Reflection

1
Chapter 29

• Reflection Refraction

2
Reflection Refraction

• Shine a beam of light on a mirrorlight does not
  go through the mirror it is returned back into
  the airit is reflected back into the same medium
  rather than entering
• Shine a beam of light into a lake at an angle and
  the direction of the beam changesit is refracted
  (transferred into a different medium)
• Usually waves are partly reflected and refracted
  when they fall on a transparent medium

Incident ray
Reflected ray
Refracted ray
3
Reflection

• As a wave reaches a boundary between to media,
  some or all of the wave bounces back into the
  first mediumthis is reflection (the bouncing of
  light)
• The more rigid the second medium, the more
  reflection occurs
• Metal is rigid to light waves and reflects the
  light with almost the same intensity as the
  incident light strikes the metal
• Glass is not as rigid to light. When light
  strikes glass at a right angle only 4 of it is
  reflectedthe rest is transmitted

4
The Law of Reflection

• In one dimension reflected waves reflect in the
  direction from which they came
• In two dimensions the incident ray and the
  reflected ray make equal angles with the line
  perpendicular to the surface (called the normal)
• This is the law of reflection and applies if the
  incident ray, normal, and reflected ray all lie
  in the same plan. It also applies to both
  partially and totally reflected rays.

5
Flat Mirrors

• Shine a light at a plane (flat) mirror
• Rays are reflected in all directionseach ray
  obeying the law of reflection
• The rays diverge and continue to diverge from
  the mirror upon reflection
• The rays appear to originate from a point located
  behind the mirrorthe virtual image (light does
  not actually start there)
• Your eye cannot usually distinguish between the
  image and the virtual image

Virtual image
Light source
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Flat Mirrors

• Characteristics of Plane (flat) Mirrors
• Plane mirror images are virtual
• The image has a left-right reversal
• If you view an image of yourself in a plane
  mirror (perhaps a bathroom mirror), you will
  quickly notice that there is a left-right
  reversal of the image.
• The image is said to be upright, as opposed to
  inverted
• The image is as far behind the mirror as the
  object
• If you stand a distance of 2 meters from a plane
  mirror, you must look at a location 2 meters
  behind the mirror in order to view your image.
• The image and the object are the same size
• If a 1.6-meter tall person stands in front of a
  mirror, he/she will see an image which is
  1.6-meters tall.
• The ratio of the image dimensions to the object
  dimensions is termed the magnification. Plane
  mirrors produce images which have a magnification
  of 1.

7
Flat Mirrors

• Consider the diagram at the right. Which one of
  the angles (A, B, C, or D) is the angle of
  incidence? Which one of the angles is the angle
  of reflection?
• A ray of light is incident towards a plane mirror
  at an angle of 30-degrees with the mirror
  surface. What will be the angle of reflection?
• A ray of light is approaching a set of three
  mirrors as shown in the diagram. The light ray is
  approaching the first mirror at an angle of
  45-degrees with the mirror surface. Trace the
  path of the light ray as it bounces off the
  mirror continue tracing the ray until it finally
  exits from the mirror system. How many times will
  the ray reflect before it finally exits?

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Flat Mirrors

• If Suzie stands 3 feet in front of a plane
  mirror, how far from the person will her image be
  located?
• If a toddler crawls towards a mirror at a rate of
  0.25 m/s, then at what speed will the toddler and
  the toddler's image approach each other?

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Mirror Vocab

• Object distance the distance from the mirror to
  the object always positive
• Image distance the distance from the mirror to
  the image
• The image can be
• realinverted and able to be projected on a
  screen
• virtualright side up and not able to be
  projected on a screen
• Focal point the point where parallel rays meet
  (or appear to meet) after reflecting from the
  mirror
• Focal length the distance from the focal point
  to the mirror
• Converging mirror focal length is always positive
• Diverging mirror focal length is always negative
• Radius of curvature distance from the mirrors
  surface to the center of curvature (is 2 times
  the focal length)

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Converging and Diverging Mirrors

• There are two types of spherical (has a shape of
  part of a spherical surface) mirrorsconverging
  (concave) and diverging (convex)

concave
convex
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Mirror Equations

• Concave mirrors are used whenever a magnified
  image of an object is needed
• Reflectors in flashlights, telescopes
• Convex mirrors are used to offer a wider view
  than a plane mirror
• The images are smallercar side view mirrors
• Location and size of the image depends on the
  radius of curvature (R) (the distance from the
  mirrors surface to the center of curvature (C))
  of the mirror
• Concave mirrors can produce both real and virtual
  images
• Convex mirrors can only produce virtual images
• Image location can be predicted by the mirror
  equation
• Use ray diagrams (drawn to scale) to check the
  equation3 rays
• 1 from top of object parallel to principle axis
  reflects off mirror through the focal point
• 2 from top of object through focal point f
  reflects off mirror parallel to the principal
  axis
• 3 from top of object through the center of
  curvature (center of curvature 2f) back along
  itself
• Images created by spherical mirrors suffer from
  spherical aberrationcertain rays do not exactly
  intersect at the image point
• Magnification relates image and object sizes
• If M is positivethe image is upright and virtual
• If M is negativethe image is inverted and real

