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Re: bending of object thrown into pool


I selected the html option when my mail program gave me the option of
selecting html, plain text, or both, the latter recommended. I think I
usually select the latter, but I was concerned that duplicate messages
would appear on phys-l. I was able to read the message as posted on
phys-l without gibberish except for the blank lines at the top, some of
which I have removed. As a test, I will submit it with the "both"
option. Should I send it with only the "plain text only" option?

Hugh Logan wrote:

Carl E. Mungan wrote:

None of this is the same as Snell's Law, in which ALL of the
trajectory change occurs at the interface between two media. For a
physical object traveling in a medium, the trajectory is
continuously altered by the medium, i.e. friction, air resistance,
or water resistance. (Vickie Frohne)

I don't see this either. If we assume drag oppositely directed to
velocity and that the object is cylindrically symmetric, it can
travel straight. Also, isn't your above example of the toy car
analogous to Snell's law? If I think of the axle as a wavefront, it
turns for what seems like the same basic reason as light does, namely
different points along the same line are traveling at different

According to the PSSC version of Newton's corpuscular model, light
particles bend in the same direction as predicted by Snell's law, the
explanation being that attractive forces in the interface between the
less optically dense medium and the more dense medium cause the normal
component of the velocity of the corpuscles to be greater after they
have passed into the more dense medium, while the tangential component
of velocity (and momentum) remains the same.

But does "attractive forces in the interface" mean "surface tension"?
In that case, I still don't see why the object should bend toward the
normal. If the idea is that the object is pulled toward the interface
as it approaches it, shouldn't it also be pulled back as it recedes
from it upon transmission? Kind of like crossing on a skateboard from
a flat, down a half-pipe, and back up to the *same* flat (assuming
the action is purely in the interface)?

A little right triangle
for a velocity diagram shows that sin(theta1)/sin(theta2)=v(2)/v(1),
where 1 refers to the medium of the incident corpuscles and 2 to that
of the refracted corpuscles. If medium 1 is vacuum,
sin(theta1)/sin(theta2)=v(2)/c. Thus the index of refraction is
n=v(2)/c, just the reciprocal of the value
according to the wave theory.

Ah, that's what was opposite in Newton's theory, thanks for the

Although Roemer had estimated the speed of
light in vacuum (outer space) in 1676, the direct measurement of the
speed of light in a medium such as water had to wait until the middle
of the nineteenth century. So there was no way to decide on the
basis of
which speed was greater in Newton's day. (I think Carl's assertion is
correct once it is known that light travels slower in the more dense


PSSC models corpuscles going from a less dense medium to a more dense
medium with a rolling ball moving on a higher horizontal to a lower
horizontal surface, the surfaces connected by a ramp. (The direction
could be reversed to model a corpuscle going from a more dense to a
dense medium.)

This is not the same as the attractive force being only in the
interface. In fact, it relies on a uniform gravitational field in
both media. Shut off gravity and this model no longer works. (The
problem now is how to keep the ball in contact with the surface.
Okay, replace the surfaces with an S-shaped tube in deep space.)

In modern terms, I think the essential point in the rolling ball
analogy to the Descartes-Newton model of refraction is a gravitational
potential difference between the two media represented by the horizontal
planes. The gravitational force only changes the speed of the ball
when it is in the interface (on the ramp). Using a conservative force
field to model the refraction is nice , because it works in both
directions as has been pointed out. The experiment wouldn't work in
outer space even if the ball were constrained to move along an
S-shaped (cross-section?) tube, because there would be no potential
energy difference or force to change the speed of the particles.

