Download 8.6 Formation of Images by Spherical Mirrors

Describe what a lens and a mirror do to light
rays.
S-97
Draw a diagram that shows how light travels
from an object to a mirror, then to your eyes.
S-99
Light and Optics
8.1 Maxwell’s Equation
After the work of Oerseted, Ampere and
Faraday
James Clark Maxwell – all
electric and magnetic
phenomena can be
described by four equations
Fundamental – even taking into account
relativity
Require Calculus
8.1 Maxwell’s Equation
1. Gauss’s Law – relates electric field to
electric charge
2. Magnetic field Law –
3. Faraday’s Law – electric field is produced
by magnetic field
4. Ampere’s Law – magnetic field produced
by an electric current, or changing electric
field
8.1 Maxwell’s Equation
8.2 Production of Electromagnetic Waves
How Electromagnetic Waves are Produced
EMR Production
The charged particle oscillate
As it travels one direction a current is
produced
This generates a magnetic field
When the direction changes, so does the
current and the magnetic field
8.2 Production of Electromagnetic Waves
Electric and magnetic fields are
perpendicular to each other
The fields alternate in
direction
These are
electromagnetic waves
Transverse
In general – accelerating electric charges
give rise to electromagnetic waves
8.2 Production of Electromagnetic Waves
8.3 Electromagnetic Spectrum
Electromagnetic Spectrum
8.3 Electromagnetic Spectrum
All EMR has a velocity of
in a Vacuum
Velocity decreases with increase in
optical density
The wave equation becomes
300, 000, 000
m
s
8 m
s
3x10
c f
Unlike Sound – energy depends on frequency
E  hf h  6.626 x10
34
J s
h – Planck’s Constant
8.3 Electromagnetic Spectrum
8.4 The Ray Model of Light
Light travels in a straight line in most cases
(away from very large gravitational fields)
Ray Model – Light
travels in
straight line
pathways called
rays
represents a narrow beam
of light
8.4 The Ray Model of Light
We see an object when rays of light come
from the object to our eyes
8.4 The Ray Model of Light
8.5 Reflection
When light strikes an object it is
Reflected – bounces off
Refracted – transmitted through
Absorbed – converted to a different form of
energy
Law of Reflection
 r  i
8.5 Reflection
Diffuse Reflection – on a rough surface
Rays don’t form an pattern
We see color
Specular Reflection –
smooth surface
Patterns form images
8.5 Reflection
A.What is the speed of light in a vacuum?
B.If the wavelength of light is 512 nm, what is
the frequency?
C.What would be the energy
in a photon of that
frequency?
S-100
How are images formed
Your eye sees the
intersection of rays
from an object
Applet
8.5 Reflection
Object Distance – from mirror to the object
Image Distance – from mirror to the image
Virtual Image – imaginary intersection of light
rays
Real Image – actual intersection of light
8.5 Reflection
A man stands in front of a mirror. He is 1.8 m
tall. What is the minimum height the mirror
must be for him to see his entire image?
S-101
8.6 Formation of Images by Spherical Mirrors
Spherical Mirrors – form a section of a sphere
Convex – reflection on outer
surface of sphere
Concave –
reflection on
inner surface
of sphere
23.3
8.6 Formation of Images by Spherical Mirrors
Terms
Principal Axis – straight line normal to the
center of the curve
Focus – point where parallel rays intersect
Vertex – center of the mirror
Focal Length – distance from vertex to focus
Images from distant objects are produced at
the focal point
8.6 Formation of Images by Spherical Mirrors
The focal point is actually an approximation
The greater the curve of a mirror, the worse is
the approximation
Called
Spherical
Aberration
Examples of Visual
Aberrations
8.6 Formation of Images by Spherical Mirrors
All rays follow the law of
r
f 
reflection
2
Two Rules
1. A ray parallel to the principle axis reflects
through the focal point
2. A ray through the focal point reflects
parallel
Examples of Diagrams – Concave Mirrors
Real Images
Virtual Image
8.6 Formation of Images by Spherical Mirrors
Convex Mirrors only form virtual images
Rules
1. Rays parallel to the principle axis reflect
away from the focal point
2. Rays headed for the focal point reflect
parallel
8.6 Formation of Images by Spherical Mirrors
Sketch the image formed by
a 2.00 m tall dog standing
4.00 m from a convex
mirror with a focal length
of 1.50 m.
S-102
Curved Mirror Equations
ho d o

hi d i
ho-object height
hi-image height
do-object distance
di-image distance
The Mirror Equation
Magnification
1
1 1


