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Reflection and Mirrors
The Law of Reflection always applies:
“The angle of reflection is equal to the
angle of incidence.”
“Plane” Mirrors form
virtual images.
Virtual: light APPEARS to
come from this location,
but does not actually
start there.
The image is the same
distance behind the
mirror as the object is in
front of the mirror.
The image is the same
size as the object.
If you wish to take a picture
of your image while
standing 2 meters in front
of a plane mirror, for what
distance should you set
your camera to provide
the sharpest focus?
Since the image is the same
distance BEHIND the
mirror as the object is in
front of the mirror….
Set the distance for 4 meters
How big does a
mirror have to be in
order for you to see
your entire image?
Concave Mirrors
*Form “real”, inverted images
are formed UNLESS the
object is inside the focal
length…
…Then the images are
“virtual” and upright!
Convex Mirrors
Focal point
The image is always
smaller, upright, and
virtual-
an SUV.
Used in security
cameras and rearview mirrors in your
car.
The Mirror Equation
1 1
1


f do di
Where f is the focal length,
do is the distance from the mirror to the object,
and di is the distance from the mirror to the image.
Magnification
hi
The magnification
m
ho
provided by a mirror
is given by
Where hi is the height of
the image and
ho is the height of the
object
d i
and m 
do
Yep, it’s time for you to
try one…
A concave mirror has a radius of curvature of 15.0 cm.
A 1.5 cm tall gummy bear is placed 19.0 cm from the
mirror. Where will the image be formed? What is the
magnification? How tall is the image?
First find the focal length. f = ½ R
f = 7.5 cm
Now solve for di using the lens equation.
di = 12.39 cm
Now, get the magnification, m = -di / do
m = - 0.65 it’s negative because the image is inverted.
Now for the height of the image: m = hi / ho
hi = -0.98 cm
Concave and Convex Lenses
Light REFRACTS as it
passes through
lenses, forming
images.
Convex lenses are
CONVERGING
lenses
Concave lenses are
DIVERGING lenses
Refraction: the change in direction as a
wave passes from one medium into
another
Measurements with lenses
f - focal length
do – distance from the lens to the object
being observed.
di – distance from the lens to where an
image is formed
m- magnification- compares the size of the
object being observed and the image formed
by the lens.
“Virtual”
A “virtual” focal point- real light waves would
appear to converge at that point, but they actually
do not. Concave lenses have a virtual focal point.
Convex lenses have a real focal point.
A “virtual” image- No real image will appear on a
screen. The light rays that reach your eye just
behave as if they came from the image position
Convex Lenses
The “focal length” will be ½ the
“radius of curvature”.
Images formed by Convex lenses
If the object is beyond twice the focal length, the
image is smaller, inverted, and real- if a piece of
paper was placed at the image location, you
would see the image on the paper.
If the object is placed at exactly twice the focal
length, the image will be exactly the same size
as the object, inverted, and real
If the object is placed exactly at the focal point,
the light rays are perfectly parallel, and NO
image will be formed!
If the object is placed within the focal length, the
image will be larger, upright, and VIRTUAL.
NO image would appear on a paper screen
placed at the image location!
Your Eye
Magnifying glasses
Magnifying glasses are convex lenses
that converge the light towards a focal point
Diverging Lenses
Concave (diverging) lenses ALWAYS form
smaller, upright, virtual images.
SUV
People who are near-sighted can
see up close but not far away.
They use concave (diverging)
lenses, which will make
something far away look like it’s
up closer.
People who are far-sighted use
convex (converging) lenses that
make near objects look as if
they are further away.
The Lens/Mirror Equation
1 1
1


f do di
Where f is the focal length,
do is the distance from the mirror or lens to the
object,
and di is the distance from the mirror or lens to the
image.