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Converging (Concave) Mirrors

• A concave spherical mirror has a focal length of
  10.0 cm. Locate the image of a pencil that is
  place upright 30.0 cm from the mirror. Find the
  magnification of the image. Draw a ray diagram
  to confirm your answer.
• Find the image distance and magnification of the
  mirror in the problem above when the object
  distances are 10.0 cm and 5.00 cm. Find the
  magnification of the image. Draw a ray diagram
  to confirm your answer.

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Diverging (Convex) Mirror

• A mirror whose reflecting surface is an outward
  curved segment of a sphere
• Incoming rays diverge after reflection as though
  the were coming from some point behind the mirror
• Passengers side side-view mirror (WARNING
  Objects are closer than they appear)
• Image created is always virtual and image
  distance is always negative
• Focal point and radius of curvature are located
  behind the mirror

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Diverging (Convex) Mirror

• An upright pencil is placed in front of a convex
  spherical mirror with a focal length of 8.00 cm.
  A upright image 2.50 cm tall is formed 4.44 cm
  behind the mirror. Find the position of the
  object, the magnification of the image and the
  height of the pencil.
• The image of a crayon appears to be 23.0 cm
  behind the surface of a convex mirror and is 1.70
  cm tall. If the mirrors focal length is 46.0
  cm, how far in front of the mirror is the crayon
  positioned? What is the magnification of the
  image? Is the image virtual or real? Is the
  image inverted or upright? How tall is the
  actual crayon?

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Diffuse Reflection

• When light is incident on a rough surface, it is
  reflected in many directions
• We see most of our environment because of diffuse
  reflection
• All rays obey the law of reflection
• Due to bumps in the surface the rays reflect in
  may directions
• What makes a surface smooth (specular
  reflection)?
• Depends on the wavelength of the light
• Some surfaces maybe polished for long wavelengths
  but not for short wavelengths

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Diffuse Reflection

• Would your book be easier to read if the pages
  were shinier? Why or why not?
• No. There would be more glare and less diffusely
  reflected light.
• Why does a wet road have a glare when a dry road
  does not?

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Reflection of Sound

• Sound can be reflected, absorbed or transmitted
• It reflects from all surfaceseach surface has
  different acoustics
• Reflection makes the sound lively and full
• If the surface is too reflective the resulting
  sound is garbled with multiple echoes
  (reverberations)
• A concert hall
• has grooved walls to reflect sound waves
• has highly reflective surfaces behind and above
  the stage to reflect the sound
• Why does your voice sound fuller when you sing in
  the shower?
• Each note lasts slightly longer as your voice
  reverberates between the walls.

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Refraction

• The change in direction of a wave as it crosses
  the boundary between two media in which the waves
  travel at different speeds
• Of light
• Occurs when lights velocity changes
• If the velocity decreases as it changes
  mediasthe ray bends toward the normal
• As light goes from air into water
• If the velocity increases as it changes
  mediasthe ray bends way from the normal
• As light goes from water into air

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Refraction

• Index of refractionthe ratio of the speed of
  light in a vacuum to the speed of light in a
  given transparent medium
• n has no units and is always greater than 1
• The larger the index of refraction, the more a
  light ray will bend when it passes from a vacuum
  into that material

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Refraction

• Objects appear to be in different positions due
  to refraction
• Both the fish and the cat see along the same
  paths
• The light ray that reaches the fish forms a
  smaller angle to the normal than the light ray
  from the cat to the waters surface (light bends
  towards the normalbecause air has a smaller
  index of refraction than water)
• To the fish, the cats image is above the cats
  actual position
• The light ray that reaches the cat from the
  waters surface forms a larger angle with respect
  to the normal (light from the fish travels from a
  medium with a higher index of refraction to a
  medium with a lower index of refraction)
• To the cat, the fishs image is above the fishs
  actual position
• An underwater object seen from the air above
  appears larger than its actual size because the
  image (which is the same size) is closer to the
  observer

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Refraction

• Wavelength affects the index of refraction
• Each color of light has a different wavelength so
  it bends different amounts
• This is why a spectrum is produced when white
  light passes through a prism
• Each color of the spectrum is refracted by a
  different amount

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Snells Law

• Determines the angle of refraction
• Find the angle of refraction of a light ray
  entering diamond (n 2.419) from the following
  materials at an angle of 35 degrees.
• Water (n 1.333)
• Cubic zirconia (n 2.20)

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Snells Law

• While fishing out on the lake one summer
  afternoon, Amy spots a large trout just below the
  surface of the water at an angle of 60.0º to the
  vertical, and she tries to scoop it out of the
  water with her net. (nwater 1.33)
• Draw the fish where Amy sees it.
• At what angle should Amy aim for the fish?
• Alison sees a coin at the bottom of her swimming
  pool at an angle of 40.0º to the normal and she
  dives in to retrieve it. However, Alison doesnt
  like to open her eyes in the water so she must
  rely on her initial observation of the coin made
  in the air. At what angle does the light from
  the coin travel as it moves toward the surface?

