### Summer 2010 Physics 102 Hour Exam 3(24 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 95. The exam period was 75 minutes; the mean score was 64.5; the median was 64. 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*

The diagram shows two lenses, one (A) thicker in the center, the other (B) thicker on the edge. We can think of three possible uses for these: correcting nearsightedness; correcting farsightedness; simple magnification. Which of these statements accurately associates lenses and applications? ("Magnification" implies using the lens as a simple magnifier.)

(a)   Use A for nearsightedness; use B for farsightedness and magnification.
(b)   Use A for farsightedness; use B for nearsightedness and magnification.
(c)   Use A for nearsightedness and magnification; use B forfarsightedness.
(d)   Use A for farsightedness and magnification; use B fornearsightedness.
(e)   Use A for magnification; use B for near- and farsightedness.

### QUESTION 2**

You hold a lens of focal length 0.25 m one meter in front of your eye. You focus on the image, created by this lens, of an object 9 meters away from that lens. Under these circumstances, what is the focal length of the lens (really lens and cornea) of your eye? Assume the distance from lens to retina in your eye is 2.55 cm.

(a)   -2.59 cm
(b)   -2.51 cm
(c)   2.43 cm
(d)   2.47 cm
(e)   2.51 cm

### QUESTION 3*

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

An unpolarized source emits light of average intensity 1.5 watts per square meter toward a stack of polarizers, each lying in the x-y plane. The transmission axis of the first makes a 45° angle with respect to the x-axis. The transmission of the second is horizontal (lies along the x-axis). The transmission axis of the third makes a 30° angle with respect to the x-axis. (In this diagram, the light moves from upper-left to lower- right.)

What is the peak magnetic field associated with this radiation?

(a)   5.6 × 10-8 T
(b)   7.9 × 10-8 T
(c)   1.1 × 10-7 T

### QUESTION 4*

What is the intensity of light emerging from the last polarizer?

(a)   0.28 W/m2
(b)   0.36 W/m2
(c)   0.46 W/m2
(d)   0.56 W/m2
(e)   0.92 W/m2

### QUESTION 5***

True or False: the intensity of light emerging from the last polarizer (at 30°) measured in this experiment would be the same if, instead of using an unpolarized source, we had used a horizontally-polarized source.

(T)   True
(F)   False

### QUESTION 6**

You hold an object in front of a mirror. The mirror projects an image of that object onto a piece of paper. True or False: the mirror must be concave. (The arrow in the diagram shows a ray reflecting off a concave mirror, just to remind you what "concave" means.)

(T)   True, the mirror must be concave.
(F)   False, the mirror does not have to be concave.

### QUESTION 7**

You hold an object in front of a mirror of focal length 75 cm. The image created by that object has a magnification of +1.3. How far from the mirror is that object? (These distances are absolute values.)

(a)   3 cm
(b)   17.3 cm
(c)   22.5 cm
(d)   133 cm
(e)   173 cm

### QUESTION 8*

The diagram shows the object and image for a mirror depicted by the vertical line. (The mirror is drawn as flat but may be slightly curved.) One of the two points on the principal axis may be the focal point of the mirror. Which?
(a)   A
(b)   B
(c)   Cannot be determined from information given.

### QUESTION 9***

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

This trapezoidal glass prism, with index of refraction 1.95, has two sloped faces, each at angle θ = 40° with respect to a horizontal reference line. (The top and bottom faces are horizontal.) The prism is surrounded by air.

Ray of light #1 enters the glass without bending. As ray #1 strikes the top face, does it experience total internal reflection?
(a)   Yes, all the incident light energy is reflected back into the glass.
(b)   No, some light refracts out, but at different angles total internal reflection will occur.
(c)   No, under these circumstances, there cannot be total internal reflection at the top face, regardless of the angle of ray #1.

### QUESTION 10***

Ray #2 propagates vertically through the air, then passes into the prism, where it strikes the top face, making an angle φ with respect to a vertical reference line. What is the value of φ?

(a)   16.7°
(b)   19.2°
(c)   20.8°
(d)   23.1°
(e)   30.8°

### QUESTION 11***

Assume now that the prism is submerged in water (index of refraction 1.33). Ray #2 still propagates vertically before striking the sloped face of this trapezoid. What can you say about φ when the prism is under water?

