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Reflection

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Title: 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
6
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?

8
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?

9
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)

10
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
11
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

12
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.

13
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

14
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?

15
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

16
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?

17
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.

18
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

19
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

20
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

21
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

22
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)

23
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?

24
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

25
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?
26
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

27
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

28
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

29
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.
30
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
31
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

32
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).
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