Spring 2007 Physics 102 Hour Exam 3(27 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 107. The exam period was 90 minutes; the mean was 63.7; the median was 64. Click here to see page1 page2 of the formula sheet that came with the exam.

• A physics 102 light bulb acts just like a resistor: its resistance is constant, independent of the current flowing through the light bulb. The bulb's brightness increases with increasing current.
• 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***

In the LRC circuit shown in the following diagram, the voltage generator operates at frequency ω0 = 2πf0 = 1/sqrt(LC).

Which one of the following phasor diagrams can correctly represent the voltages across the inductor, resistor, and capacitor at some particular time t > 0 ?

(a)
(b)
(c)
(d)
(e)

QUESTION 2**

An electromagnetic wave travels through space. A device that measures the wave's electric and magnetic fields at one point in space and at one instant of time finds them oriented as shown in the diagram at right.

Which one of the arrows below best indicates the direction in which the wave is traveling as it passes through this point in space?

(a)
(b)
(c)

QUESTION 3*

High frequency electromagnetic waves travel through empty space at slower speed than do low frequency electromagnetic waves.

(T)   True
(F)   False

QUESTION 4*

Which one of the following statements is correct?

(a)   In an electromagnetic wave the oscillations of the electric field differ in phase from the oscillations of the magnetic field by 1/4 cycle.

(b)   An electromagnetic wave is a transverse wave because the electric and magnetic field are both perpendicular to the wave's direction of travel.

(c)   Light from a distant star found to be moving away from the Earth at half the speed of light is Doppler shifted towards shorter wavelengths when viewed from the Earth.

QUESTION 5*

An electromagnetic wave traveling in space is found to have a maximum magnetic field of 0.1 T. What is the value of the maximum electric field to be found in this electromagnetic wave?

(a)   3.33 × 10-10 V/m
(b)   0.1 V/m
(c)   30 MV/m

QUESTION 6**

A newly discovered comet is exposed to sunlight with an rms intensity of 100 kW/m2 at the point in its orbit where it is closest to the sun. What is the rms value of the electric field of the electromagnetic radiation striking the comet at this point in its orbit?

(a)   Erms = 377 V/m
(b)   Erms = 8.99 MV/m
(c)   Erms = 120 V/m
(d)   Erms = 5.37 kV/m
(e)   Erms = 6.13 kV/m

QUESTION 7*

Which one of the following statements is correct?

(a)   In an electromagnetic wave the energy density of the magnetic field cancels the energy density of the magnetic field so that the net energy density in any electromagnetic wave is zero.

(b)   The relationship between the energy density uB of the magnetic field in an electromagnetic wave and the energy density uE of the electric field is uB = c2uE.

(c)   The average energy density in an electromagnetic wave whose electric and magnetic fields vary sinusoidally with time depends on the amplitudes of the wave's electric and magnetic fields but not on the fields' oscillation frequency.

QUESTION 8**

Two different stacks of polarizing filters are constructed, as shown in the following figure. The angle between each filter's transmission axis and the x axis is indicated in the figure. In the four-filter stack the transmission axis of each successive filter is rotated by -30° relative to the previous filter. In the seven-filter stack the transmission axis of each successive filter is rotated by -15° relative to the previous filter. The filters are placed so their centers lie along a line parallel to the z axis. A beam of unpolarized light of intensity I0 traveling parallel to the z axis strikes the first filter.

If the intensity of light leaving the last filter in the four-filter stack is Ifour and the intensity of light leaving the last filter in the seven-filter stack is Iseven what is the ratio Ifour / Iseven?

(a)   Ifour / Iseven = 0.51
(b)   Ifour / Iseven = 0.64
(c)   Ifour / Iseven = 0.80
(d)   Ifour / Iseven = 1.00
(e)   Ifour / Iseven is undefined since it is 0/0

QUESTION 9**

Three mirrors, an object (represented by the star) and an observer (represented by the circle with an inscribed cross) are positioned as shown in the figure.

How many reflected images of the object are visible to the observer?

(a)   one
(b)   two
(c)   three

QUESTION 10**

The inner surface of a hollow metal sphere 5 m in radius is highly polished so that it acts like a concave mirror. The center of the sphere is located at the origin of an (x,y) coordinate system. The sphere contains an arc lamp and a match, positioned along the x axis at distances darc and dmatch from the origin as shown in the figure. When positioned correctly inside the sphere, light from the arc light reflected from the inside of the sphere will ignite the match.

Which one of the following pairs of values of darc and dmatch will ignite the match most rapidly?

(a)   darc = 5.00, dmatch = 5.00
(b)   darc = 3.14, dmatch = 3.14
(c)   darc = 2.50, dmatch = 2.50

QUESTION 11***

The great Italian astronomer/physicist Galileo Galilei (1564-1642) invented a type of telescope that consists of one divergent lens and one convergent lens, as shown in the figure below. In a typical design, the focal length of the divergent lens is f1 = -5cm, and that of the convergent lens is f2 = 100cm. Incoming light rays from a distant object are parallel to each other and the principal axis at the convergent lens.

What distance must separate the two lenses so that the rays out of the divergent lens are parallel?

