### Spring 2011 Physics 102 Hour Exam 3(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 127. The exam period was 90 minutes; the mean score was 94.0; the median was 98. 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 question and the next pertain to the the following situation.

A message is sent via radio wave (λ = 10 m) from Earth to a nearby star, Proxima Centauri, which lies 1.3 parsecs from Earth. A parsec is a unit of length and 1 parsec = 3.1 × 1016 m. How long will it take the message to reach Proxima Centauri traveling through vacuum?

(a)   0 yrs, the message arrives instantly.
(b)   1.38 yrs
(c)   4.26 yrs
(d)   255.0 yrs
(e)   1.38 × 108 yrs

### QUESTION 2*

If microwaves (λ = 10 cm) are used instead of radio waves, the message would

(a)   take less time to reach its destination.
(b)   arrive at its destination in the same amount of time.
(c)   take longer to reach its destination.

### QUESTION 3*

This question and the next pertain to the the following situation.

Unpolarized light with intensity I0 travels through a linear polarizer whose transmission axis forms a 45° angle with respect to the vertical. The light then travels through another polarizer whose transmission axis makes a 33° angle with respect to the previous polarizer. What is ratio of the final intensity I2 of the light relative to its initial intensity I0?

(a)   I2 / I0 = 0.35
(b)   I2 / I0 = 0.43
(c)   I2 / I0 = 0.50
(d)   I2 / I0 = 0.72
(e)   I2 / I0 = 1.00

### QUESTION 4**

The light source is replaced with a new source. It has the same intensity I0 but is vertically polarized. The new final intensity I2' relative to the previous final intensity I2 is:

(a)   I2' < I2
(b)   I2' = I2
(c)   I2' > I2

### QUESTION 5*

Consider a solenoid with current I = 4 A, 200 turns and a length of 0.65 meters. What is the magnetic energy density inside the solenoid?

(a)   0.95 J/m3
(b)   1.30 J/m3
(c)   1.43 J/m3
(d)   1.88 J/m3
(e)   2.44 J/m3

### QUESTION 6*

An oncoming car A emits light. It has a very powerful engine so it can accelerate very quickly to high speeds.

The light-emitting car speeds up. A detector in car B notices the emitted light

(a)   shifts to longer wavelength.
(b)   shifts to shorter wavelength.
(c)   remains unchanged.

### QUESTION 7**

A light shines from 2 meters above the water surface through 4 meters of water and is reflected back. Calculate the total transmission time from point A to point B and back to point A.

Ignore any reflections at the air-water interface and assume the light travels exactly perpendicularly to the surface of the Earth. The index of refraction of water n = 1.33.

(a)   20 ns
(b)   24 ns
(c)   40 ns
(d)   48 ns
(e)   53 ns

### QUESTION 8**

Two linear polarizers are placed in a row. The first has its transmission axis θ1 = 50° (counterclockwise) from vertical while the second polarizer has its transmission axis oriented θ2 = 31° (clockwise) from vertical, as shown below. A beam of vertically polarized light with initial intensity I0 goes through the two polarizers.

What is the ratio of the final electric field E2 to the initial electric field E0?

(a)   E2 / E0 = 0.00
(b)   E2 / E0 = 0.01
(c)   E2 / E0 = 0.10
(d)   E2 / E0 = 0.60
(e)   E2 / E0 = 0.95

### QUESTION 9*

This question and the next pertain to the the following situation.

Light, an electromagnetic wave, leaves a distant star. The light from this star enters the Earth's atmosphere, which has a refractive index n = 1.0003.

Which of the following of the properties of light does not change during this transition?

(a)   wavelength
(b)   speed
(c)   frequency

### QUESTION 10*

The light from this star strikes a telescope, which can be approximated as a concave mirror. The incident light comes from so far away that you can assume the incident rays are parallel to each other. Where will the light rays from this star converge?

(a)   at a location beyond c, the center of curvature
(b)   These rays will never converge.
(c)   half the focal point, f/2
(d)   between half the focal point and the focal point
(e)   the focal point, f

### QUESTION 11*

This question and the next two pertain to the the following situation.

An object is placed 1 cm from a concave mirror of focal length f = 2 cm as shown along the principle axis.

Where is the image formed in the system?

(a)   10 cm in front of the mirror
(b)   3.33 cm behind the mirror
(c)   2.0 cm behind the mirror
(d)   3.33 cm in front of the mirror
(e)   infinitely far in front of the mirror

### QUESTION 12*

The resulting image is

(a)   real and upright.
(b)   virtual and upright.
(c)   virtual and inverted.

### QUESTION 13*

Where would you place the object to make the resulting image real and inverted?

(a)   to the left of the focus
(b)   to the right of the focus

### QUESTION 14*

A ray of light travelling through the air (n = 1) hits the boundary between air and water (n = 1.33). What is the refracted angle from the normal if the light ray is coming in at an angle of 30° from the normal?

