PHIL 4120 Lecture Notes - Salva Veritate, Logical Truth, Empiricism

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15 Nov 2011

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W. v quine two dogmas of empiricism, on what there is [trained as a lp] Grice, strawson in defense of a dogma. Responding to the lp tradition every meaningful sentence is a truth of def. , or a sentence that can be true of false through observation of the world. Theoretical sentences (ex. electrons) can be defined through other things you can observe. Logical truth of empirical truth direct empirical truth or definable in terms of empirical truths. Could be such because of definitions, rules of language, subject terms of sentences, etc. Method is a priori (truth or false in advance of) True contingently, could be false in diff. circumstances. All you had to know if the meaning of the terms in them. Thought to be such because given their meanings they said they could be true in some situations and false in others.

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(1) Using Equation delta.d = 2do+ n glass d glass - d1 and Figure 1-3 and 1-4 located in theExperimental
Procedure, determine the speed of light assuming that the distancebetween
the transmitter-side mirror and the face of the corner-cube do is1.7m and the
distance between the two mirrors d1 is 4 em. (Note: The corner-cubeis
designed so that light always travels 6.7 em within the corner-cube- i.e.
dglass)). nglass=1.5
(2) Calculate the time-of-flight you expect for light to propagatea distance of 20
m in (a) vacuum and (b) a medium with an index of refraction n =1.5.
Express your answer in nanoseconds (ns).
(3) In telephone calls using a satellite, you sometimes can hear adelay in the
response of the other person. Satellites are usually either inlow-Earth orbit
Uust above the atmosphere) or much higher in geosynchronous orbit.The
latter is at an altitude of 35,785 kilometers (22,236 miles), wherethe satellite
completes one orbit in exactly one day. Because the orbitalvelocity matches
the spin rate of the Earth, a satellite in a circular equatorialgeosynchronous
orbit appears to hover motionless over a single location on theequator. The
total delay in hearing your correspondent's reply, due to thefinite speed of
light, is due to two round trips. If you and your correspondentwere located
nearby, and on the equator, the only distance involved is thedistance from
you to the satellite, the total distance corresponding to the delayis 4 x 35,785
km. Calculate this delay, assuming the radio signal travels at thespeed of
light in a vacuum. Report your answer in units of seconds, anddiscuss in one
sentence whether this delay is long enough for you to notice.Identify at least
one factor that could cause the actual delay to be longer than whatyou
calculated.

DUE DATE: 12 00 noon Monday. Dec 6. 2010. The problems on this assignment are quite word because strong direction is being given to Students in how to proceed. Two problems will be selected at random for marking. Percentage polarization. It is useful to characterize partially polarized light in terms of its "percentage polarization". A light beam of constant intensity Io. is allowed to fall at normal incidence on an "ideal linear polarizer" (a linear polarizer is "ideal" if it panes all light polarized parallel to the polarizer's axis, and stops all light polarized perpendicular to that axis.) As the ideal polarizer is rotated continuously (see Figure 8.1; about an axis perpendicular to its plane, the transmitted intensity I passes through successive maximum and minimum values (denoted by I max and I min). The percentage polarization of the incident light is denned to be Find the percentage polarization measured in this way for the following light beams: "Unpolarized natural light" tor which I max = I min = Io/2. A beam of light. Initially unpolarixed. that has been passed through an ideal linear polarizer before being measured for percentage polarization. A beam of light, initially unpolarizcd, that has been passed through a non-ideal polarizer that (in terms of light intensity) transmits 70% of light polarized parallel to its polarizing axis and 20% of light polarized perpendicular to its polarizing axis. Circularly polarized light. (Circular polarization means that at any given fixed observation point In the beam, the E-vector has constant magnitude but rotates at the frequency of the electric field oscillations so that the tip of the vector describes a circle in the zy plane (perpendicular to the light ray at the point in question). Elliptically polarized light for which the tip of the E-vector moves on an ellipse in the x y plane, defined by where Ax and Ay are the amplitudes of the oscillating Ex and E y components of the electric field vector, and is the phase difference between those oscillations. NOTE: Do your calculation for the special case Ax = 2Ay and e =pi / 2. [(8.2) taxes a particularly simple form when e = pi / 2.]

The emergence of line spectra from a gas when a current passesthrough it was an observed phenomenon waiting for an explanation inthe early 20th century. The atomic line spectra coming fromelements such as hydrogen had been analyzed since the late 19thcentury. By studying the wavelength of the emerging radiation ofhydrogen, experimenters found (often by trial and error) that thewavelengths in those spectra were described by the formula

\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2}\right),
where R is known as the Rydberg constant. It has a value of R =1.097 \times 10^{7}\; \rm m^{-1}. The variables n_1 and n_2 areinteger numbers (n_1 = 1,2,3,4,\dots). As experiments continued,scientists began to see more and more characteristic lines emergingfrom the hydrogen spectrum. Each of them corresponded to awavelength predicted by this formula with some integer values forn_1 and n_2.

In 1913, Niels Bohr provided an explanation for the observationsmade in experiments by proposing that each electron in an atom hadonly certain allowable energy levels. Furthermore, he postulatedthat when an electron changed its energy level, it must emit orabsorb a single photon with the energy equal to the energydifference between the two levels.

With this interpretation, the variables n_1 and n_2 acquired newsignificance. Bohr's model predicted that n_2 was the initialenergy state of the atom (n_initial) and that n_1 was the finalstate of the atom (n_final). A photon with the predicted wavelengthwas created when an atom made a transition from its initial energystate to a lower final energy state. The equation now read

\frac{1}{\lambda} = R \left( \frac{1}{n_{\rm final}^2} -\frac{1}{n_{\rm initial}^2} \right).
Bohr's model also predicted that a photon of the appropriatewavelength (given by the same formula) could promote an atom from alower energy level to a higher one.

In this problem, we explore the photon characteristics necessaryfor transitions between energy levels in hydrogen and singlyionized {\rm He}^+, whose energy levels are accurately predicted bythe Bohr model.
What is the change in energy DeltaE of the hydrogen atom as theelectron makes the transition from the n=3 energy level to the n=1energy level?
Express your answer numerically in electron volts.

b. When an atom makes a transition from a higher energy level to alower one, a photon is released. What is the wavelength of thephoton that is emitted from the atom during the transition from n=3to n=1?
Express your answer numerically in angstroms.

c.

When the hydrogen atom makes the transition from the n=2 to the n=1energy level, it emits a photon. This photon can be absorbed by toa singly ionized helium atom ({\rm He}^+) in its second energylevel (n_{\rm initial} = 2), causing it to move to a higher energylevel. To what final energy level number n_final can the photonpromote the helium ion?

Note that {\rm He}^+ has two protons in its nucleus and a singleelectron.
Express your answer as an integer.

Please answer fully, Thank you
a.

PHIL 4120 Lecture Notes - Salva Veritate, Logical Truth, Empiricism

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