### Spring 2009 Physics 102 Hour Exam 2(28 questions)

The grading button and a description of the scoring criteria are at the bottom of this page. Basic questions are marked by a single star *. More difficult questions are marked by two stars **. The most challenging questions are marked by three stars ***.

True-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 147. The exam period was 90 minutes; the mean score was 99.3; the median was 100. Click here to see page1 page2 page3 of the formula sheet that came with the exam.

• A reminder about prefixes: p (pico) = 10-12; n (nano) = 10-9; μ (micro) = 10-6; m (milli) = 10-3; k (kilo) = 10+3; M or Meg (mega) = 10+6; G or Gig (giga) = 10+9.

### QUESTION 1*

This and the next three questions pertain to the following situation.

Consider this L-R-C circuit. E(t) is given in volts and t is in seconds.

What is the phase angle Φ between the current and the AC source in the circuit?

(a)   -73.8°
(b)   -24.3°
(c)   +54.3°
(d)   +61.2°
(e)   +73.8°

### QUESTION 2***

When the generator voltage is at a maximum, what is the instantaneous voltage across the capacitor?

(a)   -12.9 V
(b)   0.00 V
(c)   80.0 V
(d)   89.2 V
(e)   92.9 V

### QUESTION 3**

What is the average power dissipated by the circuit?

(a)   4.97 W
(b)   14.2 W
(c)   17.8 W
(d)   24.2 W
(e)   35.7 W

### QUESTION 4**

If the frequency is changed so that the circuit is now at resonance, what is the power dissipated by the circuit?

(a)   17.8 W
(b)   35.7 W
(c)   50.0 W
(d)   64.0 W
(e)   128.0 W

### QUESTION 5*

A series RLC circuit is used in a radio to tune to an FM station broadcasting at 103.7 MHz. The resistance in the circuit is 10 Ω and the inductance is 2.0 μH. What is the best estimate of the capacitance that should be used?

(a)   210 pF
(b)   57 pF
(c)   1.2 pF
(d)   0.24 pF
(e)   0.019 pF

### QUESTION 6*

This and the next question pertain to the following situation.

An inductor, a resistor, and a capacitor are all in series with a voltage generator which outputs a signal V(t) = V0sin(2π f t).

Which one of the following actions will decrease the total impedance Z of this circuit, given that the voltage signal has frequency equal to the resonant frequency of the circuit, and assuming all other quantities remain constant?

(a)   decreasing the frequency f of the voltage signal
(b)   decreasing the resistance R
(c)   decreasing the inductance L
(d)   decreasing the maximum voltage V0
(e)   decreasing the capacitance C

### QUESTION 7**

Still assuming the circuit is being driven at its resonant frequency, which one of the following statements about the average power P dissipated in the circuit relative to the rms current Irms in the circuit and the rms generator voltage Vrms is true?

(a)   P  <  Irms Vrms
(b)   P  =  Irms Vrms
(c)   P  >  Irms Vrms

### QUESTION 8**

A white screen is set up 10 meters in front of a converging lens with a refractive power of 0.2 diopters. How far behind the lens must you stand so that your image is focused on the screen, and will your image be upright or inverted?

(a)   5 m behind, upright image
(b)   10 m behind, upright image
(c)   20 m behind, upright image
(d)   10 m behind, inverted image
(e)   5 m behind, inverted image

### QUESTION 9*

A man stands in front of a mirror. He has normal vision (near point = 26 cm). How close can he stand to the mirror and still see himself in focus?

(a)   13 cm
(b)   26 cm
(c)   52 cm

### QUESTION 10*

A green laser emits light at a wavelength of 532 nm. What is the frequency of the emitted light? (Recall that the speed of light is 3 × 108 m/s.)

(a)   5.6 × 107Hz
(b)   5.6 × 1014Hz
(c)   1016 Hz
(d)   2.8 × 1018 Hz
(e)   5.6 × 1018 Hz

### QUESTION 11**

In an RLC circuit at resonance, the voltage across the capacitor

(a)   is in phase with the voltage across the inductor.
(b)   is out of phase with the voltage across the inductor by 180°.
(c)   is in phase with the voltage from the generator.
(d)   is out of phase with the voltage from the generator by 180°.
(e)   is in phase with both the voltage across the inductor and the generator.

### QUESTION 12**

Light passes from one medium (in which the speed of light is v1) into another (in which the speed of light is v2). If v1 < v2, as the light crosses the boundary,

(a)   both frequency and wavelength increase.
(b)   neither frequency nor wavelength changes.
(c)   frequency increases, wavelength decreases.
(d)   frequency does not change, wavelength increases.
(e)   frequency decreases, wavelength stays the same.

### QUESTION 13**

A person using lens as a simple magnifying glass sees an

(a)   inverted virtual magnified image.
(b)   inverted real magnified image.
(c)   upright virtual magnified image.
(d)   upright real magnified image.
(e)   real virtual magnified image.

### QUESTION 14*

This and the next question are conceptually related.

To transmit an electromagnetic field from one place to another, we have a long hollow tube with a square cross section, 10 cm by 10 cm. The tube confines the electromagnetic field to the inside of the tube, but other than this the transmitted field has the exact same properties as an infinite plane wave. If the electric field has an rms value of 3000 N/C, what is the rms value of the magnetic field?

