AJM:5/5/10 Score /100
Physics 235 Midterm Exam Spring 2010
Name
• Tim e limit: 55 minutes
• Please remove your hat and turn off and put away all commu nication devices.
• You may use one sheet of notes (8 ½ x 11, bo th sides). Please staple it to the back of this exam when you are finished.
• Perform all of your work on separate, b lank sheets of paper and staple this sh eet to the front.
• The credit you receiv e on each problem will depend more on how you get your answer than on what answer you get.
There is no need to be as “wordy” as I ask you to be on hom ework, but you must show your work or give at least a brief
explanation for how you obtain ever y answer. I give no credit for unsup ported answers even if correct. I do give
partial credit for par tially correct solutions, but only when I can determine that what you are doing is partially correct.
• M ake certain that all numerical answers are given with a reasonable number of significant digi ts (when in doubt, three is
usually a good compromise) and that you have included appropriate and simplified units.
• Check your answers for physical reasona bleness when possible; I do deduct a small number of points for plainly
ridiculous answers that you don’t comment on.
• Some potentially usefu l information:
c=3.00 !108 m/s
e=1.60 !10"19 C
h=6.63 !10"34 J #s
!c=197 eV !nm
e2
4
!"
o
=1.440 eV #nm
En=n2
!
2!2
2mL2
E2=p2c2+m2c4
!
*
!
!dx
"#
#
$=1
!z=z2"z2
1. Consider the pattern produced on a screen by monochro matic light of
wavelength 600 nm that is normally in cident on a triple slit. This arrangement
differs from the mor e standard situation only in that the middle slit is narrow er
than the other two and, therefore, produces light of ha lf the amplitude on the
screen (i.e., its associated phasor is half as long as those of the other two) on the
screen. The intens ity produced at the central maximum in the pattern on the
screen is
Io
and you may consider the slits to be narrow enough to permit
ignoring any “sing le slit” diffraction effects.
a) [5] Draw two phasor d iagrams that can be used to determine the ratio,
Imiddle slit /Io
, where
Imiddle slit !
the intensity produced on the screen wh en the two side slits are blocked.
b) [5] At the point on the screen as sociated with a “pa th difference” (see figure) of 300 nm (i.e.,
!
/ 2
), what is the
ratio
I/Io
? [Hint: Again, use a phasor diagram.]
Now consider the po int on the screen nearest to the central maximum where the intensity van ishes.
c) [5] Construct the phasor diagram associated with that point.
d) [10] What “path difference” is associated with tha t point?
2. Consider the wave function:
!
x
( )
=
Nx
L+i
"
#
$%
&
', 0 (x(L
0 , elsewhere
)
*
+
,
+
a) [8] Find the value of th e normalization constant N in terms o f L.
b) [4] Sketch a reasonably accurate plot of the probab ility density,
!
*
!
, as a function of x. Be sure to label and scale
your axes.
c) [10] Find the expectation value for the pos ition,
x
.
d) [3] Does your value for
x
make sense given your plot in part b? (Reminder: I give no credit for unsupported
answers.)
(Over for problems 3 and 4)
