Transcript Spherical Mirrors

A “Visual” Review
Lyzinski
Physics
Light? Where does it come from?
It comes from moving electrons
- different energy levels in an atom
- when light jumps UP, it absorbs energy (usually in the
form of heat)
- when light jumps DOWN, it emits energy in the form of
light.
- the color of the light depends on the size of the jump.
Moving electrons set up a changing electric field that also
induces a changing magnetic field.
 Electromagnetic Waves!!!!
Light? What is it (what is it like)?
• It is both wave-like AND particle-like.
• It is a transverse, electromagnetic wave
- Transverse (light) vs. longitudinal (sound)
- Electromagnetic wave
The approximate speed of
light in a vacuum (or in air)
- No medium needed
• It travels at the speed of light (c = 3E8 m/s)
• It travels in straight lines  rectilinear propagation
• It travels in rays (infinitely thin)
The Wave Equation
v  f
Velocity
Frequency
c  f
Light Equation
General Equation: works for sound,
water, slinkies, light, etc.
Wavelength
For light,
• Increase , decrease f.
• Decrease l, increase f.
The Electromagnetic Spectrum
Radio
AM
FM
Micro
Infra
ROYGBIV
Ultraviolet
X
Gamma
AM vs. FM
535-1605 kHz
88-108 MHz
Lower frequency
Higher frequency
Longer wavelength
Shorter wavelength
kHz = kilohertz = 103 Hz
MHz = megahertz = 106 Hz
Some Helpful Applets
Applets showing longitudinal AND transverse waves.
http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html
Applet explaining how a moving electron (jumping and falling in
energy level) produces a wave.
http://www.colorado.edu/physics/2000/waves_particles/wavpart4.html
Applets showing a 3D electromagnetic wave.
http://www.walter-fendt.de/ph14e/emwave.htm
http://www.amanogawa.com/archive/PlaneWave/PlaneWave-2.html
Plane Reflectors
Incident Ray
Normal
Reflected Ray
 i r
Rule #1: The angle of Incidence equals the angle of reflection.
Rule #2: The normal, incident ray, and reflected ray all lie in the same plane.
Drawing PLANE
MIRROR Ray Diagrams
1. Draw two incident rays from a
point.
2. Find the intersection of the two
reflected rays.
C
C’
3. Repeat for every point on the
object
B’
B
mirror
Spherical Mirrors
Light “Caves in” on the Focus
CONCAVE
(CONVERGING)
C
F
i
r
Notice that i  r
Principal Axis
Center of Curvature
Focus
f = focal length
R = radius of curvature
Spherical Mirrors vs. Parabolic Mirrors
Large spherical mirrors have
an avoidable issue.
Near the edges, reflected
rays might not reflect through
the focus.
w
R
This is known as SPHERICAL
ABBERATION .
It can be corrected by…..
…..using mirrors whose width (w)
is smaller than its radius of
curvature (R).
OR
…..using mirrors that are
PARABOLIC, instead of
spherical
Spherical Mirrors
i
CONVEX
(DIVERGING)
r
C
F
Principal Axis
Center of Curvature
Again, Notice
that i  r
f
“Virtual” Focus
R
Image Formation
Cone of rays
seen by the
human eye
What does your
eye see???
Object
Image
Virtual
(cannot be formed on a screen)
Plane Mirror
Characteristics of Images
Real
VS
Virtual
Can be formed on a screen
ATTITUDE
Can NOT be formed on a screen
Upright
VS
Inverted
TYPE
or “Orientation”
Larger
Smaller
Same size
Image Formation (continued)
In Spherical, CONCAVE
mirrors, a clear image is
formed where all the
reflected rays emitted from
any single point on the object
intersect.
A screen placed here
will have a focused
image on it.
A screen placed here will have a “fuzzy”, unfocused image on it.
How do you locate the image in
a Spherical Mirror Situation.
Pick a point on the object (usually the one furthest from the principal axis),
and then draw 2 intersecting rays that obey the following rules:
1. Any ray parallel to the principal axis is reflected through the focus.
2. Any ray through the focus is reflected parallel to the principal axis.
3.
Any ray through the center of curvature is reflected back along the
incident ray (back along itself)
Concave
Mirrors
“OUTSIDE“
the focus
C
F
Moving towards the focus, the image is REAL, inverted, and gets larger.
Concave
Mirrors
“ON”
the focus
C
F
When an object is at the focus, it doesn’t have an image.
Concave
Mirrors
C
F
“INSIDE”
the focus
Moving towards the mirror, the image is VIRTUAL, UPRIGHT, and gets
smaller (although the image is still larger than the object itself).
Convex
Mirrors
Note: All images are in front
of the virtual focus.
F
C
When an object gets closer to the mirror, its image is VIRTUAL, UPRIGHT, and
keeps getting smaller (and the images are always smaller than the object).
Wanna play with mirrors?
try an applet at …..
http://webphysics.davidson.edu/physlet_resources/optics4/default.html
Mathematically locating an image
1 1
1


di do f
All distances are measured from the mirror’s vertex
Distances are POSITIVE for REAL images/objects
Mirror
Equation
f  12 R
Distances are NEGATIVE for VIRTUAL images/objects
Heights are positive when measured upward and
negative when measured downward.
hi
di
 M
ho
do
Magnification
Equation
M is the magnification.
A few Helpful tips to using the
equations.
Always write out a list of do, di, ho, hi, f, and M
first.
Using knowledge of the type of mirror you have
and where the object is placed, make sure the
SIGNS are correct on your variables before
plugging the variables into the equations.
ALWAYS check your answers to makes sure that
they 1) match your drawing 2) have signs that
make sense 3) have numbers that make sense.
Example
A converging mirror is used to take a 4 meter tall
object and create a 2 meter tall image of it that is
formed on a screen. If the object is 3 meters from
the mirror, find the mirror’s focal length, the image
distance, and the magnification.
hi = -2m (negative because it must be upside down, since real images in a
converging mirror are always inverted).
ho = 4m
do = 3m
f = + ___ (since it’s a concave, converging mirror)
di = +___ (since it’s real)
-1 < M < 0 (since its inverted and smaller)
Another Example
A mirror is used to create a small, upright image.
If the radius of curvature of the mirror is 40 cm,
and if the image is 4 times smaller than the
object, how far in front of the mirror has the object
been placed?
THE mirror must be diverging since only convex mirrors can create smaller,
upright images! Therefore, f = -20 cm.
Also, M = +1/2 (since the image is half the size of the object).
You have to use a substitution method on this problem, yielding:
di = - ___ (since the image is virtual)
do = + ___ (since the object is real)
Concave mirrors
Can make small objects appear larger
Make-up mirrors, shaving mirrors
Convex mirrors
Can make large objects appear smaller
(see a WIDE view)
Security mirrors, Driveway
mirrors, Car door mirrors
Uses for PARABOLIC mirrors (in
case you were wondering )
At solar power plants,
parabolic “troughs” (as
they’re called) are used to
focus light onto a fluid
carrying pipe, thus heating
the fluid and producing
useable energy.
Fluid filled pipe
being heated
http://www.solarserver.de/lexikon/parabolrinnenkraftwerk-e.html
Parabolic trough