Download Exam 3 with Answer Key | Waves | PHYS 123 and more Exams Physics in PDF only on Docsity!
last first
I. Ray optics [10 pts.]
1. [3 pts.] An experimenter is using parallax to locate objects on a table with one eye and a finger. In the two pictures below, the experimenter first sees the image at left. Then he moves his head to the right, without moving his finger , and sees the second image.
Which diagram below represents the correct ordering of objects and finger, as would be seen from above the experimenter, looking down?
Finger:
Finger: Finger:
Finger:
Finger:
A B C D E
2. [4 pts.] An object at left makes an image at right via an unknown mirror, as shown below. The distance between the object and the center of the mirror is 20 cm. What type of mirror with what radius of curvature R could create the image shown? The drawing below is to scale (distances and image/object heights are proportionally correct).
VERTEX of MIRROR OBJECT
IMAGE
A. Convex, R 20 cm B. Convex, R 10 cm C. Concave, R 10 cm
D. Concave, R 20 cm E. Convex, R 20 cm
last first
of Slit Screen
Y
Magnified View
Light P Q
I. Ray optics, continued
3. [3 pts.] An experiment is setup with an optical bench as shown below. Rays are drawn to locate the image of the lamp made by the flat side of the three sided mirror. Which of the labeled dots is closest to the image position?
Source
White Light
Slit plate
3−sided mirror
Lamp location
Paper
A
B
C
D
E
II. Diffraction & Interference, A. Light passes through a single slit of width a and strikes a screen, producing a varying intensity. At a certain point (Y) on the screen, light from a point at one side of the slit (P) and light from a point at the other side (Q) are out of phase by exactly one-half wavelength so that they cancel.
4. (5 pts) Which choice best represents the intensity on the screen at point Y for this situation? (Assume that the maximum central intensity for this case is 1 unit).
A. Zero B.
2
C.
2
D.
2
E. None of these / need more information
last first
E 4
E 3
E 2
E 1
III. Quantization, B. Electrons in Atoms
8. (4 pts) The diagram shows the first four energy levels in a Bohr model of a single-electron atom. Consider all possible transitions between only these four levels, involving both absorption and emission of photons. What is the maximum number of different energy changes an electron could experience in moving between these levels?
A. Three B. Four C. Six D. Twelve E. None of these is correct.
9. (5 pts) Which choice best represents the energy released as an electron jumps from the n = 3 level to the n = 2 level in the Bohr model for the Hydrogen atom?
A. 12. 1 eV. B. 3. 40 eV. C. 1. 89 eV. D. 1. 51 eV. E. None of these / not possible.
10. (4 pts) Which choice best represents the number of distinct quantum numbers necessary to describe the behavior of the electron in an excited state of the Hydrogen atom?
A. Four B. Three. C. Two. D. Only one is required for each electron. E. There can be many quantum numbers for each electron.
last first
IV. Relative Motion Observer O sets up two identical blinkers (flashing lights) at rest, the first (#1) at position x = -100 m, y = z = 0.0 m, and the second (#2) at x = +200 m, y = z = 0 m. The blinkers are wired to flash in phase once each second according to observer O. Observer P moves along the x-axis with constant velocity v = +0. 8c relative to O.
11. (4 pts) Which choice best represents the distance between the two blinkers as measured by observer P?
120 m 180 m 240 m 500 m Need more Information A B C D E
12. (5 pts) Which choice best represents the elapsed time between consecutive flashes from blinker #2 as measured by observer P?
0. 6 s 1. 0 s 2. 5 s 1. 7 s Need more Information A B C D E
13. (4 pts) Which of the following statements will both observers O and P agree on?
A. The speed of light from each blinker is 3. 0 x 10 8 m/s. B. The two blinkers are separated by the same distance x. C. The two blinkers flash simultaneously (in phase). D. Both A and C. E. Both B and C.
x , m
y , m
z , m
-100 O +100 +
P 0. 80 c 1 2
Name ______________________________________ Student ID _______________ Score______ __ last first
Physics 123X, Spring 2012 Exam 3 WO-UWA123X122T-E3(MSI,SSD)sol.doc
VI. [20 points total] This page consists of two unrelated parts, A and B.
A. Monochromatic light is normally incident on two very narrow slits (1 and 2) separated by a distance d. The slits are narrow enough to model as point sources of light. Points X and Y mark a minimum and a maximum, respectively on the distant screen. Slit 3 is added a distance d /2 from the right slit, as shown below. i. [4 pts] On the close-up view:
- Draw three rays from the slits to a single arbitrary point to the right of the center of the distant screen.
- Indicate the extra distance ∆ D 2 , 3 that light must travel from slit 2 than from slit 3 to the point on the screen. [No explanation required.]
ii. [5 pts] Will the brightness at point Y increase, decrease, or remain the same? If there is not enough information to answer, describe what additional information is needed. Explain. For point Y, ∆D1,2 = λ since point Y is the first non-central maximum for two slits. For point Y, ∆D 2 , 3 = λ/2, since slits 2 and 3 are separated by half the distance as slits 1 and 2. Therefore, one may think of the light from slits 2 and 3 as undergoing complete destructive interference at point Y, leaving the light from slit 1. Thus, light from just one slit, rather than two in phase, is now incident at point Y, so the brightness decreases.
Slit 3 is removed. Two slits (4 and 5), identical to the others above, are added a distance d apart, as shown. The distance s is unknown. iii. [5 pts] After the additional slits are added, will the brightness at point X increase, decrease, or remain the same? If there is not enough information to answer, describe what additional information is needed. Explain. For point X, ∆D 1 , 2 = λ/2 since point X is the first minimum for two slits. The light from this pair of slits continues to undergo complete destructive interference after slits 4 and 5 are added. For point X, ∆D 4 , 5 = λ/2 since they are separated by the same distance d as slits 1 and 2. Thus, light from this pair undergoes complete destructive interference as well. Therefore, the brightness at point X will remain the same.
B. [6 pts] Monochromatic light is normally incident on a single slit of width a. Point Z (not shown) marks the location of the first diffraction minimum to the right of the central maximum on a very distance screen. The entire apparatus is now submerged in a liquid with index of refraction of 1.5 ( i.e., v liquid = c /1.5.) After this change, will point Z remain a diffraction minimum? If there is not enough information to answer, describe what additional information is needed. Explain. Since point Z is the first diffraction minimum, the angle θZ from the center of the screen to this point may be found using a sinθZ = λorig. The original and new wavelengths are related to the propagation speeds and the frequency by λorig f = c and λnew f = vliquid, respectively. Using vliquid = c/1.5 yields λorig = 1.5 λnew. Therefore, after this change the angle θZ may be found by a sinθZ = 1.5 λnew, which does not describe a diffraction minimum. Therefore, point Z is no longer a point of zero intensity.
X Y
Center of screen
Distant screen with slits 1 and 2
d (^) d / Close-up of slits Slit 3 added
1 2 3 d d / Close-up of slits Slit 3 added
1 2 3
∆ D2,
d
s
Slits 4 and 5 added Distance s is unknown
1 4 2 5
λ/2 λ/
