Download How can I predict how big my reflection will appear in a mirror?

How can I predict how big my
reflection will appear in a
mirror?
•  Think about it and we might try your
solution…….
Introduction to Optics
Lecture 12
(See Giancoli Chapter 23)
Refraction
Phenomena
Silas Laycock, UML, General Physics II. Spring 2014.
Lecture slides not to be disseminated on the internet or shared
beyond this class
Optics: Summary
•  The Ray Model of Light
•  Image formed by a pinhole
•  Reflection; Image Formed by a Plane Mirror
•  Formation of Images by Spherical Mirrors
•  Index of Refraction
•  Refraction: Snell’s Law
•  Total Internal Reflection; Fiber Optics
•  Thin Lenses; Ray Tracing
•  The Thin Lens Equation; Magnification
•  Lens power and diopter
•  Combinations of Lenses (extra)
•  Lensmaker’s Equation (extra)
Beam of Light bent upon entering water
•  Ray bends toward the normal
•  Angles obey Snell’s Law
ConcepTest 23.5a Gone Fishin’ I
To shoot a fish with a gun,
1) aim directly at the image
should you aim directly at the
2) aim slightly above
image, slightly above, or slightly
3) aim slightly below
below?
ConcepTest 23.5a Gone Fishin’ I
To shoot a fish with a gun,
1) aim directly at the image
should you aim directly at the
2) aim slightly above
image, slightly above, or slightly
3) aim slightly below
below?
Due to refraction, the image will
appear higher than the actual
fish, so you have to aim lower to
compensate.
Refraction: Snell’s Law
•  Light changes direction when crossing a boundary from one medium to another.
•  This is called refraction.
•  The angle the outgoing ray makes with the normal is called the angle of refraction.
•  The angle of refraction depends on a property of the two media, called the
refractive index
What can you say about the index of refraction of the
3 materials shown here?
A. 
B. 
C. 
D. 
n1 > n3 > n2
n2 > n 1 > n 3
n1 > n2 > n3
n3 > n2 > n1
Index of Refraction
In general, light slows when traveling through
a medium. The index of refraction of the
medium is the ratio of the speed of light in
vacuum to the speed of light in the medium:
(23-4)
Fine Print:
In truth there is some
additional subtlety, see e.g.
Feynman’s lectures on
Physics, volume 1
Say a laser beam is passing from air into a piece
of glass (say a prism) at an incident angle of about
30 degrees. The prism is then immersed in a fluid
other than air (say water). What happens?
A.  The angle of refraction increases
B.  The angle of refraction decreases
C.  The angle of refraction does not change
because the refractive index of the glass is
unchanged
D.  No refraction occurs
Total Internal Reflection
If light passes into a medium with a smaller index of refraction, the angle
of refraction is larger. There is an angle of incidence for which the angle of
refraction will be 90°; this is called the critical angle:
If the angle of incidence is larger than this, no transmission occurs. This
is called total internal reflection.
See what happens when you wear your (waterproof) watch in the
bath and tilt the angle of your wrist
At the Critical Angle, Total internal
Reflection renders the transparent
glass watch face as if it were a
shiny metal mirror!
An individual optical fiber
Fiber optic cables consist of many
individual fibers, each can carry multiple
optical signals
High performance data cables for
computers and communications
Medical Endoscope, used to see inside
the body
Snell’s Window, or the Optical Manhole
•  The view from under-water is a bizarre and dramatic manifestation of refraction and
total internal reflection.
•  No matter how deep you go, the entire world above the surface appears, compressed
into a 90 degree-wide image.
•  The rest of the water’s surface looks like a liquid metal mirror.
•  This is what fish see!
•  Be very careful if you try to see it for yourself!
Lenses
•  Lenses bend light by
refraction, an are
designed to bring light
to a focus, or diverge it.
•  Thin lenses are those
whose thickness is
small compared to their
radius of curvature.
•  They may be either
converging (a) or
diverging (b).
•  Thin lenses obey
similar rules to mirrors
23.7 Thin Lenses; Ray Tracing
Parallel rays are
brought to a focus by
a converging lens
(one that is thicker in
the center than it is at
the edge).
23.7 Thin Lenses; Ray Tracing
A diverging lens (thicker at the edge than in
the center) make parallel light diverge; the
focal point is that point where the diverging
rays would converge if projected back.
Lens Power, Diopters and Spectacles
The power of a lens is the inverse of its focal
length.
(23-7)
Lens power is measured in
diopters, D.
1 D = 1 m-1
Optician use this notation
because the total power of a set
of lenses is the sum of their
diopters
The Thin Lens Equation & Magnification
• The thin lens equation, and lens magnification eqn are
the same as for mirrors:
• The power of a lens is positive if it is converging and
negative if it is diverging.
• Mirrors and Lenses obey the same math rules and are
used for much the same purposes.
If I have a converging lens and want to make an
image of a nearby object, how can I predict where
the image will form?
(In other words how do I calculate how to focus a
camera? )
EXTRA Material: Combinations of Lenses
In lens combinations, the image formed by the
first lens becomes the object for the second
lens (this is where object distances may be
negative).
EXTRA MATERIAL: Lensmaker’s Equation
This useful equation relates the radii of
curvature of the two lens surfaces, and the
index of refraction, to the focal length.
(23-10)
Summary of Chapter 23
•  Light paths are called rays
•  Angle of reflection equals angle of incidence
•  Index of refraction:
•  Upon passing into a material with larger n, ray deflects toward the normal
•  Plane mirror: image is virtual, upright, and the same size as the object
•  Focal length of the mirror:
• Spherical mirror can be concave or convex
•  Mirror equation:
•  Magnification
•  Real image: light passes through it
•  Virtual image: light does not pass through
•  Law of refraction (Snell’s law):
•  Total internal reflection critical angle:
•  A converging lens focuses incoming parallel rays to a point
•  A diverging lens spreads incoming rays so that they appear to come from a point
•  Power of a lens (diopters):
•  Thin lens equation:
Heiligenschein - Dew drops acting as
millions of tiny spherical mirrors or lenses.
Only YOU can see your own halo, try it and try to explain why.
Highly Recommended
Reading
Team Research Challenge
• 
In teams you will select a piece of technology that relies on applications of the
physics in this course. Each team member then researches the physics behind a
different component. They discuss as a group outside class (in person, by Piazza,
email, etc.) and produce a report. Then they present the report to the class, using
(upto) one slide or diagram per person.
Ideas –your own suggestions encouraged!
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Radio/CD player [radio receiver, CD player, Battery, Speaker]
Digital Camera
[Optics, Image sensor, Flash, Display]
X-ray imager
[X-ray Source, Detector, Display, Safety]
Nuclear power station [Reactor, Generator, Transmission, Safety and Control]
Laptop computer [Hard Drive, Display, Optical Drive, Battery, CPU]
Nuclear Weapons
Electric Guitar
Alternative Energy generation
Medical Physics Applications
Think about this over spring break, so that you will be ready to get started.