Intro to Physics
San Dieguito Academy
2011 - 2012
Note: all situations described in this text are fictional and do not
represent the views of the school, its sponsors, or the S.P.C.A.
A digital copy of this book can be found at
Light and Optics
Newton was great at treating things as particles. Rocks, planets, cars, air could all be treated as
particles. It was no big jump for him to imagine light as a particle. As a particle, light had to obey
certain rules that applied to all particles:
1. light travels in uniform motion. (straight lines at a constant speed)
2. When light collides with a surface, it experiences an impulse.
3. When light bounces off of a surface it acts as a billiard ball would when it hits the side of a
a. Angle of reflection = angle of incidence
b. All angles are measured from the normal to the surface.
Nature of mirrors
1. If it is clean, you cannot see a mirror’s surface. This is very important. Please think about it.
a. Why is the surface of a clean mirror invisible?
b. Why do we normally see mirrors even when they appear clean?
2. Real objects that are in front of a flat mirror will have virtual images behind the mirror given
by the following rule: The mirror is the perpendicular bisector of the segment created by the
object and its image.
a. Where does the perpendicular bisector requirement force the image to be?
3. Notice that no matter where you, the observer stand, you will always look to the same image
location in order to see the object’s reflection in the mirror.
Some Questions Concerning Mirrors
Mirrors in deep space
1. A true mirror cannot be seen. It just reflects. Imagine an infinitely large mirror
somewhere in deep space. You are standing 20 meters in front of this mirror. What
will you see?
2. Now imagine that between you and this mirror is another mirror. Only this
intermediary mirror is a two way mirror. That is one that allows you to look through
but people on the other side cannot see out. What will you see as you look toward these
1. How come when you look at a newspaper in a mirror the letters are reversed but they
are not upside down.
2. If you are 6 feet from a mirror and are five feet tall, what is the smallest sized flat
mirror that can be used to show you your complete reflection? If you are not reversed
vertically in the mirror why are your hands reversed?,
3. You are driving your car. There is a rear view
mirror mounted on the top center of the front
window. It blocks a bit of your forward view and
you wonder what idiot mandated rear view
mirrors. During the day you can see cars that
are behind you. During the night you see the
bright lights of those cars. It is really disconcerting. One day you notice that
there is a little flip-switch on the mirror. It has two words on it “day” and “night”
It is purely a mechanical switch (no electricity) How does the switch cause the
mirror to dim the car’s lights at night?
4. On the side of your car are your side view mirrors. One
day you notice that on the mirror are the following
words: “Objects in mirror are closer than they appear.”
Why would anyone make a mirror that mislead you into
thinking a car is behind you when it is really beside you ?
Concave parabolic mirrors are mirrors that “cave in” toward the center. There is a point
called the focus point (f) in front of the mirror.
1. If you place a candle at the focus point, all light hitting the mirror will reflect forward,
parallel to the major axis.
2. The converse is true as well. If light comes at the mirror in rays parallel to the major
axis, all the light will come together at the focus.
This follows Newton’s third law, for every action, there is an equal but opposite reaction.
3. Notice that for every ray of light, the angle of reflection always equals the angle of
Object Major Axis
Concave mirrors have the special property that objects (such as candles) place in
front of them can produce images in other locations. We can find these images by
tracing just three of the millions of possible paths that light can travel from the
Rules for finding images on concave mirrors
1. Draw a ray from the object that is parallel to the major axis. When it hits the
mirror it will reflect back through the focus point of the mirror.
2. Do the converse of the above. Draw a ray from the object goes through the
focus. When it hits the mirror, have it reflect back parallel to the major axis.
3. Draw a ray to the center of the mirror. (the only point on the mirror which is
perpendicular to the major axis. When it hits the mirror, reflect it back at the
same angle below the major axis as it hit from above the axis.
For those of you who want equations to help you find answers try this
___1___ = ___1____ + ____1____ Magnification = image distance
focal dist object dist image distance object distance
Try the following problems
Problem #1 Ray Diagram Math
20 cm concave
So far all of the object and concave mirror problems have given us real images.
That is images where the light really comes together to create a real image. If there
were a screen at that location, there would be a bright image on the screen. What
happens if we move the object inside of the focal distance?
Here we have an object which is 20 cm from a 40 cm focal length mirror
20 cm mirror
Notice how we cannot make a ray leave the object, go through the focus and then hit
the mirror. But wait. Every observer believes that he/she sees light come at their
eyes in a straight line. Let us backtrack from the observer’s eye. There is a point
behind the mirror where the rays appear to converge. The image is called “virtual”
because no light reaches there.
