Refraction

1
Chapter 15

• Refraction

2
Chapter 15 Objectives

• Law of Refraction
• Snells Law
• Recognize the sign conventions for refracting
  surfaces
• Characterize images formed by thin lenses
• Recognize the sign conventions for thin lenses
• Utilize the lens makers equation
• Phenomena of the eye
• Total Internal Reflection
• Define Critical Angle

3
Refraction

• When a light ray encounters a boundary of a
  different density medium, part of the ray is
  reflected and the rest enters the medium.
• The portion that enters the new medium is bent
  slightly, or refracted.

4
Angle of Refraction

• The angle of refraction, ?2, depends on
• properties of the two media
• angle of incidence
• Using those two qualities we can derive an index
  of refraction that is unique to each substance.
• We use air as our reference material to have an
  index of refraction of n 1.000

?1
?1
?2
5
Snells Law

• Willebrord Snell (1591 1626) is the man credited
  with the discovery of how light behaves when it
  changes medium.
• He saw a relationship between the angle of
  incidence and the speed of light traveling
  through that medium.
• The density difference of the material created a
  change in the speed at which light travels
  through that medium.

sin ?2
v2

sin ?1
v1
6
Law of Refraction

• When light passes from one transparent medium to
  another, it is refracted because the speed of
  light is different in the two media.
• As light travels from one medium to another, its
  frequency does not change.
• That comes from the wave nature of light.
• So if frequency stays the same, then wavelength
  and speed are the variables that can change.

7
Index of Refraction

• To establish a consistent system for how light
  behaves at boundary encounters, we establish an
  index of refraction.
• That is, a relationship of how the speed of light
  changes from one substance to another.
• And we use the speed of light in a vacuum as the
  baseline.
• So the smallest index of refraction is air, n
  1.000.

c
speed of light in a vacuum
n


v
speed of light in the medium
8
Snells Law Revised

• With some mathematical manipulation, we can
  identify the angle of refraction by simply
  knowing the indices of the mediums in play.

angle of refraction
n1 sin ?1
n2 sin ?2

angle of incidence
9
Images Formed by Refraction

• Lenses using the refraction property of light to
  perform their duties.
• Whereas mirrors use the reflection property of
  light.

10
Sign Conventions for Spherical Lenses

• The sign conventions are the same as mirrors
  except when it comes to the image and the center
  of curvature.
• p is positive if the object is in front of the
  lens. (real object)
• p is negative if the object is behind the lens.
  (virtual object)
• q is negative if the image is in front of the
  lens. (virtual image)
• q is positive if the image is behind the lens.
  (real image)
• R is negative if the center of curvature is in
  front of the lens. (concave lens)
• R is positive if the center of curvature is
  behind the lens.(convex lens)
• If M is positive, the image is upright.
• If M is negative, the image is inverted.

11
Thin Lenses

• A typical thin lens consists of a piece of glass
  or plastic, ground so that each refracting
  surface is a segment of a sphere or plane.
• There are two types of thin lenses
• Converging lenses
• The initial surface of incidence is typically
  convex.
• This type of lens causes the rays to converge, or
  meet, at a single point after passing through.
• Diverging lenses
• The initial surface of incidence is typically
  concave.
• This type of lens causes the rays to diverge, or
  separate, after passing through.

12
Focal Point of a Lens

• The focal point of a lens is found by the same
  method as a mirror.
• That is the location that a set of parallel rays
  will intersect once they pass through the lens.
• There are two focal points for every thin lens
  because of the two refracting surfaces.
• Light could enter from the left or the right!

F
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Focal Length of a Lens

• The focal length, ƒ, of a lens, and a mirror, is
  the image distance that corresponds to an
  infinite object distance.

F
ƒ
14
Magnification of a Lens

• The magnification formula and notation is the
  same for a lens as it was for a mirror.
• Just remember the sign conventions are a little
  bit different based on the location of the image.

q is negative for a virtual image, and positive
for a real image.
q
h
image height

M


h
p
object height
Negative sign shows the object is inverted.
p is always positive, that way it acts as our
point of reference.
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Thin Lens Equation

• The thin-lens equation looks and acts very
  similar to the mirror equation.
• Except for the different sign conventions based
  on the location of the image.
• ƒ is positive for a converging lens
• ƒ is negative for a diverging lens

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Lens Makers Equation

• Because lenses have two refracting surfaces, we
  need to account for the radius of curvature for
  both surfaces.
• Since the radius of curvature can be different
  for each surface, the thin lens equation turns
  into this more useful form
• Assuming that the lens is being used for light
  traveling through air.
• This will determine the overall focal length of
  any lens.

(
)


(n 1)
Index of refraction of the lens material
Radius of curvature of the front surface
Radius of curvature of the rear surface
17
Ray Diagrams for Thin Lenses

• The first ray is drawn parallel to the principal
  axis and then refracted so it goes through the
  focal point of the incident surface.
• A second ray is drawn through the center of the
  lens and passes straight through to the other
  side.
• The last ray is drawn through the focal point of
  the rear surface of the lens and emerges from the
  rear surface parallel to the principal axis.

18
Internal Reflection

• Internal reflection can only occur when light
  attempts to travel from a medium with a high
  index of refraction to a medium with a lower
  index of refraction.
• At a particular angle of incidence called the
  critical angle, ?c , the refracted light ray
  moves parallel to the reflecting boundary.
• Refraction will occur when ?1 lt ?c
• Reflection will occur when ?1 gt ?c
• This reflection will keep the light ray inside
  the original medium, thus internal reflection.

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Calculating Critical Angle

• Knowing that the critical angle is found when the
  light ray is refracted parallel to the reflecting
  surface.
• Plug 90o into Snells Law as the angle of
  refraction, and you will see the following

n1 sin ?1
n2 sin ?2

n1 sin ?c
n2 sin 90o

n1 sin ?c
n2

n2
sin ?c

n1
20
Fiber Optics

• Fiber optic cables use internal reflection to
  send a light pulse to a receiver.
• By knowing the critical angle of the fiber
  medium, the light source is transmitted at an
  angle larger than that so it will continue to
  internally reflect itself until it reaches its
  destination.
• Fiber optic cables allow information to be
  transmitted faster because it uses light versus
  sound.
• Speed of light gtgtgt speed of sound.
• Fiber optic cables are better than using
  electrical pulses because the cables are less
  likely to build up heat.
• Heat creates resistance in electrical circuits.

The first fiber optic semi-flexible gastroscope
was patented by Basil Hirschowitz, C. Wilbur
Peters, and Lawrence E. Curtiss, researchers at
the University of Michigan, in 1956.
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Dispersion

• Because Snells Law relates the angle of
  refraction to the wavelength of light, waves of
  differing lengths bend at different angles.
• In general, the index of refraction decreases as
  the wavelength increases.
• So blue light (?470 nm) will bend more than red
  light (?650 nm)

22
Light Spectra

• Because of the effects of dispersion, the
  emerging light rays fan out to show the spectrum
  of light.
• Every energy source has it unique spectrum.
• Each energy source can be identified by its light
  spectrum much like people are identified by their
  fingerprints.
• A prism spectrometer is used to identify the
  fingerprint of any gas by emitting light at
  unique wavelengths.

23
Atmospheric Refraction