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Optics
LCHS
Notation for
Mirrors and Lenses
• The object distance is the
distance from the object to the
mirror or lens
• The image distance is the
distance from the image to the
mirror or lens
• The lateral magnification of
the mirror or lens is the ratio
of the image height to the
object height
Types of Images
• A real image is formed
when light rays pass
through and diverge
from the image point
• A virtual image is
formed when light rays
do not pass through the
image point but only
appear to diverge from
that point
Flat Mirrrors
Law of Reflection
“The angle of incidence equals the
angle of reflection.”
This is true for both flat mirrors and
curved mirrors.
Normal Line
A
Angle of
Incidence
=
Angle of
Reflection
MIRROR
B
Diffuse Reflection
Locating the Image for
Plane Mirrors
1. Draw the image the same distance behind
the mirror as the object is in front.
2. Draw a connector line from each object to
each image.
3. If the connector line passes through the
mirror, the image will be seen.
Mirror Images
E
D
C
B
A
These lines are
pointed to the only
images that will be
seen from each of
the original
locations (A-E)
NOTE: No
images will be
seen from E
A
B
C
D
E
Lateral Magnification
Lateral magnification, M, is defined as
Im age height h'
M

Object height h
– This is the general magnification for any
type of mirror
– It is also valid for images formed by lenses
– Magnification does not always mean bigger,
the size can either increase or decrease
Lateral Magnification of a Flat
Mirror
• The lateral
magnification of a
flat mirror is 1
• This means that
h' = h for all
images
Reversals in a Flat Mirror
• A flat mirror produces an
image that has an apparent
left-right reversal
– For example, if you raise
your right hand the image
you see raises its left hand
• The reversal is not actually a left-right reversal
• The reversal is actually a front-back reversal
– It is caused by the light rays going forward toward the
mirror and then reflecting back from it
Summary
• The image is as far behind the mirror as the object
is in front
– dd = |do|
• The image is unmagnified
– The image height is the same as the object height
• h' = h and M = 1
• The image is virtual
• The image is upright
– It has the same orientation as the object
• There is a front-back reversal in the image
The angle of incidence equals the
angle of what?
a) Dispersion
b) Refraction
c) Reflection
Specular reflections are images
seen after __ surface(s).
a) rough
b) smooth
c) no
Can you see a reflection of
yourself in a diffuse reflection?
a) yes
b) no
Where do you draw the
connector lines?
a) from the lens to object
b) from image to lens
c) from object to each image
What happens if the connector line
passes through the mirror?
a) image is invisible
b) image is seen
Light doesn’t pass through __
images.
a) virtual
b) real
c) large
d) small
Spherical
Mirrors
Spherical Mirrors
• A spherical mirror has the shape of a segment of
a sphere
• The mirror focuses incoming parallel rays
to a point
• A concave spherical mirror has the light reflected
from the inner, or concave, side of the curve
• A convex spherical mirror has the light reflected
from the outer, or convex, side of the curve
Concave and Convex Mirrors
Concave and convex mirrors are curved mirrors similar to portions
of a sphere.
light rays
Concave mirrors reflect light
from their inner surface, like
the inside of a spoon.
light rays
Convex mirrors reflect light
from their outer surface, like
the outside of a spoon.
Concave Mirrors
Light from Infinite Distance
C
F
Focuses
at the
focal
point
Two Rules for Concave Mirrors
• Any incident ray traveling parallel to
the principal axis on the way to the
mirror will pass through the focal
point upon reflection
• Any incident ray passing through the
focal point on the way to the mirror will
travel parallel to the principal axis upon
reflection
C
F
C
F
C
F
Virtual
Image
C
F
Real Image
C
F
Virtual
Image
C
F
Convex Mirrors
• A convex mirror is sometimes called a
diverging mirror
– The light reflects from the outer, convex side
• The rays from any point on the object
diverge after reflection as though they were
coming from some point behind the mirror
• The image is virtual because the reflected
rays only appear to originate at the image
point
Will an image ever
focus at a single
point with a
convex mirror?
