### Summer 2007 Physics 102 Hour Exam 3(21 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 83. The exam period was 75 minutes; the mean was 57.6; the median was 60. Click here to see page1 page2 page3 of the formula sheet that came with the exam.

### QUESTION 1**

This and the next two questions concern the following situation:

Suppose the distance between the lens in your eye and the retina of that eye is 2.65 cm. Do not assume you have normal vision as defined in lecture.

Assume the lens of your eye needs to be able to focus on objects as far as 40 cm and as close as 20 cm. To what shortest focal length must your lens be able to adjust?

(a)   2.34 cm
(b)   2.49 cm
(c)   2.65 cm
(d)   20 cm
(e)   40 cm

### QUESTION 2**

Assume you can focus on no object closer than 20 cm. You would like to be able to focus on a stamp 5 cm from your eye. You will put an additional lens right up against your eye (ignore the distance between this additional magnifier and your eye's own lens). What focal length of magnifier should you use?

(a)   4 cm
(b)   5 cm
(c)   6.67 cm

### QUESTION 3*

To focus on distant objects, you wear contact lenses. Which of these is true regarding their focal length f ?

(a)   f > 0
(b)   f < 0

### QUESTION 4*

This and the next question concern the following situation:

The picture shows two glass blocks, the upper one having an index of refraction of 1.48, and the lower one with an index of refraction of 1.38. Light enters the top block at y = 15 mm above the boundary between them, entering at an angle θ with respect to a horizontal reference line. The two blocks are surrounded by air (n = 1).

If θ = 20°, find x, the distance measured from the left edge of the blocks to the point at which the light hits the boundary between them.

(a)   3.6 mm
(b)   6.3 mm
(c)   63 mm

### QUESTION 5**

Find the largest angle θ at which no light enters the bottom block.

(a)   30°
(b)   32°
(c)   38°
(d)   43°
(e)   52°

### QUESTION 6**

This shows a lens, depicted as a flat plate to obscure its profile. Its focal length is -5 cm. Three rays start at an object and pass through the lens, but one is drawn incorrectly. Which one of them is wrong?

(a)   A
(b)   B
(c)   C

### QUESTION 7*

A thin, spherical glass bowl is silvered on both sides so that it may serve as either a convex (left) or concave (right) mirror. Its radius of curvature is 20 cm. In each case, an object is held 15 cm in front of it.

What can we say about the images formed in these two cases?

(a)   Both images are real.
(b)   One image is virtual; the other is real.
(c)   Both images are virtual.

### QUESTION 8*

A real object held in front of a mirror with focal length f = 30 cm produces a real image three times as large as the object. How far is the object from the mirror?

(a)   40 cm
(b)   90 cm
(c)   120 cm

### QUESTION 9*

This and the next question concern the following situation:

A single slit of width a = 0.5 mm produces, on a screen L = 2.8 m away, a central bright fringe of width 6 mm when illuminated by light of wavelength λ. (The central bright fringe is delimited by two dark spots labeled in the diagram. Those are the two dark spots closest to the center of the screen.) What is λ?

If θ = 20°, find x, the distance measured from the left edge of the blocks to the point at which the light hits the boundary between them.

(a)   180 nm
(b)   270 nm
(c)   400 nm
(d)   540 nm
(e)   810 nm

### QUESTION 10**

Suppose instead we had a pair of very narrow slits separated by the same distance d = 0.5 mm. These produce dark spots at the same locations as the dark spots in the previous problem if the slits are illuminated by light of wavelength λ'. Assume, again, that these are the two dark spots closest to the center of the screen. What is λ'?

(a)   λ' = λ /2
(b)   λ' = λ
(c)   λ' = 2 λ

### QUESTION 11*

Glass slabs of equal thickness but different indices of refraction are stacked. Light in air is incident on the top slab at some angle of incidence other than zero. True or false: light travels a greater distance in the slower slabs than in faster ones.

(T)   True
(F)   False

### QUESTION 12**

Light in air (n = 1) enters water (n = 1.33) at unknown angle θ and from there a triangular glass prism (n = 1.5). It strikes the long side of the prism. A small fraction of the light energy is reflected along its original path. Find θ.

(a)   θ = 54°
(b)   θ = 45°
(c)   θ = 39°
(d)   θ = 32°
(e)   θ = 28°

### QUESTION 13**

Two bright beacons on the moon (384,000 km from earth) can just barely be resolved by a person with pupil diameter 2.5 mm. How far apart are those lights if they emit light of wavelength 550 nm?

(a)   10 m
(b)   102 m
(c)   103 m
(d)   105 m
(e)   107 m

### QUESTION 14**

A real object is held a distance x in front of a lens of focal length f1= 5 cm. A second lens, of focal length f2=10 cm, is 40 cm from the first. Light travels from the object through the first and second lenses and forms a sharp image on a screen 12 cm from the second lens. Find x.

(a)   2 cm
(b)   4 cm
(c)   6.7 cm
(d)   10 cm
(e)   12 cm

### QUESTION 15*

Because the electric field in an electromagnetic wave is larger than the magnetic field, more energy is transported in its electric field than in its magnetic field.

(T)   True
(F)   False

### QUESTION 16**

This and the next question concern the following situation:

A deep, rectangular tank (1 meter long by 2 meters wide) is partially filled with water (n = 1.33). The bottom of this tank reflects no light. Light of wavelength 640 nm shines directly downward into the tank from the air above. A layer of transparent oil (n = 1.4) will be poured onto the surface of the water, on which it will float without mixing. What smallest volume of oil will prevent reflection of light back up towards the source? Note that there are 106 cc (cubic centimeters) in one cubic meter.

(a)   0.229 cc
(b)   0.320 cc
(c)   0.457 cc
(d)   0.640 cc
(e)   0.914 cc

### QUESTION 17**

Suppose instead we had used an oil with index of refraction n = 1.2. What thinnest layer of such oil would cause strongest reflection of 500 nm light? Solve for its thickness.

(a)   104 nm
(b)   208 nm
(c)   417 nm

### QUESTION 18*

Unpolarized light of intensity 4 W/m2 strikes a linear polarizer. What is the intensity of light which emerges from this polarizer?

(a)   1 W/m2
(b)   2 W/m2
(c)   The answer depends on the orientation of the polarizer.

### QUESTION 19*

A certain diffraction grating (unknown number of lines per cm) is tested by shining light of wavelength 589 nm onto it, with the resulting pattern projected onto a screen 1.2 meters from the grating. A first-order maximum is measured to be 18 cm from the bright spot in the center. If an unknown source -- emitting light of wavelength λ, which we wish to measure -- produces a first-order maximum 21 cm from the central peak, what is λ?

(a)   620 nm
(b)   639 nm
(c)   650 nm
(d)   667 nm
(e)   684 nm

### QUESTION 20***

Light of wavelength λ illuminates a single slit. The diagram shows distances x1 and x2, from top and bottom of the slit to point P. These distances obey the equation x2 - x1 = 4λ . Is point P bright or dark?

(a)   bright
(b)   dark

### QUESTION 21**

Unpolarized light propagates in the positive z-direction. It strikes three polarizers lying in the x-y plane: the first with transmission axis along the x-axis, the second with transmission axis at angle φ with respect to the x-axis, and the third with transmission axis in the y-direction. Of the following three choices, what value of φ results in the greatest intensity of light emerging from the last polarizer?

(a)   41°
(b)   51°
(c)   71°

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.