Reflection and Refraction of Light

1
Chapter 22

• Reflection and Refraction of Light

2
Dual Nature of Light

• Experiments can be devised that will display
  either the wave nature or the particle nature of
  light in some experiments light acts as a wave
  and in others it acts as a particle
• Nature prevents testing both qualities at the
  same time
• Particles of light are called photons
• Each photon has a particular energy E h ƒ
• h 6.63 x 10-34 J s Plancks constant
• Each photon encompasses both natures of light
  interacts like a particle and has a frequency
  like a wave

3
Geometric Optics and 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
• A wave front is a surface passing through points
  of a wave that have the same phase
• The rays, corresponding to the direction of the
  wave motion, are perpendicular to the wave front

4
Geometric Optics and 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
• A wave front is a surface passing through points
  of a wave that have the same phase
• The rays, corresponding to the direction of the
  wave motion, are perpendicular to the wave front

5
Reflection of Light

• A ray of light (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

6
Specular Reflection

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

7
Diffuse Reflection

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

8
Law of Reflection

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

9
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
  refracted bent at the boundary

10
Refraction of Light

• 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 and the angle of
  incidence
• The path of the light through the refracting
  surface is reversible

11
Refraction of Light

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

12
Refraction of Light

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

13
Refraction of Light

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

14
The Index of Refraction

• When light passes from one medium to another, it
  is refracted because the speed of light is
  different in the two media
• The index of refraction, n, of a medium can be
  defined
• n is a unitless ratio
• For a vacuum, n 1 whereas for other media, n gt 1

15
The Index of Refraction

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

16
The Index of Refraction

• v1 ƒ ?1 v2 ƒ ?2
• The ratio of the indices of refraction of the two
  media can be expressed as various ratios

17
Snells Law of Refraction

• n1 sin ?1 n2 sin ?2

18
Chapter 22Problem 19

• When a light ray passes through the glass block,
  it is shifted laterally by a distance d (see the
  figure). Find the value of d.

19
Chapter 22Problem 25

• A beam of light both reflects and refracts at the
  surface between air and glass, as shown in the
  figure. If the index of refraction of the glass
  is ng, find the angle of incidence, ?1, in the
  air that would result in the reflected ray and
  the refracted ray being perpendicular to each
  other.

20
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 made when light enters a material
  depends on the wavelength of the light
• The index of refraction for a material usually
  decreases with increasing wavelength

21
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 and red deviates the
  least

22
Spectroscopy

• A prism spectrometer uses a prism to cause the
  wavelengths to separate (to study wavelengths
  emitted by a light source)
• All hot, low pressure gases emit their own
  characteristic spectra with the particular
  wavelengths emitted by a gas serving as
  fingerprints of that gas
• Spectral analysis identification of molecules,
  minerals, elements in distant stars, etc.

23
The Rainbow

• A ray of light strikes a drop of water in the
  atmosphere and undergoes both reflection and
  refraction
• First refraction at the front of the drop violet
  light will deviate the most and red the least
• At the back surface the light is reflected and
  refracted again as it returns to the front
  surface and moves into the air
• The rays leave the drop at various angles

24
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

25
Huygens Principle

• 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
• All points on a given wave front are taken as
  point sources for the production of spherical
  secondary waves (wavelets) propagating 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

26
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

27
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

28
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
• Triangle ADC is congruent to triangle AAC
• ?1 ?1

29
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

30
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

31
Critical Angle

• A particular angle of incidence (critical angle)
  will result in an angle of refraction of 90
• 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

32
Chapter 22Problem 43

• The light beam in the figure strikes surface 2 at
  the critical angle. Determine the angle of
  incidence, ?i .

33
Fiber Optics

• Utilizes internal reflection
• Plastic or glass rods are used to pipe light
  from one place to another
• Applications include diagnosis and correction of
  medical problems, telecommunications, etc.

34
Chapter 22Problem 52

• An optical fiber with index of refraction n and
  diameter d is surrounded by air. Light is sent
  into the fiber along its axis, as shown in the
  figure. (a) Find the smallest outside radius R
  permitted for a bend in the fiber if no light is
  to escape. (b) Does the result for part (a)
  predict reasonable behavior as d approaches zero?
  As n increases? As n approaches unity? (c)
  Evaluate R, assuming that the diameter of the
  fiber is 100 µm and its index of refraction is
  1.40.

35
Answers to Even Numbered Problems Chapter 22
Problem 8 2.09 10 -11 s
36
Answers to Even Numbered Problems Chapter 22
Problem 20 1.06 10 -10 s
37
Answers to Even Numbered Problems Chapter 22
Problem 38 67.2
38

• Answers to Even Numbered Problems
• Chapter 22
• Problem 44
• ?1 30.0, ? '2 18.8
• ?1 30.0, ? '2 50.8

39
Answers to Even Numbered Problems Chapter 22
Problem 56 82