### Summer 2011 Physics 102 Hour Exam 3(25 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 97; the mean score was 69.6; the median was 73. The exam period was 75 minutes. 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**

A lens of focal length f = 24 cm is held a distance y = 58 cm in front of this eye. There is an object at x = 18 cm in front of this lens, as shown. How far from the eye must the eye focus so that it produces a clear image on its retina?

(a)   14 cm
(b)   34 cm
(c)   58 cm
(d)   72 cm
(e)   130 cm

### QUESTION 2*

You hold a real object 18 cm in front of a mirror. The image created by that object has a magnification of +2.6. What is the focal length of that mirror?

(a)   9 cm
(b)   13 cm
(c)   29 cm
(d)   47 cm
(e)   65 cm

### QUESTION 3*

True or false: a diverging lens can never produce a real image of a real object.

(T)   True
(F)   False

### QUESTION 4*

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

In the diagram, the horizontal dashed lines indicate horizontal axes (x-axes). The angles θ1 = 80°, θ2 = 40° and θ3 = 60° are the angles of transmission axes of three polarizers; these angles are measured with respect to the positive x-axis, and are not necessarily drawn to scale. Unpolarized light of average intensity 4 watts per square meter is incident along an axis perpendicular to these polarizers.

What is the average intensity of light emerging from the third polarizer?

(a)   0.063 W/m2
(b)   0.29 W/m2
(c)   0.58 W/m2
(d)   1.04 W/m2
(e)   2.1 W/m2

### QUESTION 5**

What is the peak strength of the magnetic field between the first and second polarizers?

(a)   9 × 10-8 T
(b)   1.3 × 10-7 T
(c)   1.8 × 10-7 T

### QUESTION 6*

You rotate the second polarizer so that θ2 = 220°, leaving all other values in this problem unchanged. Does this have any effect on the intensity of light emerging from that polarizer?

(a)   Yes, the light intensity in this case does not equal the intensity when θ2 = 40°.
(b)   No, the intensity is the same when θ2 = 220° as when θ2 = 40°.

### QUESTION 7**

Now rotate the polarizers so that θ1 = 90° and θ3 = 0°. Does light emerge from the third polarizer?

(a)   Light might or might not emerge from the third polarizer, depending on θ2.
(b)   Yes, light always emerges from the third polarizer, regardless of θ2.
(c)   No, no light emerges from the third polarizer, regardless of θ2.

### QUESTION 8*

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

The diagram shows a real object and its image for a lens depicted by the vertical line. (Details of the shape of the lens are not revealed.)

There is a focal point along the principal axis to the left of the lens. Where is it located?

(a)   to the left of the object
(b)   between the object and the image
(c)   between the image and the lens

### QUESTION 9**

What can we say about the focal length of this lens?

(a)   f > 0
(b)   f < 0

### QUESTION 10*

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

A rectasngular glass prism with index of refreaction n = 1.6 is surrounded by air. Light enters from the left. Inside the prism, the light makes an angle φ = 23° with respect to the top surface of the prism.

What is the angle θ made by the light with respect to the left face?

(a)   33°
(b)   39°
(c)   45°
(d)   51°
(e)   57°

### QUESTION 11**

What can one say about the light inside the prism as it reaches the top face?

(a)   Some of it will escape through the top surface of the prism.
(b)   None of the light can escape through the top surface of the prism.

### QUESTION 12**

Two tiny red bulbs (wavelength λ = 680 nm) are lit on a control panel at one end of a huge hall. You stand at the other end, 70 meters away. Given that you are able to resolve them at that distance, how closely can those two bulbs be spaced? Assuming your pupils have dilated to a diameter 6 mm, find the smallest separation between the bulbs.

(a)   1 mm
(b)   1 cm
(c)   10 cm
(d)   1 m
(e)   10 m

### QUESTION 13**

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

This shape is a (highly exaggerated) depiction of a corrective lens. The dashed line shows the principal axis.

Consider a ray of light parallel to the principal axis, striking this lens from the left. What effect does each surface have on this incident ray?

(a)   The ray bends toward the principal axis as it enters the lens, and toward the principal axis even more as it exits.