Interestingly you can trace backwards a ray from the focus that goes through the
object and find the image this way.
Now lets do the math.
___1___ = ___1____ + ____1____ image distance
focal dist object dist image distance object distance
___1___ = ___1____ + ____1____ Magnification = ___________
When a mirror vexes outward at its center, it is called convex. All images created by it
are virtual (negative) Lets see if you can figure out where the images are.
convex - 20 cm
convex - 20 cm
convex - 20 cm
Check here for help http://fmp.shep.net/physics/Physics_20/UNIT_4/sim/dmirr/index.html
Speed of Light
In the early 1600’s Galileo attempted to measure the speed of light using two
lanterns. He and an assistant got on hills that were separated by about a half a mile.
He opened the shutter on one lantern. When the light reached the assistant, the
assistant then opened his lantern shutter. Galileo was then to measure the time it
took for the light to make the round trip. Needless to say, they were unable to
measure light’s speed. His conclusion was that light must be very fast.
In the early 20th century Albert Abraham Michelson came up with an ingenious
method to measure the speed of light using a very bright light source, a rotating
mirror. and a fixed mirror on a mountain top 20 miles away.
The following applet gives a very good graphical demonstration of how it was done.
First run the experiment in the light ray mode
To better understand what is happening view the light pulse
If the distance between the spinning disk and the reflecting disk is 35 kilometers and the disk has
32 mirrors on it, how fast would the disk have to be spinning if to give a measurement of 3.0E8
Refraction and the Speed of Light
It turns out that while the speed of light is constant, light does not travel at the
same speed in every material. The more optically dense the material the slower
light travels. A vacuum is the least optically dense. In it light travels the fastest.
There is a simple equation for determining the speed at which light travels in a
Vel of light = ______
c = 3.0 x 108 m/sec n = index of refraction the material
When light goes through any material, it travels at a speed determined by the
material itself. The material’s ability to determine the speed at which light
propagates is called the material’s index of refraction. The higher the index of
refraction, the slower the speed of light in it. Below are some sample indexes of
Material Index of refraction Velocity of light percent vel in vacuum
Vacuum 1.0000 300.000,000 m/sec __100 %__
Air 1.003 ________________________ _________
Water 1.33 ________________________ _________
Plexiglas 1.51 ________________________ __________
flint glass 1.58 ________________________ _________
Dense flint 1.66 ________________________ ___60.2 %_
Zircon 1.923 ________________________ __________
Cubic Zirconium 2.17 ________________________ _________
Diamond 2.42 ________________________ _________
Rutile 2.9 ________________________ _________
Gallium phosphide 3.5 ________________________ _________
Refraction and Bending
There is a side effect of refraction that we can easily see. Usually when light enters
a material of higher or lower index of refraction it will change direction.
There are two factors that determine the amount of bending. The first is the
difference between the indices of refraction (n) of the materials and the angle of
incidence of the light. It happens to a greater degree as light enters more obliquely
to the surface of the material (at a bigger angle)
Below is a diagram of light entering a semicircular clear plastic tub of water. The
angle of incidence (i) is measured from the normal to the surface. As it enters the
tube it bends toward the normal on the other side of the front surface. Once it is
inside of the water, light travels in a perfectly straight line. The bending only occurs
when light moves from one index of refraction to another.
Notice that light leaving the water does not bend. This is because the angle of
incidence on the back side is zero degrees. In 1621 Willebrord Snellius derived
what would come to be known as Snell’s Law. The law is as follows.
ni sin ( i ) = nr sin ( r )
In the following pages we will empirically verify this.
Determining the Index of Refraction in H2O
We will be using half round plastic cheese containers to determine the index of
refraction of water and another substance. What you will be comparing is the angle
of incidence of light in air as it enters the flat side of the container with the angle of
refraction as it moves through the water, curved side of the container.
Angle of incidence Angle of refraction
0 10 20 30 40 50
Angle of refraction (q water)
After a lot of trial and error work someone decided to see if there was a relationship between
the sin incidence and sin refraction.