(a)   The angle φ will be smaller when the prism is submerged.
(b)   The angle φ will be unaffected by the surrounding water.
(c)   The angle φ will be larger when the prism is submerged.

### QUESTION 12**

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

Two lenses, with focal lengths f1 = 16 cm and f2 = -15 cm, are separated by a distance L = 10 cm. (The diagram shows the lenses as flat plates to obscure their shapes.)

You hold a real object at x = 8 cm in front of the first lens. What is the magnification of this system? (The answers below are for the absolute value of the magnification.)

(a)   0.37
(b)   0.73
(c)   1.59
(d)   1.67
(e)   2.73

### QUESTION 13*

True or False: the final image is inverted with respect to the original object.

(T)   True
(F)   False

### QUESTION 14**

True or False: if the object were instead placed 16 cm to the left of the first lens (f1), then an observer to the right of the second lens would focus on an image at a focal point of the second lens.

(T)   True
(F)   False

### QUESTION 15**

A bit of alcohol (index of refraction = 1.36) remains, inexplicably unconsumed, at the bottom of this tilted cup, made of plastic with index of refraction = 1.58. Assume monochromatic light shines downward from above. Is this light reflected strongly from the extremely thin layer of alcohol at point A? (A points to the very edge of the fluid.)

(a)   Yes, that edge of the fluid is bright.
(b)   No, that edge of the fluid is dark.

### QUESTION 16**

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

A layer of oil (index of refraction = 1.47) sits on top of vinegar (index of refraction = 1.31). Find the smallest (but non-zero) thickness t of oil at which blue light (λ = 450 nm) shining straight downward from the air above is not reflected from the surface.

(a)   77 nm
(b)   86 nm
(c)   113 nm
(d)   153 nm
(e)   172 nm

### QUESTION 17**

Suppose the thickness of the oil starts at t = 1000 nm, and that you slowly add more oil, building to a final thickness of t = 1600 nm. In the course of doing this, at how many different thicknesses will green light (λ = 520 nm) be strongly reflected?

(a)   3
(b)   4
(c)   5

### QUESTION 18*

Late at night, a distant building is completely dark, except for two bulbs visible in one window. Given the constraints of diffraction, how far from this building can you stand and still resolve (see as distinct) those two bulbs? Assume the bulbs are 0.85 meters apart, and that they emit light of wavelength λ = 550 nm. Since it is dark outside, your pupils have dilated to a diameter 8 mm

(a)   10 m
(b)   100 m
(c)   1 km
(d)   10 km
(e)   100 km

### QUESTION 19*

You can focus on no object farther than 33 cm from your eye. A randomly-chosen lens allows you to focus on objects as far as 52 cm from your eye. What is the focal length of this randomly-chosen lens?

(a)   -90.3 cm
(b)   -20.2 cm
(c)   +20.2 cm

### QUESTION 20*

True or False: in an electromagnetic wave, the electric and magnetic fields peak at the same time.

(T)   True
(F)   False

### QUESTION 21***

How many bright spots for red light (λ = 650 nm) would be visible, in total, after that light has passed through a diffraction grating containing 1200 lines per cm?

(a)   12
(b)   24
(c)   25

### QUESTION 22**

A sodium lamp (emitting light of wavelength λ = 589 nm) is used to calibrate an unknown diffraction grating. It is found that the first order bright spot on either side is 24 cm from the center bright spot, when this pattern is projected onto a screen 1.8 meters away from the grating. How far from the center bright spot would the third order maximum be when illuminated by blue light (λ = 450 nm)?

(a)   49.1 cm
(b)   52.3 cm
(c)   55.0 cm
(d)   57.2 cm
(e)   72.0 cm

### QUESTION 23*

Two slits are separated by 0.65 mm. When illuminated by green light of wavelength 530 nm, at which of these angles is the second-order maximum detected?

(a)   0.093°
(b)   0.47°
(c)   0.93°
(d)   1.47°
(e)   14.7°

### QUESTION 24**

A single slit of width 0.65 mm is illuminated by green light of wavelength 530 nm. True or False: this experiment will give a dark spot at the same angle at which the previous experiment (where 2 slits had separation 0.65 mm) gave a bright spot.

(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.