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Refraction of Sound

• Sound waves diffract when they travel at
  different speeds
• Uneven winds
• Uneven temperatures
• Sound waves bend away from the warm ground and
  toward the cool ground

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Atmospheric Refraction

• Miragea floating image that appears in the
  distance and is due to the refraction of light in
  the Earths atmosphere
• On warm days there can be a layer of hot air in
  contact with the ground
• Molecules in hot air are farther apartlight
  travels faster in the cool air above
• The wave nearest the ground speeds up making the
  light waves bend producing an imagejust as if it
  were reflected from the surface of waterbut it
  is not reflected it is refracted

Cool air
Warm air
Surface of water?
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Atmospheric Refraction
Sun
Earth
Sun

• Atmospheric refraction causes lingering
  elliptical sunsets
• When you watch the sun setyou see the sun for
  several minutes after it has sunk below the
  horizon
• Light is refracted by the earths atmosphere and
  the rays bend into a curved path
• This makes the sun appear ellipticalrays from
  the lower edge are bent more than the rays from
  the upper edge

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Dispersion in a Prism

• The average speed of light is less than c in a
  transparent medium
• How much less depends on the medium the
  frequency of light
• Light frequencies closer to the natural frequency
  of the electron oscillators travel more slowly
• Violet light travels 1 slower in glass than red
  light
• Colors in between travel at their own
  intermediate speeds
• So all the colors of the spectrum refract and
  bent at different angles
• Separation of light into colors arranged
  according to their frequency is called dispersion
• This is what produced Newtons spectrum
• http//www.physics.mun.ca/jjerrett/dispersion/pri
  sm.gif

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The Rainbow

• A rainbow is an illustration of dispersion
• For a rainbow to appear the
• Sun must be shining in one part of the sky
• Water droplets in a cloud or in falling rain must
  be in the opposite part of the sky
• When you turn your back to the sun, you see the
  spectrum of colors in a bow
• Rainbows would be complete circles if the ground
  didnt get in the way

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Rainbows

• Some of the light that hits the drop of water is
  reflected
• The rest is refracted into water and dispersed
  into its spectral colors
• Violet is bent the most, red is bent the least
• The rays reach the opposite part of the drop and
  are partly refracted again and partly reflected
  back into the water
• As the rays leave the water they are refracted
  again (much like in a prism) this second
  refraction increases the first refraction
• Each drop of water disperses a full spectrum of
  colors
• As an observer you only see a single color from
  any one dropdepending on the angle between the
  sunlight and the dispersed light
• You see red when the angle is 42 degrees
• You see violet when the angle is 40 degrees
• Arcs for each color have their own angleand
  together they form the shape of the rainbow
• The sky is brighter inside the bow because
  rainbows are disks of light rather than sets of
  colored rings.

Rainbows are twice refracted, once reflected
sunlight.
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Two Rainbows?

• Sometimes we see two rainbows at once, what
  causes this?
• We have followed the path of a ray of sunlight as
  it enters and is reflected inside the raindrop.
• Not all of the energy of the ray escapes the
  raindrop after it is reflected once.
• A part of the ray is reflected again and travels
  along inside the drop to emerge from the drop.
• The rainbow we normally see is called the primary
  rainbow and is produced by one internal
  reflection
• The secondary rainbow arises from two internal
  reflections and the rays exit the drop at an
  angle of 50 degrees rather than the 42degrees
  for the red primary bow.
• Blue light emerges at an even larger angle of 53
  degrees.
• This effect produces a secondary rainbow that has
  its colors reversed compared to the primary

Double reflection
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Total Internal Reflection

• The complete reflection that takes place within a
  substance when the angle of incidence of light
  striking the surface boundary is greater than the
  critical angle (the angle of incidence at which
  refracted light makes a right angle with the
  normal)
• Diamonds have a high index of refractionwith a
  critical angle of 24.4º.
• Most of the light that enters a cut diamond is
  totally internally reflected
• The reflected light eventually exits the diamond
  from the most visible faces

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Total Internal Reflection

• Find the critical angle for a quartz-air boundary
  if the index of refraction of quartz is 1.46.
• Suppose that the angle of incidence of a laser
  beam in water and heading towards air is adjusted
  to 50-degrees. Use Snell's law to calculate the
  angle of refraction? Explain your result (or lack
  of result).