(b)   The ray bends away from the principal axis as it enters, and toward the principal axis as it exits.

(c)   The ray bends toward the principal axis as it enters the lens and away from the principal axis as it exits.

### QUESTION 14**

How might a lens of this shape be employed? The three possibilities are to compensate for farsightedness, compensate for nearsightedness, and serve as a simple magnifier.

(a)   It corrects farsightedness only.
(b)   It corrects nearsightedness only.
(c)   It serves as a magnifier only.
(d)   It can be used to correct for farsightedness and serve as a magnifier (but nothing else).
(e)   It can be used to correct for nearsightedness and serve as a magnifier (but nothing else).

### QUESTION 15*

You can focus on no object closer than 28 cm from your eye. Holding a particular lens right up to your eye, you can focus on objects as close as 18 cm. What is the focal length of this lens?

(a)   -11 cm
(b)   +11 cm
(c)   +50 cm

### QUESTION 16*

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

Two lenses, with focal lengths f1 = -10 cm and f2 = 8 cm, are separated by a distance L. (The diagram shows the lenses as flat plates to obscure their shapes.)

You hold a real object at x = 5 cm in front of the first lens. The second lens produces a real image 28 cm away from that lens. Under these circumstances, what is L?

(a)   1.2 cm
(b)   7.9 cm
(c)   11.2 cm
(d)   14.5 cm
(e)   21.2 cm

### QUESTION 17**

This real object has a height 0.4 mm. (Note that it points upward in the diagram.) What is the height of the final image produced by the second lens? In these choices, a negative answer imples the final image is pointing downward.

(a)   -1.67 mm
(b)   -0.67 mm
(c)   +0.4 mm
(d)   +0.67 mm
(e)   +1.67 mm

### QUESTION 18*

Now move the object to x = 10 cm. True or false: the final image (created by the second lens) is at the focal point of the second lens.

(T)   True
(F)   False

### QUESTION 19**

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

Water (index of refraction n = 1.33) sits in the bottom of a glass cup. The glass underneath the water is thicker near the edge; the water is deepest in the center. The index of refraction of the glass is n = 1.53. Light shines downward onto the water from above.

For what thinnest (non-zero) layer of water are reflections of yellow light (λ = 580 nm) extinguished?

(a)   91.7 nm
(b)   109 nm
(c)   184 nm
(d)   218 nm
(e)   275 nm

### QUESTION 20**

Assume now that the thickness of the water ranges from 1000 nm to 1500 nm. For how many thicknesses in that range is green light (λ = 520 nm) strongly reflected?

(a)   2
(b)   3
(c)   4

### QUESTION 21*

As the water evaporates, its thickness approaches zero. Is the green light (previous question) strongly reflected as that thickness goes to zero?

(a)   Yes
(b)   No

### QUESTION 22**

Parallel beams of red and violet light, starting inside a glass prism, are incident on the surface of that prism. At a certain angle of incidence, only one color is completely reflected back into the prism. (At that same angle of incidence, the other color is only partially reflected; some of it escapes into the surrounding air.) Which color is trapped in the glass?

(a)   red
(b)   violet

### QUESTION 23**

Red light (λ = 640 nm) passes through a pair of slits separated by 0.1 mm, projected onto a distant screen. One point on the screen is 1600 nm closer to one slit than the other. Is that point bright or dark?

(a)   bright
(b)   dark

### QUESTION 24**

Blue light (λ = 450 nm) passes through a diffraction grating with 1800 lines per cm. The resulting pattern is projected onto a screen 2.2 meters away. How far from center is the fifth-order bright spot?

(a)   8.9 mm
(b)   8.9 cm
(c)   18 cm
(d)   97 cm
(e)   In this situation, there will be no fifth-order bright spot.

### QUESTION 25**

In a single-slit diffraction experiment, green light (λ = 540 nm) passes through a narrow slit and is projected onto a screen 1.2 meters away. The central maximum (the bright spot between the minima on either side) is 8 mm wide. How wide is the slit?

(a)   0.04 mm
(b)   0.08 mm
(c)   0.16 mm

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.