Physics 123A Waves and Modern Physics

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Physics 123A Waves and Modern Physics
Lecture 10 (TM 32.1-2)Snells Law and Ray
Optics October 26, 2009 (26 Slides)

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

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Lecture 10 Announcements

• Lecture Homework 4 has been posted on the
  WebAssign system. It is due at 1159 PM on
  Friday, October 30.
• Exam 1 will be returned on Wednesday, but the
  grades for the three parts are available on
  WebAssign now. The Exam 1 Average is 64.76 and
  the Std. Dev. is 16.17.
• So far 179/196 students have registered their
  clickers. A clicker response that shows up as a
  number may indicate a registration problem.

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Lecture Schedule (Part 2)
We are here!
October 26, 2009
Physics 123A - Lecture 10
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Plane Mirrors

• 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.

October 26, 2009
Physics 123A - Lecture 10
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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?
October 26, 2009
Physics 123A - Lecture 10
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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.
A coordinate system with this property is
called a left-handed coordinate system.
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Multiple Reflections
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Clicker Question 1
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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October 26, 2009
Physics 123A - Lecture 10
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Clicker Question 1
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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October 26, 2009
Physics 123A - Lecture 10
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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. If the
surface was parabolic rather than spherical,
there would be no aberration for distant objects.
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.
October 26, 2009
Physics 123A - Lecture 10
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Spherical Aberration
Only rays that strike the spherical mirror
at points near the axis (line AV) are reflected
through the image point. Rays that are almost
parallel with the axis and are near to the axis
are called paraxial rays. Rays that strike the
mirror at points far from the axis upon
reflection pass near the image point, but not
through it. Such rays cause the image to appear
blurred, an effect called spherical aberration.
A parabolic mirror focuses parallel rays to a
point, but even then, will produce aberration for
off-axis imaging,
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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.

October 26, 2009
Physics 123A - Lecture 10
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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.
October 26, 2009
Physics 123A - Lecture 10
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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.
October 26, 2009
Physics 123A - Lecture 10
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Mirror Equation Derivation
October 26, 2009
Physics 123A - Lecture 10
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The Mirror Equations
October 26, 2009
Physics 123A - Lecture 10
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ExampleImage in a Concave Mirror
A point source is 12 cmfrom a concave
mirror and3.0 cm above the axis ofthe mirror.
The radius ofcurvature of the mirroris 6.0 cm.
Find (a) the focal length of the mirror (b)
the image distance(c) Find the position of the
image relative to the axis.
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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.
October 26, 2009
Physics 123A - Lecture 10
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ExampleImage in a Convex Mirror
An object that is 2.0 cm high is 10 cm from
a convex mirror that has a radius of curvature
equal to 10 cm.(a) Locate the image(b) find the
height of the image.
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Snells Law
The Dutch physicist and mathematician
Willebrord Snell of the University of Leiden in
1621 discovered the law of refraction, also
called Snells Law.
In a medium in which light slows down, a ray
bends closer to the perpendicular.
October 26, 2009
Physics 123A - Lecture 10
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Refractive Surfaces Imaging
October 26, 2009
Physics 123A - Lecture 10
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Example Image Seen from a Goldfish Bowl
Goldie sees Fluffys image fartherfrom the
bowl than Fluffy actually is. Goldie the goldfish
is in a 15.0-cmradius spherical bowl of water
withnw 1.33. Fluffy the cat is sitting onthe
table with her nose 10.0 cm fromthe surface of
the bowl. The light from Fluffys nose is
refracted by the airwater boundary to form an
image. Find (a) the image distance and (b) the
magnification of the image of Fluffys nose.
Neglect any effect of the bowls thin glass wall.
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Thin Lenses
(fgt0)
When parallel rays pass through a diverging
lens, the rays diverge away from the focal point
f of the lens, and must be extrapolated back to
find it. The image is virtual.
When parallel rays pass through a converging
lens, the rays converge at the focal point f of
the lens. They form a real image of an object at
infinity.
October 26, 2009
Physics 123A - Lecture 10
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Thick and Thin Lenses
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Physics 123A - Lecture 10
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Lens Sign Convention
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Physics 123A - Lecture 10
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End of Lecture 10

• Before the next lecture, read TM, Chapter 32.3
  32.4
• Lecture Homework 4 has been posted on the
  WebAssign system. It is due at 1159 PM on
  Wednesday, October 28.
• So far 172/196 students have registered their
  clickers. A clicker response that shows up as a
  number may indicate a registration problem.