Physics 123C Waves

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Physics 123C Waves
Lecture 15Ray Optics May 9, 2005

• John G. Cramer
• Professor of Physics
• B451 PAB
• cramer_at_phys.washington.edu

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Lecture 15 Announcements

• Lecture Homework 5 will be posted on the
  Tycho system later this week. It is due at 900
  PM on Wednesday, May 18.

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Lecture Schedule (Weeks 7-10)
We are here
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Models of Light
Is light a particle or a wave? Physics in
the 20th century has shown that this simple
question does not have a simple answer. The
behavior of light, depending on the
circumstances, can be described by three distinct
(and seemingly contradictory) models. We will
introduce all of them and learn the conditions
and circumstances under which each is valid.
The Wave Model This model works in many
circumstances. When it is applicable, light
shows the same interference behavior as water
waves and sound waves. Lasers and
electro-optical devices, critical technologies of
the 21st century, are best understood with the
wave model of light, which we will call wave
optics.
The Photon Model This model works in
circumstances where energy detection is
important, as describes light as a stream of
photons, particles that carry packets of energy
called quanta.
The Ray Model Light travels in straight lines,
modified by reflection and refraction. This
model works best for optical instruments and
lenses, and is the basis for ray optics.
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The Ray Model of Light
Light travels in straight lines.
Light rays can cross. They do not interact.
Light rays travel forever unless they interact
with matter. Matter can reflect, refract, and
absorb light.
An illuminated object is a source of light rays.
The eye sees by focusing a diverging bundle of
light rays to an image.
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Objects
A source of light can be either
self-luminous (e.g., the Sun or a light bulb) or
reflective (e.g., the page of a book or a
projection screen). Most objects are reflective.
Light rays exist everywhere, independent of
whether you see them or not.
We will often idealize groups by describing
them as rays from a point source or in a parallel
bundle. A light from a laser or from a distant
object can be considered a parallel bundle.
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Ray Diagrams
We will often simplify the situation in ray
optics by drawing a ray diagram, in which we
consider only the light emitted from a few
representative points. For example, we
consider rays from the top and bottom of a tree
rather than from the whole tree.
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A Pinhole Camera
In Roman and medieval times, the camera
obscura (literally darkened chamber) was a
popular form of entertainment. Participants
would enter a darkened room with a pinhole
admitting light at one end. When their eyes
adapted, they would see full color images of the
outside world on the opposite wall, but with
everything turned upside down.
Ray tracing explains this device. The
pinhole admits only selected rays, and these
trace the image on the wall. By similar
triangles, the image height is hi hodi/do.
Thus, the magnification is m hi/ho di/do.
The smaller the pinhole (ignoring diffraction),
the sharper (and dimmer) is the image.
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Apertures
A hole or restriction through which light
passes is called an aperture. It selects the
rays that are allowed to pass from light source
to screen.
A point source and extended aperture create
an upright image of the aperture on the screen.
An extended source and point aperture create an
inverted image of the source on the screen.
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Clicker Question 1
A long thin fluorescent tube illuminates a
vertical slit aperture. Which pattern would
you see on the screen behind the aperture?
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Reflection
Reflection from a flat smooth surface is
called specular reflection (from speculum, Latin
for mirror). The figure shows a bundle of
parallel rays striking a reflective surface. The
plane of the bundle is perpendicular to the
reflective surface, and the reflected rays lie in
the bundle plane. A better way of
representing the situation is to draw the plane
formed by the incident and reflected rays. Here

• The incident and reflected rays are in the same
  plane, which is normal to the reflecting surface.
• The angle of incidence qi, (as measured from the
  normal) is equal to the angle of reflection qr.

