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# Re: bending of object thrown into pool

According to Eugene Hecht's _Optics_, 4th ed., p. 141, the derivation of
Snell's law on the basis of Newton's corpuscular law was actually first
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

[h/v(1)]*sin(theta1)=[h/v(2)]*sin(theta2)

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).

This latter "derivation" was first pointed out to me by my major
professor, Dr. Earle K. Plyler of FSU, in connection with some ideas he
had about photons -- in 1965, before I saw it in any text.

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 more
optically dense medium -- before the definitive experiments of Foucault
in 1850 (with a rotating mirror and a long column of water.)

Hugh Logan

Hugh Logan wrote:

Carl E. Mungan wrote:

I have a dim memory that Newton once argued from his corpuscular view
that light particles should bend *opposite* to the wave prediction of
Snell's law. If someone remembers why that should be so, I'd be
grateful for a primer on the subject.

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. A little right triangle
trigonometry
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. 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
medium.)