(a)   20 cm
(b)   52.5 cm
(c)   95 cm
(d)   105 cm
(e)   500 cm

QUESTION 12***

Light from a car headlight is aimed onto the surface of a water puddle. As shown in the figure, the light is polarized vertically. At what angle θ relative to the puddle surface must the light be aimed such that there is no reflection off the puddle? The index of refraction of air is nair = 1, and that of water is nwater = 1.33.

The angle θ is:

(a)   48.8°
(b)   41.2°
(c)   20.6°
(d)   53.1°
(e)   36.9°

QUESTION 13**

This and the next two questions concern the following situation:

A ray of white light passes through a glass prism, dispersing into the colors of the rainbow. The index of refraction of the prism nglass = 1.33 at the wavelength of red light.

Calculate the angle the red ray of light makes relative to the incoming beam.

(a)   70.1°
(b)   45.0°
(c)   32.1°
(d)   25.1°
(e)   12.9°

QUESTION 14**

The blue ray of light is refracted as shown in the figure. How does the prism's index of refraction for red light compare to that for blue light?

(a)   nred < nblue
(b)   nred > nblue

QUESTION 15**

What would the prism's index of refraction have to be so that the red ray is totally internally reflected?

(a)   less than 1.33
(b)   1.414 or greater
(c)   The light can never be internally reflected.

QUESTION 16**

This and the next question concern the following situation:

A magnifying glass is used to read the fine print on a document. The focal length of the lens is f = 10 mm.

At what distance from the lens must the document be held in order to obtain an image magnified by 5 that is NOT inverted?

(a)   1.7 mm
(b)   8 mm
(c)   12 mm
(d)   40 mm
(e)   60 mm

QUESTION 17*

Is the image real or virtual?

(a)   real
(b)   virtual

QUESTION 18***

This and the next question concern the following situation:

We learned in class that mirrors can be used to focus light. The same principle also applies to sound.

You are eavesdropping on your neighbor's conversation using a concave spy dish of focal length f = 50 cm to focus his voice onto a microphone. As shown in the figure, the neighbor is 20 m away from the dish, and his mouth is 1.7 m above the ground. The center of the dish is at a height of 1m from the ground. Ignore any effects from interference.

You're adjusting the distance between the microphone and the dish. At what height from the ground should you ideally place the microphone?

(a)   104.4 cm
(b)   101.8 cm
(c)   100.0 cm
(d)   98.2 cm
(e)   95.6 cm

QUESTION 19***

Your neighbor walks toward you and your dish. In which direction should you move the microphone to continue to hear him best?

(a)   Move the microphone to the right and up.
(b)   Move the microphone to the right and down.
(c)   Keep the microphone where it is.
(d)   Move the microphone to the left and up.
(e)   Move the microphone to the left and down.

QUESTION 20*

This and the next two questions concern the following situation:

Light of 500 nm wavelength due to a light source far away is impingent on the slits from the left. The two slits are separated by 0.01 mm, and an interference pattern is formed on a screen placed a distance L from the slits. The first minimum of the interference pattern is found to be 10 cm above the center of the screen.

What is the distance L between the slits and the screen?

(a)   2.5 meter
(b)   4.0 meter
(c)   10 meter

QUESTION 21*

Now, let us turn off the 500 nm light source, and turn on another light source at the same location with a wavelength of 600 nm. How would the first minimum above the center of the screen move?

(a)   Move up by 2 cm.
(b)   Move up by 6 cm.
(c)   Move down by 2 cm.
(d)   Move down by 6 cm.
(e)   It does not move

QUESTION 22**

If both 600 nm and 500 nm light sources are turned on, would the 600 nm light form an interference pattern with the 500 nm light?

(a)   Yes
(b)   No

QUESTION 23*

This and the next question concern the following situation:

A thin layer of oil with index of refraction n1 = 1.45 is placed on top of a glass slab with index of refraction n2 = 1.5. Light with a wavelength of 532 nm is incident on the thin oil film (thickness t) nearly normal to the surface (note that deviation from the normal is exaggerated!). An observer is right above the film looking at the light reflected from the air-oil interface (labeled 1) and reflected from the oil-glass interface (labeled 2).

What is the minimal thickness t of the oil layer that would allow destructive interference between the reflections off the two interfaces?

(a)   91.7 nm
(b)   133 nm
(c)   183 nm
(d)   266 nm
(e)   532 nm

QUESTION 24**

For the thickness determined in the above problem, let us replace the glass slab with water with index of refraction n2 = 1.33. Would the observer see destructive or constructive interference?

(a)   constructive interference
(b)   destructive interference

QUESTION 25*

This and the next question concern the following situation:

These intensity distributions were observed from two different multiple slit devices illuminated by light of the same wavelength.

Which device has the larger number of slits?

(a)   A
(b)   B

QUESTION 26**

If the multiple slit devices that produce the interference patterns are completely immersed in water, how would the intensity distributions change?

(a)   The patterns would expand (larger spacing between peaks).
(b)   The patterns would compress (smaller spacing between peaks).
(c)   The patterns would not shift (same spacing) but will become sharper.

QUESTION 27**

You are trying to read the small print in a letter inviting you to sign up for a new credit card. One set of letters is written in blue and the other set in red. Except for the color difference, the two sets of letters are identical in text and font size. Which colored text would be easier to resolve? Remember that blue light has a shorter wavelength than red light.

(T)   True
(F)   False

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.