Problem 1 [5 Points Each; No Partial Credit] NAME: ________________________
Please clearly indicate your answer by circling the letter (a), (b), (c), etc., of the choice
you make.
1.1 Polarizers P1 and P3 are aligned so that no light passing through P1 gets through P3.
Polarizer P2 is then inserted between P1 and P3. Which one of the following is true?
(a) Irrespective of how P2 is oriented, no light gets through P3.
(b) Irrespective of how P2 is oriented, some light will get through P3.
(c) Whether light will get through P3 or not depends on the orientation of P2.
1.2 A wave is represented by the expression y(x) = Acos(kx - t), where both k and  are
positive. This wave
(a) Moves “to the left” (towards lower x) with speed /k
(b) Moves “to the right” (towards higher x) with speed /k
(c) Is a standing wave that moves neither to the left or right
(d) None of these
1.3 [This was a lens problem and so I deleted it]
1.4 [This was also a lens problem]
1.5 A beam of light passes through a microscope slide. The surfaces of the glass slide are
perfectly parallel, and the light is incident on the slide at 30o. What can you say about the
beam after it exits the slide, relative to the beam before it enters the slide?
(a) The exiting beam continues on as if the slide weren’t there.
(b) The exiting beam continues in the same direction as the entering beam, but is
offset slightly.
(c) The exiting beam continues in a direction different to that of the entering beam.
Problem 2 [25 Points]
A steel wire has a cross-sectional area of 0.02 cm2. The density of the steel in the wire is
6 g/cm3, and it is held with a tension of 10N.
(a) What is the speed of propagation of traveling waves along the wire?
(b) If a 2m section of the wire is fixed a both ends, with the same tension, what are
the frequencies of the fundamental mode and the first harmonic?
(c) If instead one end of the wire were allowed to travel freely up and down, what
would the frequency of the fundamental and first harmonic be? Assume that the
tension is maintained at 10N.
Problem 3 [25 points] {don’t forget to include surface area of sphere, and that
intensity is proportional to amplitude squared?}
A stereo speaker puts out a pure tone, i.e., a tone with a single frequency, with a power of
30W.
(a) What is the intensity, in W/m, heard by someone listening to this tone at a
distance of 5m from the speaker?
(b) Express the same intensity in dB.
(c) A second speaker, also 5m from the listener, is set up, and emits a tone with
identical frequency and power to that of the first speaker. The frequency is
adjusted so that the sound waves from the two speakers are exactly in phase, i.e.,
they add together so that the amplitude of the combined sound wave reaching the
listener is exactly doubled. By how many decibels does the sound heard by the
listener increase?
(d) Instead, a second speaker, also 5m from the listener, is set up, and emits a tone
with identical frequency and power to that of the first speaker. The frequency is
adjusted so that the sound waves from the two speakers are exactly out of phase,
i.e., they add together so that the amplitude of the combined sound wave reaching
the listener is exactly 0 W/m. The power of the second speaker is then reduced
from 30W to 15W. By how many decibels does the sound heard by the listener
decrease relative to what she heard in part (a)?
Problem 4 [25 Points]
A light ray enters a 45o prism with an incident angle of 30o (see first diagram). The prism
is made of glass with and index of refraction of n=1.5.
(a) At what angle, relative to the normal of the surface at which it enters, does the ray
travel inside the material of the prism?
(b) At what angle, relative to the normal of the surface at which it exits, does the ray
travel upon leaving the prism?
(c) What would your answer to part (b) be if the light came in from the other side of
the perpendicular (see second diagram)?
45
30
45
30
Diagram I
Diagram II