### Spring 2008 Physics 102 Hour Exam 3(29 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 144. The exam period was 90 minutes; the mean was 110.7; the median was 114. Click here to see page1 page2 page3 of the formula sheet that came with the exam.

Some helpful information:
• 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 question concern the following situation:

The intensity of the sunlight that reaches Earth's atmosphere is approximately 1400 W/m2.

What is the average energy density u of the sunlight?

(a)   u = 8.1 × 10-9 J/m3
(b)   u = 4.7 × 10-6 J/m3
(c)   u = 4.7 × 10-3 J/m3
(d)   u = 9.0 × 103 J/m3
(e)   u = 5.8 × 106 J/m3

### QUESTION 2**

What is the rms value of the electric field Erms ?

(a)   Erms = 1.2 mV/m
(b)   Erms = 7.0 V/m
(c)   Erms = 730 V/m
(d)   Erms = 9.1 kV/m
(e)   Erms = 34000 kV/m

### QUESTION 3**

This and the next question concern the following situation:

Light linearly polarized in the x-direction shines through two polarizers. The first polarizer's transmission axis makes an angle θ with the x-axis and the transmission axis of the second is parallel to the y-axis.

If the incident light has intensity I0, what is the intensity of the light transmitted through the second sheet, I2,, for any θ ?

(a)   I2 = 0
(b)   I2 = I0 cos4θ
(c)   I2 = I0 cos2θ sin2θ
(d)   I2 = I0 sin4θ
(e)   I2 = I0

### QUESTION 4**

At what angle θ is the transmitted intensity I2 maximal?

(a)   I2 does not depend on θ.
(b)   θ = 0°
(c)   θ = 30°
(d)   θ = 45°
(e)   θ = 60°

### QUESTION 5*

Unpolarized light is incident on a system of three polarizers. The second polarizer is oriented at an angle of 30° with respect to the first and the third is oriented at an angle of 45° with respect to the first. The transmission axes of the second and third polarizers are rotated clockwise with respect to the first polarizer's transmission axis.

If the light that emerges from the system has an intensity of 23.0 W/m2, what is the intensity of the incident light I0 ?

(a)   I0 = 95.7 mW/m2
(b)   I0 = 65.7 W/m2
(c)   I0 = 96.4 W/m2
(d)   I0 = 15.7 kW/m2
(e)   I0 = 97.0 kW/m2

### QUESTION 6*

This and the next question concern the following situation:

Two polarizers are placed with their transmission axes at right angles to each other. A third polarizer is placed between them with its transmission axis at 45° to the axes of the other two.

If unpolarized light of intensity I0 is incident on the system, what is the intensity of the transmitted light I3 ?

(a)   I3 = I0 / 8
(b)   I3 = I0 / sqrt(3) /2
(c)   I3 = I0 × 2 / sqrt(3)
(d)   I3 = I0
(e)   I3 = 0

### QUESTION 7*

What is the intensity of the transmitted light I3 when the middle sheet is removed?

(a)   I3 = I0 / 8
(b)   I3 = I0 / sqrt(3) / 2
(c)   I3 = I0 × 2 / sqrt(3)
(d)   I3 = I0
(e)   I3 = 0

### QUESTION 8*

This and the next question concern the following situation:

Abraham Lincoln is standing in front of a mirror, wearing a tall hat. The distance h from his toes to the top of his hat is 220 cm.

What is the minimal vertical length m of a plane mirror in which Lincoln can see his full image (from his toes to the top of his hat)?

(a)   m = 80 cm
(b)   m = 110 cm
(c)   m = 220 cm
(d)   Any mirror size will be sufficient.
(e)   No mirror size will be sufficient.

### QUESTION 9**

At what distance x from the mirror must Lincoln stand in order to see his full image?

(a)   x = 80 cm
(b)   x = 110 cm
(c)   x = 220 cm
(d)   Any distance will be sufficient.
(e)   No distance will be sufficient.

### QUESTION 10***

Two plane mirrors form a 70° angle as shown in the picture below. The angles may not be drawn accurately.

For what angle θ is the final ray horizontal?

(a)   θ = 30°
(b)   θ = 40°
(c)   θ = 45°
(d)   θ = 70°
(e)   Any value of θ will yield a horizontal final ray.

### QUESTION 11*

This and the next three questions concern the following situation:

A radio tuner has a 400 Ω resistor, a 0.5 mH inductor, and a variable capacitor, all connected in series. Suppose the capacitor is adjusted to 72 pF.

What is the resonant frequency fo of the circuit?

(a)   fo = 50 Hz
(b)   fo = 120 Hz
(c)   fo = 840 kHz
(d)   fo = 5.3 MHz
(e)   fo = 102 MHz

### QUESTION 12*

What is the reactance of the inductor XL at the resonant frequency?