Had Descartes and Newton lived in modern times, I think they would
have interpreted the force that
"shoved" (or resisted) the corpuscles across the interface would be
the negative gradient of some kind of conservative potential. I can't
speculate on what kind of field this might have been, since I don't know
the nature of their corpuscles (not photons.) Besides, the corpuscular
hypothesis had to be abandoned, because experiment showed it to be

I am not bothered by the uniform gravitational field throughout the
entire apparatus. About thirty -five years ago, I saw a large -1/r
shaped bowl into which a ball bearing was thrown to simulate the orbit
of a satellite (or planet). I believe this was in a space exhibit at
the IBM building in New York. The actual gravitational field was
essentially uniform over the dimensions of the apparatus. However,
they were modeling motion in a central inverse-square force field --
gravity in this case.

In principle, it would be possible to model refraction of particles
with a beam of electrons, causing them to enter an "interface" in
which there is a uniform electric field. It might be difficult to
model the media on either side of the interface.

There are photographs of this in Chapter 14 of the 2nd ed. of _PSSC
Physics_ and Chapter 5 of _College Physics, Physical Science Study
Committee_. This is actually a basis for a PSSC experiment, "The
'Refraction" of Particles" to see if they change direction according to
Snell's law. It is in the PSSC _Laboratory Guide_ at least through the
4th ed. I could not find the corpuscular model of refraction in either
the text or lab guide for the latest (7th) edition from around 1991.

I would like to see such photos. Maybe I can track down one of these
references. Did they smooth off the sharp corners getting onto and
off of the ramp?

From what I can see of the pictures, the corners do not appear to be
rounded off. The ramp seems to be rather steep so that the interface
is narrow. Ball bearings were used for the "corpuscles." The apparatus
was actually manufactured for student use in PSSC experiments. I
recall doing this experiment as a TA at FSU and later while teaching
PSSC Physics. One of the FSU professors designed apparatus for PSSC
labs such as the angular momentum experiment for the Advanced Topics.
The PSSC refraction of particles apparatus is still listed at science
education supply houses such as Science Kit and Boreal Laboratories
(equipment for the 6th ed. of PSSC, so refraction of particles must
have survived through that edition.) There may be some of this type of
apparatus lying around at schools that once used PSSC.

I've always associated the question of changes in direction in terms
of a boundary, not in terms of the actualy media, at least for

For example, consider a golf ball rolling (without friction) at a
steady speed on a level surface. Now suppose the ball obliquely
hits a ramp to a higher, but also level surface. Once it reaches
the top surface, it will be a) travelling at a slower, steady speed,
and b) heading farther away from the normal. The higher the ramp
and the slower the ball is going at the end, the more it bends. If
the ramp is high enough, you observe "total external reflection".

This is the opposite of how waves behave. (Tim F)

As Hugh points out, this depends on which side of the ramp you
associate with which medium.

According to Eugene Hecht's _Optics_, 4th ed., p. 141, the
derivation of
Snell's law on the basis of Newton's corpuscular law [ I meant
"model."] was actually first
published by Rene' Descartes in 1637. Hecht gives a modern, quantum
mechanics version of this for photons which he regards as being "a bit
simplistic," but of some pedagogical value. Equating the tangential
components of the momenta of the incident and refracted photons as
Descartes did for Newtonian corpuscles,
p(1)*sin(theta1)=p(2)*sin(theta2). Recognizing that the momentum of a
photon is p=h/lambda, this becomes

[h/lambda1]*sin(theta1)=[h/lambda2]*sin(theta2) .

Multiplying through by c/f, where f is the frequency, and using
f*lambda=v, one gets


or sin(theta1)/sin(theta2)=v(1)/v(2), the correct result (upside down
from the Newton-Decartes result.) Thus

sin(theta1)/sin(theta2)=n(2)/n(1) where the index of refraction is
defined as in the wave theory (n=c/v).

According to Hecht, the fact that light travels slower in the denser
medium was probably first inferred from experiment by Thomas Young in
1802, from the fact that the measured wavelength was shorter in the
optically dense medium -- before the definitive experiments of Foucault
in 1850 (with a rotating mirror and a long column of water.) (Hugh

Hugh Logan
Flagler Beach, FL
(where one has to do physics near the eye of a hurricane and wait
twenty hours for
power to return.)