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ExampleLight Reflecting from a Mirror
A dressing mirror on a closet door is 1.5 m
tall. The bottom is 0.5 m above the floor. A
bare light bulb hangs 1.0 m from the closet door
and 2.5 m above the floor. How long is the
streak of light reflected across the floor?
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Diffuse Reflection
The reflection from an irregular surface
obeys the law of reflection at any point, but the
net effect is to reflect rays in many random
directions, so that each small region becomes
effectively a point source of reflected light.
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Analysis of a Plane Mirror

• Any point P on an object acts as a point source
  of light, producing many rays that are reflected
  by the mirror in different directions.
• The reflection of each incident ray can be
  constructed using the law of reflection.
• The reflected rays can be extrapolated backward
  to the point P from which they seem to emanate.
  Point P is the virtual image of point P, when
  viewed by reflection. This construction shows
  that the object distance s and the image distance
  s are equal.

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Mirror Images

• Rays from the extended object spread out and
  strike every point on the mirror surface.
  However, only a few of these rays reach your
  eye.
• Rays from points P and Q enter your eye after
  reflection from different regions of the mirror
  surface. If the lower part of the mirror were
  removed, point Q would not be visible.

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ExampleHow High is the Mirror
If your height is h, what is the shortest
mirror in the wall that will show your full
image? Where must the top of the mirror be
hung?
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Left/Right Reflection
Paradox Why does a mirror reverse left and
right when it does not reverse up and down?
Answer A mirror reverses neither left and
right nor up and down. It reverses front and
back. This has the effect of making a left hand
into a right hand, and vice versa.
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Clicker Question 2
Two plane mirrors form a right angle.
How many images of the ball can you see in the
mirrors?
(a) 1 (b) 2 (c) 3 (d) 4 (e)
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Clicker Question 2
Two plane mirrors form a right angle.
How many images of the ball can you see in the
mirrors?
(a) 1 (b) 2 (c) 3 (d) 4 (e)
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Curved Mirrors
If a mirror is part of a spherical surface,
parallel rays at different distances from the
center line will converge in different places.
This is called spherical aberration.
However, if the mirror is only a small part
of the spherical surface (so that the small-angle
approximation is valid), parallel rays will focus
at a distance that is ½ the mirrors radius of
curvature r. This is called the focal point f.
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Ray Tracing
For spherical mirrors, one can geometrically
construct the image point by using special rays

• A ray from the object that is parallel to the
  principal axis will be reflected through the
  focal point
• A ray from the object through the focal point
  will be reflected parallel to the principal axis
• A ray from the object along a radius will be
  reflected back along the radius
• A ray (dashed) to the mirror center (A) will be
  reflected at an equal and opposite angle
• The image is at the cross point.

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Object Outside the Focus
When the object is farther from the mirror
than the focal point f, a real inverted image is
formed. Here real means that rays actually
pass through the image point I and inverted
means that the image is upside-down with respect
to the object.
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Object Inside the Focus
When the object is closer to the mirror than
the focal point f, a virtual upright image is
formed. Here virtual means that rays do not
pass through the image point I and upright
means that the image has the same up/down
orientation as the object. This gives the
magnifying effect of a shaving mirror.
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Mirror Equation Derivation
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The Mirror Equations
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Convex Mirrors
Convex mirrors have a virtual focus, in that
reflected parallel rays diverge, but can be
extrapolated backwards to the focal point F.
The image of an object in front of a convex
mirror is always virtual upright with a
magnification less than 1.
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Five Things You Should Have Learned from This
Lecture

• The ray model of light assumes that light travels
  as a ray in a straight line unless reflected or
  refracted.
• Apertures restrict light rays from an object, and
  can be used to form pinhole camera images.
• A plane mirror reflects light so that the angle
  of incidence and the angle of reflection are
  equal. A plane mirror forms an image that is the
  same distance behind the mirror as the object is
  in front.
• A spherical mirror can bring parallel rays to a
  focus and form images of objects. Ray tracing
  with special rays can be used to geometrically
  construct image positions and sizes.
• A concave mirror has a virtual focal point and
  produces virtual upright images with
  magnification less than 1.

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End of Lecture 15

• Lecture Homework 5 will be posted on the
  Tycho system later this week. It is due at 900
  PM on Wednesday, May 18.
• Read Knight, Chapter 23.3-5 for Wednesday, May
  11.