(a)   XL = 0 kΩ
(b)   XL = 0.4 kΩ
(c)   XL = 0.8 kΩ
(d)   XL = 2.6 kΩ
(e)   XL = 5.4 kΩ

### QUESTION 13*

The applied EMF coming from the antenna at the resonant frequency is 20 mV (rms). What is the rms current Irms in the circuit?

(a)   Irms = 0 mA
(b)   Irms = 0.05 mA
(c)   Irms = 0.12 mA
(d)   Irms = 0.45 A
(e)   Irms = 5A

### QUESTION 14*

What is the capacitance C required to tune to a station broadcasting at 1420 kHz?

(a)   C = 25 pF
(b)   C = 72 pF
(c)   C = 95 μF
(d)   C = 34 μF
(e)   C = 48 mF

### QUESTION 15*

This and the next two questions concern the following situation:

Light (λ = 500 nm in air) impinges at normal incidence from air (n = 1) onto a thin plastic film (n = 1.4) of thickness t which is on top of a thick glass plate (n = 1.5).

Find the minimum (non-zero) thickness t of the film which gives constructive interference.

(a)   t = 75 nm
(b)   t = 107 nm
(c)   t = 178 nm
(d)   t = 214 nm
(e)   t = 300 nm

### QUESTION 16*

If the thickness of the plastic film were doubled, the light would interfere

(a)   constructively.
(b)   destructively.

### QUESTION 17*

If the entire apparatus were placed in a tank of water (n = 1.33), your answer to the previous question would

(a)   remain the same.
(b)   change to the opposite choice.

### QUESTION 18*

This and the next two questions concern the following situation:

An object of height 5 cm is at a position 15 cm away from a spherical concave mirror. The image is located 30 cm to the left of the mirror.

What is the focal length of the mirror?.

(a)   5 cm
(b)   10 cm
(c)   15 cm
(d)   20 cm
(e)   25 cm

### QUESTION 19*

What is the height of the image?

(a)   2.5 cm
(b)   5.0 cm
(c)   10 cm

The image is

(a)   upright.
(b)   inverted.

### QUESTION 21**

This and the next two questions concern the following situation:

Which ray in this ray diagram is not correct?

(a)   1
(b)   2
(c)   3

### QUESTION 22**

Where would the image be formed in the picture above?

(a)   to the left of the left focal point
(b)   between the left focal point and the lens
(c)   between the right focal point and the lens
(d)   at the right focal point
(e)   to the right of the right focal point

### QUESTION 23**

Suppose the object is 20 cm to the left of the lens, which has a focal length of magnitude |f | = 10 cm. What is the magnification of the image?

(a)   +1.
(b)   +0.33
(c)   -0.33
(d)   +0.67
(e)   -0.67

### QUESTION 24*

This and the next two questions concern the following situation:

A man requires bifocals to correct both his near and far vision problems. Consider the bifocals to be a pair of glasses with a "main" lens and an additional "add-on" lens placed at the bottom. The main lens corrects his vision of distant objects. The add-on lens corrects his vision for reading.

Which of the following figures qualitatively represents the lenses in a pair of bifocals as described above?

(a)
(b)
(c)

### QUESTION 25*

The absolute value of the power of the main lens is | P | = 2.4 diopters. Without the glasses, how far away can the man see clearly?

(a)   41.7 cm
(b)   53.9 cm
(c)   66.3 cm

### QUESTION 26**

Looking through only the main lens, our man can read a book no closer than 35 cm away. But, he would like to read at a distance of 25 cm. What is the absolute value of the power of the add-on lens which will permit him to do this?

(a)   | P | = 1.05 diopters
(b)   | P | = 1.09 diopters
(c)   | P | = 1.14 diopters
(d)   | P | = 1.23 diopters
(e)   | P | = 1.40 diopters

### QUESTION 27**

A ray of red light passes through a series of media with different refractive indices: n1, n2 and n3. It then enters a medium with an index of refraction n1 as shown.

In what medium does the light travel the fastest?

(a)   medium with index n1
(b)   medium with index n2
(c)   medium with index n3

### QUESTION 28*

This and the next question concern the following situation:

In the figure to the right, a light beam starts from the lower left corner in air, enters a box with a transparent material inside, strikes a mirror and reflects, then exits the box back into the air along the direction shown.

For nstuff = 1.5, calculate L.

(a)   L = 6.39 cm
(b)   L = 7.14 cm
(c)   L = 8.05 cm
(d)   L = 8.88 cm
(e)   L = 9.32 cm

### QUESTION 29*

If the index of refraction of the material in the box is increased from nstuff = 1.5 to nstuff = 1.6, the distance L will

(a)   increase.
(b)   decrease.
(c)   remain the same.

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.