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Unformatted text preview: Physics 171.102 Exam 3 Answers November 20, 2008 Prof. Barnett Write your TA’s name, conference time and your name on each blue book. Write everything
in ink. You may utiiize materiai written on both sides of ONE 3”x5” index card. Copy the foiiowing declaration onto your blue book inside cover and sign it. I agree to compiete this exam without receiving unauthorized assistance from any person,
materiai or device. 1. A thin film of water (71mm 2 1.35) lies on a ﬂat pane of glass (7191,17,, x 1.50). It is
illuminated normaily from above with white light containing wavelengths ranging from 400 nm to 700 nm. The thickness of the water layer is 4.00 X if)"7 m. A) (10 pts) What phase shifts occur during the reﬂections from the interface between
the air and water layers and the interface between the water and glass layers?
Ad) 2 7r radians at each interface. B) (10 pts) What phase change would a light beam with wavelength A = 500 nm
undergo as it travels through the water iayer from the water / air interface to the
. water / glass interface and back to the water / air interface?
Agb x 13.6 radians. C) (10 pts) Which wavelength(s) of the incident white light would be missing in the
reﬂected radiation? 432 nm '2. A light emitter, E, and receiver, R, are a distance L’
apart in the 8’ system of our standard special reiativity
geometry. The emitter, IE, is at located at X}; and the 5'
receiver is at X’ : X}; + L’ in the 3’ system. The 3’
system moves at speed '0 in the positive X direction in the -- ,_-_ L, _ if,
5' system. The origins of the S and 8’ systems overlap L Measured in Sr when t and 15’ each equal 0.0. A very short light flash is I 53'
emitted at t’ t 0 and travels toward the receiver. 0 W A) (5 pts) At what time, t’R, as measured in the 8’ system does the light fiash arrive
' at the receiver? is a L’ / c. B) (5 pts) What is the position, X E, of the emitter as measured in the 5' system when
the light ﬂash is emitted? X E 2 7X5 C) (5 pts) What is the position of the receiver, X R, as measured in the 3 system when
the light ﬂash is received by the receiver? X R x we, + L’ + “HE/c). D) (5 pts) What is the time, 7513, as measured in the 6‘ system when the light flash is
emitted by the emitter? t5 2 '1va f5 / c2. E) (5 pts) What is the time, 15R, as measured in the 5' system when the Eight ﬂash is
received by the receiver? 753 = o/(L’/c + + L’)/c2). F) (10 pts) From the distance traveied, AX, by the light flash between when it was
emitted and received as measured in the S system and the time difference, At, between when it was emitted and received as measured in the 5' system, calculate 93-. Comment on whether your result is what rcu would ex set.
A: 3 i3
At = 7LT} -i- v/c)/c, AX : c, as expected. AXE’YL’U‘i'v/C): z;
TURN PAGE OVER 3. The adjacent figure shows a candle 1 meter to the left
of a converging lens. Beyond the lens is a flat mirror
rotated by 45 degrees relative to the axis of the lens and
candle system. The distance of the mirror from the lens
along the central axis is 1.5 m. The magnitude of the
focal length of the lens is ‘50 cm. The candle is 2 cm tall.
The “bottom” of the candle is marked with “B” in the
diagram. A) (5 pts) ignore the ﬂat mirror for the moment and
draw a clear ray diagram to locate the image of the
candle formed by the lens. State whether the image
is real, virtual, upright or inverted. Real and inverted. Plane mirror B) (5 pts) Still ignoring the flat mirror, ﬁnd mathematically the location of the candles image relative to the lens.
Image is 1 meter to the right of the lens. C) (5 pts) What is the magnitude of the height of the candle’s image made by the lens?
The image is 2 cm tall. D) (5 pts) Now include the ﬂat mirror in the system.
Draw a clear ray diagram to locate the image of
the candle formed by the lens and mirror system.
State whether the image formed by the mirror is
real or virtual. What is the orientation of image
of the candle, is is it upright or inverted relative
to the original candle orientation, or is the image
rotated by some amount relative to the original can—
dle orientation. If it is rotated, by how much is it
rotated? The image is virtual and is rotated by 900 with the ﬂame on the right. E) (10 pts) Find mathematically the location of the bottom, B, of the candle in the
image of the candle formed by the flat mirror, i.e. what is the location of the image]
of the bottom of the candle horizontally and vertically relative to the center of
the converging lens? :1:=l.5m,y=(}.5 m. F) (5 pts] What is the magnitude of the height of the candle’s image made by the ﬂat
mirror, i.e. what is the distance between the bottom of the candle and the top of the flame in the image formed by the ﬂat mirror?
The image is still 2 cm long. ...
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