Magnification
hi
m
ho
d i
and m 
do
The magnification provided by a lens or mirror
Where hi is the height of the image and
ho is the height of the object
Yep, it’s time for you 1  1  1
f do di
to try one…
m
hi
ho
and m 
d i
do
A convex lens has a radius of curvature of 8.0 cm. A
12 cm tall troll is placed 7.0 cm from the lens. How far
from the lens should a screen be placed in order to
have a sharp image? What is the magnification? How
tall is the image?
First find the focal length. f = ½ R
f = 4.0 cm
Now solve for di using the lens equation.
di = 9.33 cm
Now, get the magnification, m = -di / do
m = - 1.33 it’s negative because the image is inverted.
Now for the height of the image: m = hi / ho
hi = -16 cm
Using the lens equation for
concave lenses
The focal point is VIRTUAL, so use a
negative value for the focal length.
Example: if the radius of curvature of a
concave lens is 10 cm, the focal length
f = -5 cm.
1 1
1


f do di
Optometrists and opthalmologists,
instead of using the focal length
to specify the strength of a lens,
use a measurement called the
power or diopter of a lens.
The power (diopter) = 1 / f
For example, a 20 cm focal length
lens has a power of 1 / 0.20 =
5.0 Diopters
Cameras
Camera Settings
Shutter speed: how
long the shutter is
open. Speeds
faster than 1/100 s
are normally used.
Fast action requires
a very small shutter
speed.
Camera Settings
F-stop:
changes the
diameter of the iris
diaphragm to control
the amount of light
reaching the film.
The SMALLER the fstop, the LARGER the
opening.
The f-stop determines
“depth of field”.
A larger f-stop
(a smaller opening)will produce an image
where everything is in
focus.
A smaller f-stop
(a larger opening)will produce an image in
which only the subject is
in focus and everything in
the foreground and
background is out of
focus.
A TELEPHOTO lens
has a longer focal
length to magnify
images.
A WIDE-ANGLE lens
has a shorter focal
length.
Telescopes
Refracting telescopes have two lenses,
the objective and the eyepiece.
The eyepiece lens has a smaller focal
length.
The objective lens has a larger focal
length.
Microscopes
Microscopes also have
two lenses, the
eyepiece and the
objective.
The eyepiece lens has the
longer focal length.
The objective has the
smaller focal length.
Fresnel Lens
The weight and bulk
of a large diameter
lens can be reduced by
constructing the lens
from small wedged
segments that follow
the curvature of the
original lens and
collapse down to a
thin layer.
Augustin Fresnel
Fresnel invented
this type of lens in
1822.
Fresnel lenses
can take a small
diverging light
source and
change it into a
powerful
straight beam of
light.
Small plastic Fresnel
lenses are sold at office
supply stores as
“Magnifying Lenses”
Fresnel Lenses are
also used in
overhead
projectors
Large glass lenses that
have Fresnel surfaces
surrounding a small
light source have
provided an
invaluable
contribution to
coastline areas for
more than 150 years.
These lenses are
used in…..
Lighthouses
Tests showed that while
an open flame lost
nearly 97% of its light,
and a flame with
reflectors behind it still
lost 83% of its light, the
fresnel lens was able to
capture all but 17% of
its light.
Because of its amazing
efficiency, a fresnel lens
could easily throw its
light
20 or more miles
to the horizon.
Refraction
• When waves enter a
new medium, they
change direction and
speed. The change
in direction is called
Refraction.
The angles of incidence,
reflection, and refraction are all
measured from a line drawn
“normal” (perpendicular) to the
surface.
The angle of reflection is
ALWAYS equal to the angle of
incidence.
That is the Law of Reflection.
q q
q
The amount that the wave refracts depends on
the kind of medium it is moving through.
The index of refraction, “n”,
of each medium determines both
the refraction and the average speed.
c/v=n
where c is the speed of light in a vacuum and
v is the average speed of light through the
medium.
For example: what is the
velocity of light through
water with an index of
refraction,
n = 1.54?