F
Therefore, the
images you see
are virtual!
Image Formed by a Convex Mirror
In general, the image formed by a convex mirror is upright,
virtual, and smaller than the object
Notes on Images
• With a concave mirror, the image may be either
real or virtual. When the object is
– outside the focal point, the image is real
– at the focal point, the image is infinitely far away
– inside the focal point, the image is virtual
• With a convex mirror, the image is always
virtual and upright
– As the object distance decreases, the virtual image
increases in size
Mirror Sign Convention
f = focal length
1
1
1
f = di + do
di = image distance
do = object distance
+ for real image
di
- for virtual image
+ for concave mirrors
f
- for convex mirrors
Magnification
hi
By definition, m =
ho
m = magnification
hi = image height (negative means inverted)
ho = object height
AND
m = hi / ho = -di / do
Magnification is simply the ratio of image height
to object height. A positive magnification means
an upright image.
•F
•C
Casey decides to join in
the fun and she finds a
convex mirror to stand
in front of. She sees her
image reflected 7 feet
behind the mirror which
has a focal length of 11
feet. Her image is 1
foot tall. Where is she
standing and how tall is
she?
do =19.25 feet
ho = 2.75 feet
Mirror Equation Sample Problem
•C
•F
Suppose AllStar, who is 3 and
a half feet tall, stands 27 feet
in front of a concave mirror
with a radius of curvature of
20 feet. Where will his image
be reflected
di = 15.88 feet
What will its size be?
hi = -2.06 feet
Determine the image distance for a
5.00-cm tall object placed 10.0 cm
from a concave mirror having a focal
length of 15.0 cm.
Use 1 / f = 1 / do + 1 / di where f = 15
cm and do = 10.0 cm
di = -30.0 cm
Determine the image height for a 5.00cm tall object placed 10.0 cm from a
concave mirror having a focal length of
15.0 cm. (di = -30.0 cm)
Then use hi / ho = -di / do where ho = 5
cm, do = 45 cm, and di = -30.0 cm
hi = +15.0 cm
A 4.00-cm tall light bulb is placed a distance of
45.7 cm from a concave mirror having a focal
length of 15.2 cm. Determine the image distance.
1/f = 1/do + 1/di
1/(15.2 cm) = 1/(45.7 cm) + 1/di
0.0658 cm-1 = 0.0219 cm-1 + 1/di
0.0439 cm-1 = 1/di
22.8 cm = di
A 4.00-cm tall light bulb is placed a distance of
45.7 cm from a concave mirror having a focal
length of 15.2 cm. Determine the image size.
hi/ho = - di/do
hi /(4.0 cm) = - (22.8 cm)/(45.7 cm)
hi = - (4.0 cm) • (22.8 cm)/(45.7 cm)
hi = -1.99 cm
Refraction
Normal
Line
Less Dense
More Dense
Normal
Line
More Dense
Less Dense
Normal
Line #1
Light Beam
Fast
AIR
Slow
WATER
AIR
Fast
Normal
Line #2
http://cougar.slvhs.slv.k12.ca.us/~pboomer/physicslectures/secondsemester/light/refraction/refraction.html
Snell’s Law
Snell’s law states that a ray of light bends in
such a way that the ratio of the sine of the
angle of incidence to the sine of the angle of
refraction is constant. Mathematically,
i
r
ni
nr
ni sin i = nr sinr
Here ni is the index of refraction in the original
medium and nr is the index in the medium the
light enters.  i and r are the angles of
incidence and refraction, respectively.
Willebrord
Snell
Index of Refraction, n
The index of refraction of a substance is the ratio of the speed in light
in a vacuum to the speed of light in that substance:
c
n=
v
n = Index of Refraction
c = Speed of light in vacuum
v = Speed of light in medium
Note that a large index of refraction
corresponds to a relatively slow
light speed in that medium.