f d o di
hi
di
m 
ho
do
8.6 Formation of Images by Spherical Mirrors
Sign Conventions
Image Height
+ upright (virtual)
- inverted (real)
Image and Object Distance
+ front of mirror
- behind mirror
Magnification
+ upright image
- inverted image
8.6 Formation of Images by Spherical Mirrors
Sign Conventions
Focal Length
+ concave mirror
- convex mirror
8.6 Formation of Images by Spherical Mirrors
8.7 Index of Refraction
Index of Refraction – the ratio of the speed of
light in a vacuum to the speed in a given
material
c
n
v
Material
Vacuum
Air at STP
Water
Quartz
Crown Glass
Index
1.00000
1.00029
1.33
1.46
1.53
Material
NaCl
Polystyrene
Flint Glass
Sapphire
Diamond
8.7 Index of Refraction
Index
1.54
1.57
1.65
1.77
2.417
Value can never be less than 1
Material
Vacuum
Air at STP
Water
Quartz
Crown Glass
Index
1.00000
1.00029
1.33
1.46
1.53
Material
NaCl
Polystyrene
Flint Glass
Sapphire
Diamond
8.7 Index of Refraction
Index
1.54
1.57
1.65
1.77
2.417
8.8 Refraction: Snell’s Law
Refraction – when a ray of light changes
direction as it changes media
The change in angle depends on the change
in velocity of light (or the index of refraction
of the two media)
8.8 Refraction: Snell’s Law
Snell’s Law – relates the index of refractions
and the angles
n1 sin 1  n2 sin 2
Also called the Law of Refraction
If light speeds up, rays bend away
from the normal
If light slows down, rays bend
toward the normal
8.8 Refraction: Snell’s Law
Refraction occurs when one side of the wave
slows down before the other
8.8 Refraction: Snell’s Law
8.9 Total Internal Reflection; Fiber Optics
When light travels into a less optically dense
medium, the ray bends away from the
normal
As the angle increases, the angle of refraction
eventually reaches 90o.
This is called the critical
angle
n2
n1 sin
n1sin
sin
c c cn
n2 90
2 sin
n1
8.9 Total Internal Reflection; Fiber Optics
Above the critical angle, light reflects following
the law of reflection
Used in fiber optics
8.9 Total Internal Reflection; Fiber Optics
A frog stands 12 cm in front of a concave
mirror with a focal length of 15 cm. The frog
is 9 cm tall.
A.What is the distance and height of the
image?
B.What would be the
distance and height
of the image if the
mirror was convex?
S-103
8.10 Thin Lenses; Ray Tracing
Thin lens – very thin compared to its diameter
Diagrams are similar to mirrors
Converging – rays converge
8.10 Thin Lenses; Ray Tracing
Converging Lenses
1. A ray parallel to the Principle Axis refracts
through F
2. A ray through F’ refracts parallel.
3. A ray through the optical center, O, does
not refract
Converging Lens
8.10 Thin Lenses; Ray Tracing
SOLAR COOKING
On a Balmy Winters Day!
S-104
A diverging lens with a focal length of 18 cm is
used to produce the image of a rather cute
rodent that is 1.3 cm tall. The rodant stands
22 cm from the lens.
A.What is the distance,
height, and magnification
of the image?
B.What would it be if the
lens was converging.
S-105
A converging lens produces an image of an
stinky fruit 17 cm from the lens. The object
was originally placed 12 cm from the lens,
and the image is projectable.
A. What is the focal
length of the lens?
B. What is the
magnification of
the image?
S-106
A diverging lens produces an image of an cat
with a bad haircut 17 cm from the lens. The
object was originally placed 12
cm from the lens.
A. What is the focal
length of the lens?
B. What is the
magnification of
the image?
S-107
Diverging Lens – spreads apart rays of light
Only produces virtual images
Rules
1. Parallel rays refract
away from F’
2. Rays headed toward
F refract parallel
3. Rays through O do not
refract
8.10 Thin Lenses; Ray Tracing
8.11 The Thin Lens Equation: Magnification
Equations are similar to Mirrors, conventions
are different
The Thin Lens Equation is
1
1 1


f do di
To Calculate Magnification
hi
di
M  
ho
do
8.11 The Thin Lens Equation: Magnification
Conventions
Focal Length
+ converging lens
- diverging lens
Object Distance
+ same side as original light
- different side (only when more than 1
lens)
8.11 The Thin Lens Equation: Magnification
Conventions
Image Distance
+ opposite side from light
- same side as light
Height
+ upright
- upside down
8.11 The Thin Lens Equation: Magnification
8.12 Combinations of Lenses
Many devices used combinations of lenses
Applet
Combination problems are treated
as separate lenses
Calculate or draw the image from the first lens
8.12 Combinations of Lenses
A hamster shoots a laser. It hits a side of a
block at an angle of 15o to the normal. At
what angle will the ray exit the block.
(n=1.51)
=42o
S-108
Test Test Test Test
Test Test Test Test
Test Test Test Test
Test Test Test Test
=42o
S-109