(a)   2 × 10-5 T
(b)   1 × 10-5 T
(c)   1 × 10-6 T
(d)   5 × 10-6 T
(e)   7 × 10-6 T

### QUESTION 15**

What is the rate at which energy is being transmitted through the tube?

(a)   60 J/s
(b)   239 J/s
(c)   1190000 J/s

### QUESTION 16***

This and the next question pertain to the following situation.

A movable object is placed in front of a diverging lens with focal length f = -10 cm. At time t = 0, the object is at position x = 15 cm from the lens and its velocity is 20 m/s.

Which one of the following statement is true regarding the motion of its image (real or virtual) at t = 0?

(a)   It moves faster than the object itself.
(b)   It moves slower than the object itself.
(c)   They are moving at the same velocity.

### QUESTION 17*

After a certain amount of time, the object has moved to the position x = 5 cm from the lens on the same side. Which one of the following statements is true?

(a)   The image is virtual; on the same side of the lens as the object.
(b)   The image is virtual; on the other side of the lens from the object.
(c)   The image is real; on the other side of the lens from the object.

### QUESTION 18**

A double slit experiment is set up using monochromatic light (frequency f = 6.0 × 1014 Hz). The screen is 2.1 m from the slits. You observe that the distance from the central fringe to the 2nd bright fringe is 2 cm. What is the spacing d between the slits?

(a)   0.025 mm
(b)   0.050 mm
(c)   0.075 mm
(d)   0.100 mm
(e)   0.125 mm

### QUESTION 19*

Unpolarized light shines through two linear polarizers as shown in the diagram below. If the final intensity is 10% of the initial, at what angle is the transmission axis of the second polarizer?

(a)   21°
(b)   46°
(c)   63°
(d)   71°
(e)   81°

### QUESTION 20**

If the intensity of a beam of light is quadrupled (increased 4 times), the value of ERMS will

(a)   increase by a factor of 2.
(b)   increase by a factor of 4.
(c)   decrease by a factor of 2.
(d)   decrease by a factor of 4.
(e)   remain the same.

### QUESTION 21*

Which one of the following is a possible trajectory of light? Recall that the index of refraction of glass is larger than that of air.

(a)   A
(b)   B
(c)   C
(d)   D
(e)   all of the above

### QUESTION 22**

A material has an index of refraction that increases continuously from top to bottom. Which of the following trajectories will the light follow?

(a)   A
(b)   B
(c)   C

### QUESTION 23**

This and the next question pertain to the following situation.

A young boy is preparing to blow a soap bubble from a wand, when he notices that there is a "rainbow" in the soap film. There is constructive interference of reflected light of wavelength 530 nm. If the index of refraction of the soap solution is 1.4, what is the minimum thickness of the soap film?

(a)   50 nm
(b)   95 nm
(c)   190 nm
(d)   285 nm
(e)   380 nm

### QUESTION 24**

If some of the soap dripped off, so that the film was half as thick as before, the light would interfere:

(a)   completely constructively
(b)   completely destructively
(c)   neither of the above

### QUESTION 25**

Two radio stations emit radio waves of wavelength 10 m in phase. The second tower is 300 m north of the first tower. If you are standing 5 km west of the center of the two radio stations, how far north must you walk to find no radio signal (the first such area)?

(a)   52.6 m
(b)   83.3 m
(c)   132.1 m
(d)   166.6 m
(e)   213.0 m

### QUESTION 26***

Consider a ray of unpolarized sunlight incident on water-air surface at Brewster's angle (index of refraction of air is 1, of water is 1.3).

An observer sees the light through a linear polarizer that is held so that the axis of transmission lies in the plane of incidence, as shown in the figure. What is the intensity of the reflected light as seen by the observer if the incident intensity is I0?

(a)   0
(b)   ¼ I0
(c)   ½ I0
(d)   ¾ I0
(e)   I0

### QUESTION 27**

The human eye can be treated as a simple optical system with the iris acting as aperture of the system. The iris of the human eyes can open from 2 mm to 8 mm. Consider the situation in which a car is approaching a person at night. The headlights of the car are 1 m apart from each other, and we can assume the light emitted from the headlights to be yellow (l = 590 nm). What is the farthest distance between the person and the car that he can tell the 2 headlights of the car apart?

(a)   2.7 km
(b)   5.4 km
(c)   8.0 km
(d)   11.1 km
(e)   120 km

### QUESTION 28**

An object is located in front of a convex mirror as shown, with the center of curvature C and focal point F indicated

The image is formed at location:

(a)   #1
(b)   #2
(c)   #3
(d)   #4
(e)   #5

Scoring of True-False (T,F) Questions:
• If you mark the correct answer, you get 2 points.
• If you mark the wrong answer or if you mark neither answer, you get 0 points.
Scoring of Multiple Choice I (a,b,c) Questions:
• If you mark the correct answer, you get 3 points.
• If you mark a wrong answer or if you mark none of the answers, you get 0 points.
Scoring of Multiple Choice II (a,b,c,d,e) Questions:
• If you mark one answer and it is the correct answer, you get 6 points.
• If you mark two answers and one of them is the correct answer, you get 3 points.
• If you mark three answers and one of them is the correct answer, you get 2 points.
• If you do not mark the correct answer, or if you mark more than three answers, or if you mark none of the answers, you get 0 points.