Medium
n
Vacuum
1
Air (STP)
1.00029
Water (20º C) 1.33
Ethanol
1.36
Glass
~1.5
Diamond
2.42
Index of Refraction Equations
• n = c/v = speed of light in a vacuum
speed of light in medium
Index of Refraction Equations
• n = c/v = speed of light in a vacuum
speed of light in medium
• n = sin i/sin r
Index of Refraction Equations
• n = c/v = speed of light in a vacuum
speed of light in medium
• n = sin i/sin r
• sin A / sin B = nB / nA
Index of Refraction
Problem
A diamond (n = 2.42) is in water (n = 1.33) and a
ray of light shines on it making an angle of
incidence of 55o. What is the angle of refraction
inside the diamond?
sin A / sin B = nB / nA
sin 55o / sin B = 2.42/1.33
B = 27o
Total Internal Reflection...
…is the total reflection of light
traveling in a medium when it strikes a
surface of a less dense medium above
the critical angle
n
r
-1
c = sin
ni
Critical Angle Animation
Refraction
Critical Angle
AIR
49
Total
Internal
Reflection
WATER
Light
Source
A diver basks in the reflection of the Northern
Lights underwater by George Karbus
Index of Refraction Problem
What is the speed of light in water,
which has an index of refraction of 1.33?
n = c/v  v = c/n
v = (2.998 x 108 m/s) / 1.33
V = 2.25 x 108 m/s
Index of Refraction Problem
A ray of light enters a piece of crown
glass at an angle of 57o and is refracted
to 31o inside the glass. What is the
index of refraction?
n = sin i/sin r
= sin 57o / sin 31o
= 1.63
Air – Water Interface
sin θ = n2/n1
Air nair = 1 and Water n2 = 1.33
sin θ = 1.00/1.33 = 0.750
sin θ = 0.750
θ = sin-1 0.750
θ = 49o
Critical Angle Sample Problem
Calculate the critical angle for the diamond (n =
2.42) -air (n = 1) boundary.
c = sin-1 (nr / ni)
air
diamond
c
= sin-1 (1 / 2.42)
= 24.4
Any light shone on this
boundary beyond this angle
will be reflected back into the
diamond.
Lenses
Focal Length and Focal Point of a
Thin Lens
A converging lens has a positive focal length
o Therefore, it is sometimes called a positive
lens
A diverging lens has a negative focal length
o It is sometimes called a negative lens
Converging or
Convex Lens
C
F
F
C
Converging or
Convex Lens
Converging or
Convex Lens
C
F
F
C
Converging
or Convex
Lens
C
F
F
C
Converging
or Convex
Lens
C
F
F
C
Converging
or Convex
Lens
C
F
F
C
Converging
or Convex
Lens
C
F
F
C
Converging
or Convex
Lens
C
F
F
C
Converging
or Convex
Lens
C
F
F
C
Converging
or Convex
Lens
C
F
F
C
Lens Sign Convention
1
1
1
+
=
f
di do
f = focal length
di = image distance
do = object distance
di
+ for real image
- for virtual image
+ for convex lenses
f
- for concave lenses
Lens/Mirror Sign Convention
The general rule for lenses and mirrors is this:
di
+ for real image
- for virtual image
and if the lens or mirror has the ability to converge light,
f is positive. Otherwise, f must be treated as negative for
the mirror/lens equation to work correctly.
Lens Equation: do> C
f = 2 cm, C = 4 cm, ho = 2 cm, do = 5cm, di = ?
1/f = 1/do + 1/di
1/2 = 1/5 + 1/di
1/di = 1/2 - 1/5 = 0.5 – 0.2 = 0.3
di = 3.33 cm
M = hi/ho = -di/do  (-ho x di )/ do = hi
hi = (-2 x 3.3)/5
hi = -1.3 cm
Lens Equation: do < f
f = 2 cm, C = 4 cm, ho = 2 cm, do = 0.5 cm, di = ?
