14 March 2000

Notes Taken by Porter Johnson

**John Bozovsky (Bowen HS)**

treated us to **A Physics Mystery!**

Using a tape player (which had crisp,loud sound), he played a
cassette of an __Ellery Queen__ mystery. John enumerated the cast
of
characters on the board for us, and also critical questions for us
to think about:

- Who is the murderer?
- Why did he dig in the wrong place?
- What is meisephobia? [ *** loathing for "dirt" -- rather than fear of mice!]
- Are units important?

__Comment by PJ__: The British fought 5 "marine trade wars" with
the Dutch
in the 18^{th} century, and lost them all, because the Dutch
had better and faster ships. As a result, anti-Dutch expressions
from British English are fairly common: i.e., "Dutch courage",
"Dutch uncle", and "Double Dutch".

**Bill Blunk (Joliet Central HS)**

set up the **Millikan Oil Drop Experiment** on the table.
It is a dandy piece of equipment sold by
**Sargent Welch**, and expensive, so his school could afford only
one,
Bill explained. So when he sets it up for his students, only one
at a time can look through the telescope to see the oil drop(s).

He then showed us a new addition to his technology - a small video
camera that he had bought for $90 at the **ISPP meeting at New Trier
HS**. (It's the sort of thing being used on computers these days when
people are "talking" to each other.) It was now connected to a
large TV set in front of us, and when Bill aimed the camera at us,
we could see ourselves on the TV.

He reviewed for us how the
**Millikan Oil Drop Experiment** works; a pair of horizontal,
parallel
conducting plates are placed about 1 cm apart, and an electric
harge is placed on them. Then some "oil drops" are squirted into
the space between them (using an atomizer with a hollow needle such
as for inflating a basketball).

Some of the drops become charged
and may have 1, 2, 3, etc electrons on them. (Millikan used oil
drops because he found small water drops evaporate rapidly, oil
drops don't.) With the aid of a dandy diagram on the board which
showed a charged sphere and a rod nearby, Bill showed us how
opposite charges attract and repel. He used colorful magnets that
had the + and - charge signs on them. They stuck to the board on
the diagram and Bill could move them around to show how charges
respond to each other -- a la **Bill Shanks**.

Bill Blunk also explained that nowadays fairly uniform latex
spheres averaging **913 nm** in diameter and carried by water drops
from the atomizer are what he squirts into the space between the
plates. A sphere (drop) with one electron negative charge would be
attracted toward the upper positively charged plate. If a drop had
2 electrons and twice the negative charge (assuming they are all
alike), then it would
move twice as fast. By observing the motion of the drops through
the telescope against a reticule (grid), one could calculate their
speeds.

At this point, Bill placed the video camera to "look" right into the telescope, and we could then see the drops on the TV screen! With the voltage off (no charge) the drops would gradually move upward (which was really down, since the telescope inverts the image) under gravity. But with the voltage on, some would move down (actually, up, as seen on the TV!). But they moved with different speeds, and the differences between their speeds was always the same amount, which means that the electron charges on the drops always differed by the same amount. Bill could now show this to the entire class at once with the aid of his new video camera. Great! And it is affordable!

**Roy Coleman (Morgan Park HS)**

told us that today was p Day!
(Today's date: 3.14) And Albert Einstein's birthday! And then he
shared some information about the AP Physics Conference at Triton
College.

- Modern physics is down to 10% of the exam.
- Coverage of fluids is decreased.
- On multiple part questions there is more severe grading so students cannot score some partial credit using a "shotgun" approach in answering.
- And no particular lab experiments are required.

explained

The Coffee Cup Caustic is shown on the website http://www.math.harvard.edu/archive/21a_spring_06/exhibits/coffeecup/index.html, on which the reflected image from a real coffee cup is shown, as well as a "Monte Carlo" simulation of the event.

Let us suppose that rays parallel to the y-axis strike an upper semi-circle of radius R from the inside, and are reflected. If we let the angle between the reflection point be q, the coordinates of the point of reflection are x = R cosq and y = R sin q. The angle of incidence of the ray, relative to the normal, is p/2 - q, and the angle of reflection has that same value, as well.

The reflected ray travels at an angle p/2+2
q relative to the positive x-axis, and
strikes the circle again at a point an angle
3 q from the horizontal, at the point
(x = R cos3 q,
y = R sin 3 q). The equation for
the reflected ray is

or

y = R sin q - (x - R cos q) / tan 2q.

As q varies, we generate a series of straight lines. To find the envelope of those straight lines, we must determine the maximum value that y can have for a given value of x, and the appropriate choice of q, by setting the derivative dy/dq equal to zero. Thus we obtain

Thus, we obtain the relation

and

y = R sin q - (x - R cos q)/ tan 2q = R sin q (1/2 + cos

or,

y(x) = R ( 1/2 + (x/R)

The reflected straight path runs between two points on the circular rim, corresponding to angles q and 3 q with respect to the x-axis. These two points on the boundary have coordinates (x, y) = (R cos q, R sin q) and (R cos 3 q, R sin 3 q), respectively. Each such straight line is tangent to the "caustic curve" at one point, which lies precisely one fourth of the way along the path, with coordinates

and

y = R (3 sin q + sin 3 q )/4

We cycle through the various striking points by letting q vary between 0

A template of a 360^{o} Protractor was handed out, and
participants made their own caustic by drawing lines from the positive
x-axis [right on the middle] from angles q
to 3 q. Here is a set of
angles relative to the horizontal to use:

10^{o} |
--- > | 30^{o} |

20^{o} |
--- > | 60^{o} |

30^{o} |
--- > | 90^{o} |

40^{o} |
--- > | 120^{o} |

50^{o} |
--- > | 150^{o} |

60^{o} |
--- > | 180^{o} |

70^{o} |
--- > | 210^{o} |

80^{o} |
--- > | 240^{o} |

90^{o} |
--- > | 270^{o} |

The right side of the caustic will arise, as if per magic!

The full curve, which
was produced using the software package __EXCEL__, is given below.
An excellent reference on using __EXCEL__ in graphics is the book
**EXCEL for Scientists and Engineers** by William J Orvis, Second
Edition [ISBN 0-7821-1761-9].

Maybe someone can show us a real, live caustic at our next meeting?!

Some really good math and Physics Phun!!

SEE YOU THERE!