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Name: _______________________________________________ Student ID: ___________________________ Section #: _________

Physics 208 Exam 1 Sep. 29, 2009 Print your name and section clearly above. If you do not know your section number,

write your TA’s name. Your final answer must be placed in the box provided. You must show all your work

to receive full credit. If you only provide your final answer (in the box), and do not show your work, you will not receive very many points.

Problems will be graded on reasoning and intermediate steps as well as on the final answer. Be sure to include units, and also the direction of vectors.

You are allowed one 8½ x 11” sheet of notes and no other references. The exam lasts exactly 90 minutes.

Problem 1: _______ / 20 Speed of light in vacuum:

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c = 3×108m /s Problem 2: _______ / 20 Permittivity of free space

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εo = 8.85 ×10−12C2 /N ⋅m2 Problem 3: _______ / 20 Coulomb constant

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k =1/4πεo = 9 ×109N ⋅m2 /C2 Problem 4: _______ / 25 Magnitude of electron charge

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e =1.6 ×10−19C Problem 5: _______ / 15 TOTAL: _______ / 100

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1) [20 points, 4 points each]. Circle the correct answer, AND write some sentences or show a calculation explaining how you obtained the answer.

i) A person has just jumped into a swimming pool, generating a huge wave. The wave has a frequency of 0.5 cycles / second, and the crests are 15 ft apart. If you are 15 ft away from a crest, how long will it be before it reaches you?

a) 0.25 s

b) 0.5 s

c) 1 s

d) 1.5 s

e) 2 s

ii) An 0.2m focal length lens is used to project an in-focus image of an ipod screen on a

wall 1m away. The ipod screen is 3cm X 2cm, how large is the projected image? a) 6cm X 4cm

b) 12cm X 8cm

c) 15cm X 10cm

d) 24cm X 16cm

e) 30cm X 20cm

iii) A +1 µC charge is on the x-axis at x=-0.1m. A -2µC charge is on the x-axis at x=+0.1m. What should be the value of a charge placed on the x-axis at x=0 that results in zero net force on the +1 µC charge?

a) 0.25 µC

b) 0.5 µC

c) 1 µC

d) 2 µC

e) 4 µC

f) cannot be done

Explanation/work:

Explanation/work:

Explanation/work:

-2µC, x=+0.1m +1µC, x=-0.1m

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iv) An astronomer calibrates her diffraction grating spectrometer with blue light of

wavelength 400 nm (1nm=10-9m). She observes the first-order interference maximum at an angle of about

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θ = 53̊ .13. What is the number of slits/mm of the grating? a) 1000

b) 2000

c) 3000

d) 4000

e) 5000

v) You hold a laser pointer in the air above an aquarium and shine it into the water. The

water has an index of refraction of 1.33, and the air above it an index of 1.0. At what angle with respect to the vertical will there be total internal reflection of the laser back into the air?

a) 22.51˚

b) 37.75˚

c) 42.54˚

d) 48.75˚

e) There will always be total internal reflection

f) There will never be total internal reflection

Explanation/work:

Explanation/work:

400 nm

Grating

θ

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2) [20 points total] This problem is about two-slit diffraction. a) [5 points] Two extremely narrow slits are 0.9 µm apart (1µm=10-6m), and are

illuminated by 500 nm (1 nm=10-9m) green light. Find all angles at which complete constructive interference occurs. θ as shown is positive. b) [5 points] What is the phase difference between the light rays from the two slits

when they come together at the same spot on a screen 2m away at an angle of

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θ = 20˚ from the incident light?

Angle(s) =

Value(s) Units

Phase difference =

Value Units

Light

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θ

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c) [5 points] Now a piece of glass (n=1.5) is put in front of the top slit, so that there is a

phase shift between the two light beams just as they emerge from the slits. Are the angles at which maxima occur increased, decreased, or the same?

θ as shown is positive. Circle the correct answer and explain. d) [5 points] With the glass, the phase shift between the two light beams just as they

emerge from the two slits is 2.7 radians. The separation between slits is still 0.9 µm, and the light wavelength is still 500 nm.

At what angle does the original (without glass) “central maximum” now occur?

Angle =

Value(s) Units

Explanation

increased

decreased

Light

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θ

Glass

same

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3) [20 points total] An aquarium is in the shape of a hexagon, with each side measuring 0.2m. You look at the aquarium as shown in the figure.

Ignore the glass in the aquarium (suppose the walls are just an air-water interface). Consider the fish to be a point source of light. The water has an index of refraction of 1.33, and the air has an index of 1.0. a) [5 points] You are far enough away from the aquarium so that all light rays from the aquarium parallel to the dashed line enter your eye, and all others miss your eye. Suppose the fish is at the back wall of the aquarium, on the dashed line (black dot). Draw light rays that explain how you see three separate images of the fish. b) [5 points] Your eye is still very far away from the aquarium. The fish swims along the

dashed line toward the front of the aquarium. At some point two images of the fish disappear. When they disappear, what is their apparent y-distance from the dashed line?

Eye infinitely far away

Apparent y-dist= Value Units

Explanation/Work:

0.2m

Top view of aquarium

120˚

60˚

y

30˚

x

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c) [5 points] Consider the light ray from one of the images that disappeared. Before the image disappeared, the light ray started at the fish, went through the water, refracted at the aquarium wall, and eventually entered your eye.

What was its angle of incidence (in the water) on the aquarium wall? d) [5 points] As the fish swims along the dashed line from the back wall of the

aquarium to the front wall (as in part b), at what distance of the fish from the front wall do you stop seeing three images of the fish?

Angle = Value Units

d = =

Value Units

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4) [25 points total] A telescope has an objective lens of focal length 50 cm and a

converging lens eyepiece with focal length 5 cm. You focus it on a bird 5 m away. At this focus, the eyepiece is 60 cm from the objective.

a) [6 points] At what location is the final image formed by this combination of lenses? b) [4 points] The final image is (circle correct answer) Upright Inverted The final image is (circle correct answer) Real Virtual. c) [5 points] If the bird is 5 cm tall, how tall is the final image formed by the telescope

as set up in the figure?

Objective lens (f=50cm)

Eyepiece lens (f=5cm)

60cm

Height final image = Value Units

Image location =

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d) [5 points] What is the angular magnification of the telescope when it is set up exactly as in the figure, and used to observe the bird 5 m away. You should use the small-angle approximation to calculate the subtended angles. e) [5 points] You now use the telescope to look at the moon. Which way do you need

to move the eyepiece in order to focus the telescope? Circle correct answer and explain.

TowardtheobjectiveAwayfromtheobjective

Angular Magnification = Value

Explanation/Work

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5) [15 pts] A charge of -5 µC is at x=-0.1mm and a charge of +5 µC is at x=+0.1mm as

shown in the figure. ( 1 µC = 10-6C ) a) [5 pts] A charge of +3 µC is put at x = -1mm. Calculate the force on the +3 µC

charge from the pair of ±5µC charges. b) [5 pts] Calculate the electric dipole moment of the

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±5µC charges.

Dipole moment=

Value Units Direction

Force = Value Units Direction

+5µC, x=+0.1mm -5µC, x=-0.1mm +3µC, x=-1.0mm

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c) [5 pts] Two electric dipoles are arranged as shown. What is the direction of the force on the

upper dipole? (You aren’t required to do a calculation, but do give an explanation).

Explanation

+5µC -5µC

+5µC

-5µC

x 

y 

Direction =