1/f = 1/do + 1/di
1/2 = 1/1 + 1/di
1/di = 1/2 - 1/0.5 = 0.5 – 2.0 = -1.5
di = -.67 cm
M = hi/ho = -di/do  (-ho x di )/ do = hi
hi = (-2 x -.67)/0.5
hi = +8/3 = +3.67
M = - di / do = +1.33
Lens Sample Problem
•2F
•F
•F
•2F
Tooter, who stands 4 feet
tall (counting his
snorkel), finds himself 24
feet in front of a convex
lens and he sees his
image reflected 35 feet
behind the lens. What is
the focal length of the
lens and how tall is his
image?
f = 14.24 feet
hi = -5.83 feet
Diverging or
Concave Lens
C
F
F
C
Concave Lenses
2•
F
•F
•F 2•
Rays traveling parallel to the
principal axis of a concave lens will
refract as if coming from the focus.
F
Rays traveling toward the
focus will refract parallel to
the principal axis.
•2F •F
•F 2•
F
•2F •F
•F 2•
F
Rays traveling directly through the
center of a concave lens will leave
the lens traveling in the exact same
direction, just as with a convex lens.
Concave Lens Diagram
object
•2F
•F
image
•F
•2F
No matter where the
object is placed, the
image will be on the
same side as the
object. The image is
virtual, upright, and
smaller than the object
with a concave lens.
Image Summary
• For a converging lens, when the object
distance is greater than the focal length (p >ƒ)
– The image is real and inverted
• For a converging lens, when the object is
between the focal point and the lens, (p<ƒ)
– The image is virtual and upright
• For a diverging lens, the image is always
virtual and upright
– This is regardless of where the object is placed
For a converging lens, the object real
and inverted when the object
distance is __.
a) Greater than the focal length
b) Less than the focal length
c) Equal to the focal length
For a diverging lens, the image is
always what?
a) virtual
b) upright
c) real
d) a and b
A converging lens has a __ focal
length and a diverging lens has a
__ focal length.
a) +, c) +,+
b) -, +
d) -,-
Fiber Optics
spool of optical fiber
Fiber optic lines are strands of glass or
transparent fibers that allows the transmission
of light and digital information over long
distances. They are used for the telephone
system, the cable TV system, the internet,
medical imaging, and mechanical engineering
inspection.
Optical fibers have many advantages over
copper wires. They are less expensive,
thinner, lightweight, and more flexible. They
aren’t flammable since they use light signals
instead of electric signals. Light signals from
one fiber do not interfere with signals in
nearby fibers, which means clearer TV
reception or phone conversations.
A fiber optic wire
Continued…
Fiber Optics Cont.
Fiber optics are often long strands
of very pure glass. They are very
thin, about the size of a human
hair. Hundreds to thousands of
them are arranged in bundles
(optical cables) that can transmit
light great distances. There are
three main parts to an optical
fiber:
• Core- the thin glass center where light travels.
• Cladding- optical material (with a lower index of refraction
than the core) that surrounds the core that reflects light back into
the core.
• Buffer Coating- plastic coating on the outside of an optical
fiber to protect it from damage.
Continued…
Light travels through the core of a
fiber optic by continually
reflecting off of the cladding. Due
to total internal reflection, the
cladding does not absorb any of
the light, allowing the light to
travel over great distances. Some
of the light signal will degrade
over time due to impurities in the
glass.
Fiber Optics
(cont.)
There are two types of optical
fibers:
• Single-mode fibers- transmit
one signal per fiber (used in
cable TV and telephones).
• Multi-mode fibers- transmit
multiple signals per fiber (used
in computer networks).