(a)   0.37°
(b)   10°
(c)   22°
(d)   60°
(e)   67°

### QUESTION 15*

A block of glass is placed in a pan of water, and a pen light is shone through the glass, as shown in the picture. In this situation, the critical angle is determined to be 57°. Now the same block of glass is placed in a pan of oil, and the critical angle is found to be 63°. What is the index of refraction of the oil?

(a)   1.20
(b)   1.33
(c)   1.41

### QUESTION 16*

A man is so nearsighted that he cannot see anything clearly past 15 cm. What power of lens (in Diopters) does this man need to correct his vision?

(a)   P = 6.67
(b)   P = 3.33
(c)   P = 2.00
(d)   P = -3.33
(e)   P = -6.67

### QUESTION 17**

This question and the next pertain to the the following situation.

A diverging lens and a concave mirror are positioned as shown in the diagram. The object is placed 7 cm to the left of the lens. The lens and the mirror are 18 cm apart.

Where is the final image located?

(a)   2.44 cm to the right of the lens
(b)   4.12 cm to the left of the lens
(c)   7.13 cm to the left of the lens
(d)   9.77 cm to the right of the lens
(e)   15.56 cm to the right of the lens

### QUESTION 18**

The final image is upright.

(T)   True
(F)   False

### QUESTION 19*

A magnifying glass with a converging lens of focal length f = 25 cm is placed a distance d = 10 cm away from a printed page. Calculate the magnification of the image.

(a)   m = 0.60
(b)   m = 0.71
(c)   m = 1.40
(d)   m = 1.67
(e)   m = 2.50

### QUESTION 20*

This question and the next one pertain to the the following situation.

A mercury-vapor lamp produces two strong emission lines in the green segment of visible light. The two wavelengths are 546.1 nm and 578.2 nm. Light from the lamp shines through a diffraction grating containing slits with separation 15 μm onto a screen 2 meters away.

What is the distance between the first-order maximum corresponding to 546.1 nm and the first-order maximum corresponding to 578.2 nm?

(a)   4.3 mm
(b)   5.1 mm
(c)   6.3 mm
(d)   7.4 mm
(e)   9.2 mm

### QUESTION 21*

Now the entire apparatus is submerged in water (index of refraction n = 1.33). What will happen to the positions of the first order maxima, compared to their positions outside the water?

(a)   They will be closer to the center of the screen.
(b)   They will be farther away from the center of the screen.
(c)   Their positions will not change.

### QUESTION 22*

A pair of glasses lenses are coated with an anti-reflective coating to reduce the amount of stray light that reflects into the wearer's eyes. The lenses are made of glass with index of refraction n = 1.52, while the coating is magnesium fluoride (n = 1.38).

If the thickness of the anti-reflective coating is 74.6 nm, what is the wavelength in air of the light that will be eliminated by the coating?

(a)   320 nm
(b)   412 nm
(c)   560 nm
(d)   732 nm
(e)   824 nm

### QUESTION 23***

A crystal lattice is investigated by means of X-ray diffraction. The second-order interference maximum is observed for X-rays of wavelength 0.17 nm at an angle of 13.1°.

What is the interplanar spacing d ?

(a)   0.039 nm
(b)   0.36 nm
(c)   0.75 nm
(d)   0.98 nm
(e)   1.5 nm

### QUESTION 24***

Two speakers and a microphone are arranged in the configuration below.

Which is the first frequency above 1 kHz that will not be picked up by the microphone? The speed of sound is 343 m/s.

(a)   3.40 kHz
(b)   3.05 kHz
(c)   2.55 kHz
(d)   1.50 kHz
(e)   All frequencies above 1 kHz will be picked up.

### QUESTION 25**

If you take a picture with a camera using a circular aperture, which color looks the sharpest (has the best resolution)?

(a)   purple = 400 nm
(b)   red = 600 nm
(c)   yellow = 580 nm

### QUESTION 26*

Your professor develops a phenomenal new glass with indices of refraction for red and blue light nred = 1.81 and nblue = 1.92. Find the ratio of the minimum angle of total internal reflection for red light to the minimum angle of total internal reflection for blue light, θred / θblue, in the following situation.

(a)   θred / θblue  =  1.50
(b)   θred / θblue  =  1.24
(c)   θred / θblue  =  1.07

### QUESTION 27*

Unpolarized sunlight hits an oily surface at an angle of 57°. The reflected light is completely horizontally polarized. What is the refractive index of the oil?

(a)   1.33
(b)   1.47
(c)   1.54

### QUESTION 28*

Which one of the three rays drawn in the figure below is incorrect?

(a)   ray 1
(b)   ray 2
(c)   ray 3

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.