Angle of Angle of Sin incidence Sin refraction
Graphing the data on the previous page gives a straight line
0.4 0.6 0.8 0.9 1.0
Sin angle refraction (q water)
In first year algebra you spent a lot of time graphing equations. The basic formula was
y=mx + B
y is the your vertical axis. Y axis = Sin ( incidence)
x is your horizontal axis X axis = Sin ( refraction)
M is the slope of the graph (rise over run)
b is the y intercept (zero in this case)
Snell then made the assumption that air if air had an index of refraction of 1 the
index of refraction of water would be equal to the slope of the graph
(slope = nwater/nair) If n air = 1 then the slope = n water
The slope of our graph is _______ thus the index of water is ________
The general form of Snell’s law is nair sin air = nwater sin water
Explaining Bending Due to Refraction
There is a simple physical analogy for the bending associated with refraction.
Imagine two wheels tied together by a rigid shaft. As the first wheel enters a section
of slower speed the other wheel continues moving forward at the higher speed,
causing the wheels to turn towards the normal.
Many scientists disagreed with Newton’s particle analogy for light. They felt that
light was really a wave. They would use a marching analogy for the bending of
light. Imagine rows of soldiers holding meter sticks between each individual. They
come marching toward a section of soggy soil.
A Fish’s View of the World
Imagine such a thing as a laser shark that has killer laser eyes. One look and you are dead.
With a protractor find the path of the light in each case shown below and draw it. Assume
that nair = 1 and nwater = 1.33.
60 50 45 40 30 20
The angle at which light can not get out is called the critical angle. It is found by using the
n1 sin ( critical) = n2 sin (90 degrees)
Find the critical angle for water.
What is the critical angle for a diamond?
Notice that there is only a critical angle when you are
trying to leave a material with a higher index of
refraction than the material the light is entering.
Looking at things from the human’s point of view we
find that the fish’s location is not where it appears to
be. This is why spear fishermen wait for the fish to
pass between their legs.
Let us imagine that light moving through air (n = 1.0) enters a prism made of ice (n = 1.33).
The prism is a 45 – 45 –90 degree triangular shape. Calculate the path of light and using a
protractor sketch this path until the light leaves the prism. Make sure to show the angle of
the emerging light.
This time imagine that light moving through air (n = 1.0) enters a prism made of
glass (n = 1.9). Calculate the path of light and using a protractor sketch this path
until the light leaves the prism. Make sure to show the angle of the emerging light.
(Answer = 38.8 degrees)
You have lots of money and buy a diamond prism. Light moves through air (n = 1.0) enters
the prism (n = 2.42) Calculate the path of light and using a protractor sketch this path until
the light leaves the prism. Make sure to show the angle of the emerging light.
Lets calculate the path of light moving through a lens. (n = 1.7)
Now lets look at a concave lens. (n = 1.7)
The Nature of Lenses
Lenses work using refraction. It turns out that parabolic shaped pieces of glass cause light to
bend in ways very similar to what happens with parabolic mirrors.
If light travels along the major axis of a convex lens, when it hits the lens the light is bent so
that it focuses on the opposite side.
The interesting thing about the lens that makes it very different form a mirror is that there is
no front side. Light traveling along the major axis from the other side will behave in a similar
Look at the picture above. It is reversible. If light were to start at or go through the focus
point on the left hand side of the lens, it would create a similar pattern.
As you can see this is very similar to what happens with a concave mirror. If we can create
images with a mirror, we should also be able to create images with a lens. On the next page
you will be asked to modify and apply the concepts learned with mirrors to the new situation
of a lens.
Convex lenses (called burning lenses by children) take light that is moving parallel to the
major axis and cause it to converge a point, the focus. We us convex lenses to produce
images in much the same way that concave mirrors do. Draw ray diagrams for the following:
1 1 1 id
Check by using the lens equation _____ = + _____
_____ and mag = ____
f od id od
Check here for help http://fmp.shep.net/physics/Physics_20/UNIT_4/sim/clens/index.html
If a convex mirror acts as the opposite of a concave mirror, then a concave lens must act as
the opposite of a convex lens. Draw the ray diagrams for each of the following:
Check here for help http://fmp.shep.net/physics/Physics_20/UNIT_4/sim/dlens/index.html
What should the lens equation for concave lenses look like?
1. The human eye is about 4 cm from lens to screen. If you are looking at an object that is 10
meters away. What focal length lens should be placed in our eye?
2. There is a problem with having a lens of fixed focal length. Now we turn our eyes toward
a book. The letters are 20 cm away. How far away should the back of the eye-ball be so that
the image of the letters will be in focus?
3. What should the focal length of the lens be if you want to keep the back of the eye ball the
same size and still read the letters?
(answer approx 0.04 cm)