Activity based questions
1. Light in air is incident on the surface of a transparent substance at an angle of 58_ with
the normal. The reected and refracted rays are observed to be mutually perpendicular.
(a) What is the index of refraction of the transparent substance? Hint: Note that
sin (90_???? _) = cos _.
(b) What is the critical angle for the total internal reection in this substance?

2. A stationary naval destroyer is equipped with sonar that sends out 40 MHz pulses of
sound. The destroyer receives reected pulses back from a submarine directly below
with a time delay of 80 ms at a frequency of 39.959 MHz.
(a) What is the depth of the submarine?
(b) Based on the frequency shift, is the submarine ascending or descending?
(c) If the speed of sound in seawater is 1.54 km/s, then what is the vertical speed
of the submarine (remember that, since the pulse is reected, it's going to be
Doppler shifted twice!).

3. When electrons transition from one orbit to lower one, they emit a photon of a speci_c
frequency (and so a speci_ccolor). In one of these cases the electron jumps from the
third to second orbit, emitting a photon of frequency f = 4:57 _ 1014 Hz, which is in
the red region. In another case the electron jumps from the _fth orbit down to the
second, and emits a photon of frequency 6:91 _ 1014 Hz, which is in the blue region of
the spectrum. This light is then sent through a di_raction grating with 4500 lines/cm.
(a) What are the wavelengths of the two spectral lines?
(b) What is the distance between the slits in the grating?
(c) What is the angular separation, __, (in degrees) between the two m = 1 spectral
lines?
(d) What about for the m = 2 spectral lines?

4. Suppose you have two in_nite straight line charges, of charge per unit length _, a
distance d apart, moving along at a constant speed v. The moving charge densities
constitute a current I = _v, and so the charges behave like currentcarrying wires.
Because the wires carry the same charge density, _, they repel each other electrically.
But, because they are currentcarrying wires, with currents moving in the same di
rection, they attract each other magnetically. How great would v have to be in order
for the magnetic attraction to balance the electrical repulsion? Work out the actual
number... Is this a reasonable sort of speed? (Hint  use Gauss's law to get the electric
_eld, and Ampere's law to get the magnetic _eld of the wire. Then determine the force
per unit length from each _eld, Felec=L = _E, and Fmag=L = IB.)

5. The galactic magnetic _eld in some region of interstellar space has a magnitude of
1:00_10????9 T. A particle of dust has mass 10:0 _g and a total charge of 0:300 nC. How
many years does it take for the particle to complete a revolution of the circular orbit
caused by its interaction with the magnetic _eld? You can assume that the orbit is
perpendicular to the magnetic _eld.

6. Inchy, an inchworm, is inching along a cotton clothesline. The 5 meter long clothesline
has a mass of 0.2 kilograms, and is pulled tight under 100 N of tension. Vivian is
hanging up her swimsuit 0 meters from one end when she sees Inchy 2.54 cm (one inch)
from the opposite end. She plucks the clothesline sending a terrifying 3 centimeter high
wave pulse toward Inchy. If Inchy crawls at 1 inch per second, will he get to the end
of the clothesline before the pulse reaches him? If so, how much time does he have to
spare? If not, how far does he make it before the pulse kicks poor Inchy o_ the line?
(Note: don't forget that Inchy is running away from the pulse, so the time for it to
reach him is not just his distance divided by the wave velocity!)

Extra Credit Question!!
The following is worth 15 extra credit points!The _gure to the right shows the actual produc
tion of the antimatter partner to the electron,the positron, in a bubble chamber immersed in
a uniform magnetic _eld. The positron has exactly the same mass as an electron, but opposite
charge. The di_erent tracks show the trajectories of the di_erent particles. In the reaction at
the top, a highenergy gamma ray (just a highfrequency light wave) is absorbed by an electron,
which scatters away to the right, producing anelectronpositron pair though the reaction
+ e ! e???? + e+ + e????;where is the incident gamma ray. A similar effect occurs in the bottom
reaction, but the originalelectron very likely had littlenal velocity. Let'ssee what we can tell about
this reaction.
(a) Is charged conserved in this reaction? Explain.
(b) Why do the electrons and positrons curve in di_erent directions?
(c) In what direction (into or out of the page) is the magnetic _eld? How can you
tell?
(d) How does the velocity of the spiraling electron compare to that of the spiraling
positron? How can you tell?
(e) Accelerating charges radiate energy. Explain why this leads to the spiralingmo
tion for the particles.
(f) Positrons and electrons can come together and annihilate, releasing two photons
in the processe???? + e+ ! + :
Explain why we get two photons, and not one. Hint: consider the the two particles
initially at rest right next to each other.

A more colorful picture is seen to the right, wherethe positrons are shown in red, and the electrons
in green.
(a) Initially we have an electron and a photon. Sincethe photon isn't charged, the initial charge is justthat on the electron,????e. After the reaction, we'veproduced an electron and positron pair. The netcharge of the pair is????e+e = 0, and since we stillhave an electron the net charge after the reactionis????e, and so charge is conserved.
(b) The electrons and positrons are oppositelycharged, and so experience opposite forces in the
magnetic _eld. This leads to motion in di_erentdirections.
(c) The electron is curving in the counterclockwisedirection, while the positron is curving in the
clockwise direction. From the magnetic force law,~F = q~v _ ~B , for the positively charged positron
the velocity is down, and the force is initially tothe left, and so the direction of the magnetic _eld
is out of the page.
(d) The faster the speed of the particle, the biggerthe radius of the curve. Since the positron has a
bigger spiral, it has a bigger speed.
(e) As the charges radiate, they lose energy. The only place that they can lose itfrom is their kinetic energy, and so, they slow down. The slower they move, thesmaller the radius of their curvature. So, the curve tightens as they slow down,leading to the spiral.
(f) Suppose we had an electron and a positron at rest and just brought them together.
In this case the initial momentum is zero, but the photon carries momentum. So,
a single photon would violate momentum conservation. Two photons, emitted
backtoback, would conserve momentum. This means we need two photons.

Rating:
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Activity based questions