Rearranging c/v = n gives
v=c÷n
v = 3 x 108 ÷ 1.54 =
1.95 x 108 m/s
The average speed of light
slows down when it goes
through water!!
Snell’s Law
Snell’s Law describes refraction as
light strikes the boundary between
two media
n1 sin q1 = n2 sin q2
The index of refraction of a pure
vacuum and of air is n = 1.
The index of refraction of every other
substance is greater than 1.
q q
q
Example:
Light traveling through air enters a
block of glass at an angle of 30°
and refracts at an angle of 22°.
What is the index of refraction of the
glass?
n1 sin q1  n 2 sin q2
n1 sin q1
n2 
sin q2
1sin 30
n2 
 1.33
sin 22 
n1 sin q1
sin q2
q q
q
Different frequencies
(colors) refract slightly
different amounts.
This means that the index
of refraction, “n”, for blue
light is slightly different
than “n” for red light.
This results in a dispersions
of colors as seen in a
prism or a rainbow.
Blue Bends Best!
(ok, actually violet refracts the
most…)
Rainbows!
Sunlight refracts as it enters a
raindrop.
Different colors refract different
amounts.
This spreads out the colors.
The light reflects off the back of the
raindrop.
The light refracts again, spreading out
the colors even more.
We see the rainbow!
The Critical Angle and Total Internal
Reflection
When light passes from a material
that is MORE dense to one that is
LESS dense, its refracts AWAY
from the Normal line.
As the angle of incidence increase,
the angle of refraction also
increases.
q
The Critical Angle and Total Internal
Reflection
At some Critical Angle of incidence,
the angle of refraction is 90°.
There is no light that is refracted!
n2
All of the light is reflected back into the
original medium.
qcritical
This is called Total Internal Reflection
n2
sin qcritical 
n1
n1
The most useful
application of the
phenomenon of
Total Internal Reflection
is in
Fiber Optics
When wavefronts pass through a narrow
slit they spread out. This effect is called
diffraction.
The amount of diffraction depends upon the size of
the slit.
If the slit is comparable in size to the wavelength of
the wave then maximum diffraction occurs.
• The number of slit openings also
determines what the diffraction pattern
looks like.
• Thomas Young, in1801, first
established the
wave theory of light
by demonstrating that light
diffracted.
• He also provided the first
measurement of the
wavelength of light.
Thomas Young’s Double-Slit Experiment
• He allowed sunlight to fall on two slits.
• He knew that if light was a wave, it would diffract as it
passed through the slits.
• The diffracted waves would have areas of both
constructive and destructive interference.
• This interference would produce bright and dark areas
on a screen.
• The pattern of bright and
dark fringes did appear on
a screen.
• The brightest area, in the
center, he called the
“central bright spot”.
• He was able to
mathematically determine
the wavelength by
measuring the distance
from the central bright
spot to each fringe.
ml = d(x ÷ L) = dsinq
m- “order” (m = 0 is the central bright spot)
l- wavelength of light
d- distance between the slits
x- distance from central bright spot to another
bright fringe
L- distance from the slits to the screen
q- the angle between the line to the central bright
spot and the observed bright fringe.
• The more slits there are, the narrower the
fringes become.
• The fringes on top are from two slits.
• The fringes on bottom are from eight slits.
• A “diffraction grating” has hundreds of slits per
millimeter.
Optical diffraction effects can be seen with eye - in fact
most of us when children have noticed it, but ignored it
when becoming adults.
Look through a narrow slit between your fingers. If you
look carefully you should see the objects behind are
distorted and that blackish bands parallel to the slit
appear in the gap. The bands are diffraction patterns.
• In the atmosphere,
diffracted light is actually
bent around atmospheric
particles -- most
commonly, the
atmospheric particles are
tiny water droplets found in
clouds.
• An optical effect that
results from the diffraction
of light is the silver lining
sometimes found around
the edges of clouds