In the second unit on waves and optics we finally turn our full attention to light. In this
particular unit we will tend to avoid the wave nature of light while emphasizing the
ability of light to travel in a straight line except at certain boundaries. At
Since there are now atoms in the way the light must change speed. What will this do to
frequency and wavelength? How do you compare the speed of light through one medium
as compared to another? Consider light moving through water and glass for example.
value of n=1.51 at the red end of the spectrum up to a value of 1.53 at the violet end of
the spectrum. As a result of variation on indexes of refraction when white light strikes a
transparent material at an angle the different colors are bent to differen
before getting to the mirror, in other cases the ray only encounters C after reflection.
In fig23.13c the ray never gets to C because that point is located behind the mirror.
Again the phrase through the center is a poor choice of words.
Ray 4 (not shown
Magnification = f(object distance)
You can see that the magnification is positive for
values of x less than the focal length. So the image is upright if you are inside of the
focal length and inverted outside of focal length. While standing outside of foc
In the last unit on Classical Mechanics we consider a special type of motion known as
harmonic motion. This type of motion is distinct because of the repetitive nature.
Consider a ball on a spring that bounces up and down or a child o
clock not started so that t = 0 seconds when M is in the center moving to the right. How
would starting the clock at different times change the equations?
Starting t = 0 seconds when M is at the far right of its motion.
The graph in this case would be as
Notice how when x = 0 then a =0 also. Maximum values for acceleration and position
take place at the same time.
Shown below are the overlapped graphs of v and x (upper) and a and x (lower).
Be sure that given either a graph or an equation of position, vel
Now you can determine the speed of the object directly when a specific position is
known. We say speed rather than velocity because the direction of the object is lost in the
above proof. How fast is the object of the previous example moving when it is at
We can once again rewrite the equation in terms of period.
Portfolio Assignment #12
Construct a pendulum of known length. Measure the time for 20 swings and calculate
g. Then using the books value of G and the radius of Earth calculate the mass of the
KE = k(A2 x2)
The kinetic energy is merely total energy minus potential energy or the difference in the
Although potential energy and kinetic energy vary, they do so in such a way to keep the
total energy constant. What is also nice is the result
Note there are no negative energies.
Kinetic Energy vs. time
KE = m v2
= (0.5)cfw_-1m (4.47/sec)sin(4.47t)2
Y4 = Y22 for TI-83
Again there are no negative energies.
By combining the equations for PE and KE you can conclude the total energy to be a
weight of the water in between top and bottom.
It happens that a point lower in a static fluid will
be at a higher pressure according to the formula
in the box to the right as well as equation 9.10. The subscripts have been modified from
the form used in