Mirage Pictures
Inferior Mirages
A person sees a puddle ahead on
the hot highway because the road
heats the air above it, while the
air farther above the road stays
cool. Instead of just two layers,
hot and cool, there are really
many layers, each slightly hotter than the layer above it. The cooler air has a
slightly higher index of refraction than the warm air beneath it. Rays of
light coming toward the road gradually refract further from the normal,
more parallel to the road. (Imagine the wheels and axle: on a light ray
coming from the sky, the left wheel is always in slightly warmer air than the
right wheel, so the left wheel continually moves faster, bending the axle
more and more toward the observer.) When a ray is bent enough, it
surpasses the critical angle and reflects. The ray continues to refract as it
heads toward the observer. The “puddle” is really just an inverted image of
the sky above. This is an example of an inferior mirage, since the cool are is
above the hot air.
Sunlight after Sunset
Lingering daylight after the sun
Apparent
is below the horizon is another
effect of refraction. Light travels position
Observer
of sun
at a slightly slower speed in
Earth’s atmosphere than in
space. As a result, sunlight is
Actual
refracted by the atmosphere. In
Earth
position
the morning, this refraction
of sun
causes sunlight to reach us
before the sun is actually above
Atmosphere
the horizon. In the evening, the
sunlight is bent above the horizon after the sun has actually set. So
daylight is extended in the morning and evening because of the
refraction of light. Note: the picture greatly exaggerates this effect as
well as the thickness of the atmosphere.
Rainbows
A rainbow is a spectrum
formed when sunlight is
dispersed by water droplets in
the atmosphere. Sunlight
incident on a water droplet is
refracted. Because of
dispersion, each color is
refracted at a slightly different
angle. At the back surface of
the droplet, the light undergoes
total internal reflection. On the
way out of the droplet, the light is once more refracted and dispersed.
Although each droplet produces a complete spectrum, an observer will
only see a certain wavelength of light from each droplet. (The wavelength
depends on the relative positions of the sun, droplet, and observer.)
Because there are millions of droplets in the sky, a complete spectrum is
seen. The droplets reflecting red light make an angle of 42o with respect to
the direction of the sun’s rays; the droplets reflecting violet light make an
angle of 40o.
Primary Rainbow
Secondary Rainbow
Secondary
Primary
Alexander’s
dark region
The secondary rainbow is a rainbow of radius
51, occasionally visible outside the primary
rainbow. It is produced when the light
entering a cloud droplet is reflected twice
internally and then exits the droplet. The color
spectrum is reversed in respect to the primary
rainbow, with red appearing on its inner edge.
Dispersion is the ___ of white light
into pure colors.
a) combination
c) absorption
b) separation
d) decomposition
What color can bend the most?
a) violet
c) red
b) cyan
d) magenta
Which of these can raindrops not
do to sunlight?
a) Refract
c) Reflect
b) Absorb
d) Disperse
Credits
Snork pics: http://www.geocities.com/EnchantedForest/Cottage/7352/indosnor.html
Snorks icons: http://www.iconarchive.com/icon/cartoon/snorks_by_pino/
Snork seahorse pic: http://members.aol.com/discopanth/private/snork.jpg
Mirror, Lens, and Eye pics:
http://www.physicsclassroom.com/
Refracting Telescope pic: http://csep10.phys.utk.edu/astr162/lect/light/refracting.html
Reflecting Telescope pic: http://csep10.phys.utk.edu/astr162/lect/light/reflecting.html
Fiber Optics:
http://www.howstuffworks.com/fiber-optic.htm
Willebrord Snell and Christiaan Huygens pics:
http://micro.magnet.fsu.edu/optics/timeline/people/snell.html Chromatic Aberrations:
http://www.dpreview.com/learn/Glossary/Optical/Chromatic_Aberrations_01.htm
Mirage Diagrams: http://www.islandnet.com/~see/weather/elements/mirage1.htm
Sir David Brewster pic: http://www.brewstersociety.com/brewster_bio.html
Mirage pics:
http://www.polarimage.fi/
http://www.greatestplaces.org/mirage/desert1.html
http://www.ac-grenoble.fr/college.ugine/physique/les%20mirages.html
Diffuse reflection: http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l1d.html
Diffraction: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/grating.html