57.. (a) For a converging lens with a focal length of 3.50 cm,
find the object distance that will result in an inverted
image with an image distance of 5.00 cm. Use a ray dia­
. gram to verify y.our calculations. (b) Is the image real or
virtual? (c)'What is the.magnification?
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63. An object of height 3.00 cm is placed 12.0 cm from a
diverging lens of focal length -12.0 cm. Draw a ray dia­
gram to find the height and position of the image.
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65. A converging lens has a focal length of 8.00 em.
(a) What are the image distances for objects placed at
these distances from the thin lens: 5.00 em, 14.0 em,
16.0 em, 20.0 em? In each case, describe the image as
real or virtual, upright or inverted, and enlarged or
diminished in size. (b) If the object is 4.00 em high,
what is the height of the image for the object distances
of 5.00 em and 20.0 em?
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1. A 60-kHz radio transmitter sends an electromagnetic
wave to a receiver 21 kIn away. The signal also travels
to the receiver by another path where it reflects from a
0
helicopter as shown. Assume that there is a 180 phase
shift when the wave is reflected. (a) What is the wave­
length ofthis EM waye? (b) Will this situation give con­
structive interference, destructive interference, or
something in between?
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2. A steep cliff west of Lydia's home reflects a 102a-kHz
radio signal from a station that is 74 Ian due east of her
home. If there is destructive interference, what is the mini­
mum distance of the cliff from her home? Assume there
0
is a 180 phase shift when the wave reflects from the cliff.
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. \4. At a science museum, Marlow looks down into a dis­
play case and sees two pieces of very flat glass lying
on top of each other with light and dark regions on the
glass. The exhibit states that monochromatic light with
a wavelength of 550 nm is incident on the glass plates
and that the plates are sitting in air. The glass has an
index of refraction of 1.51. (a) What is the minimum
distance between the two glass plates for one of the
dark'regions? (b) What is the minimum distance
between the two glass plates for one of the light
regi6ns? (c) What is the next largest distance between
the plates for a dark region? [Hint: Do not worry about
the thickness of the glass plates; the thin film is the air
between the plates.]
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17. A thin film
spread over
wavelength
constructive
incidence?
of oil (n = 1.50) of thickness 0.40 J.UlllS
a puddle of water (n = 1.33). For which
in the visible spectrum do you expect
interference for reflection at normal
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26. Light of 650 nm is Inc1dent on two s 1tS. max1mum is
seen at an angle of 4.10° and a minimum of 4.78°. What
is tl,1e order m of the maximum and what is the distance
d between the slits?
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27. You are given a slide with two slits cut into it and asked
how far apart the slits are. You shine white light on the
slide and notice the first-order color spectrum that is,
created on a screen 3:40 ill away. On the screen, the red
light with a wavelength of 700 nm is separated from the
violet light with a wavelength of 400 nm by 7.00 rom.
What is the separation of the two slits?
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~36. A grating has exactly 8000 slits uniformly spaced over
I
2.54 cm and is illuminated by light from a mercury vapor
discharge lamp. What is the expected angle for the
third-order maximum of the green line (A, = 546 nm)?
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37. A red line (wavelength 630 nm) in the third order over­
laps with a blue line in the fourth order for a particular
grating. What is the wavelength of the blue line?
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-38. Red light of 650 nm can be seen in three orders in a par­
l'n A
ticular grating. About how many slits per centimeter
does this grating have?
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