts do not pile up, nor are created or
  destroyed at the boundary, so must stay the same

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Change of Wavelength
Wavelength of a medium with the refractive index
n
nl0/ln
Vacuum wavelength
26
Refraction Details

• Light may refract into a material where its speed
  is lower
• The angle of refraction is less than the angle of
  incidence
• The ray bends toward the normal

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Refraction Details, cont.

• Light may refract into a material where its speed
  is higher
• The angle of refraction is greater than the angle
  of incidence
• The ray bends away from the normal

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Index of Refraction Extended

• The frequency stays the same as the wave travels
  from one medium to the other
• v ?
• The ratio of the indices of refraction of the two
  media can be expressed as various ratios

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Snells Law of Refraction

• n1sin?1n2sin?2
• ?1 is the angle of incidence
• 30.0 in this diagram
• ?2 is the angle of refraction

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Some indices of refraction for various substances
at 590 nm
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Example and Application

• A digital information on a DVD consists of a
  series of pits that are read by a laser beam.
  The surface of a DVD is shown on the right side.

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Example and application, cont.

• The picture shows the cross section of a
  cone-shaped laser beam used to read the
  information on the DVD. Find the required angle
  ?1 at which the conical beam should enter in
  order to achieve a1 mm.

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Example and application, cont.

• The following informations are given t1.2 mm,
  w0.70 mm, and the refractive index of the
  plastic is 1.55

w2ba b(w-a)/2
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Example and application, cont.
b(0.70?10-3 m - 1?10-6 m)/2699 mm/2349.5
mm tg?2b/t349.5 mm/1200 mm0.29 ?2
16.2? Snells law n1sin?1n2sin?2 sin?1n2sin?2/
n11.55sin(16.2?)/1.00 ?125.6?
Air
Plastic