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8/15/2019 Chapter 22 Problems
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PROBLEMS
1, 2, 3 = straightforward, intermediate, challenging = full solution available in Student Solutions
Manual/Study Guide = biomedical application
Section 22.1 The Nature of Light
1. During the Apollo X Moon landing, a retro!
reflecting panel was erected on the Moon"s
surface# $he speed of light may be found by
measuring the time it ta%es a laser beam to travel
from &arth, reflect from the panel, and return to
&arth# f this interval is measured to be '#() s,
what is the measured speed of light* $a%e the
center!to!center distance from &arth to the Moon
to be +#- . ) m# Assume the Moon is directlyoverhead and do not neglect the si0es of &arth
and the Moon#
2. 1igure 2''#' shows the apparatus used by
Armand 3# 4# 1i0eau 5))67)689 to measure
the speed of light# $he basic idea is to measure
the total time it ta%es light to travel from some
point to a distant mirror and bac%# f d is the
distance between the light source and the mirror
and if the transit time for one round trip is t , then
the speed of light is c = 'd /t # $o measure the
transit time, 1i0eau used a rotating toothed
wheel, which converts an otherwise continuous
beam of light to a series of light pulses# $he
rotation of the wheel controls what an observer
at the light source sees# 1or e:ample, assume
that the toothed wheel of the 1i0eau e:periment
has +8 teeth and is rotating at a speed of ';#(rev/s when the light from the source is
e:tinguished<that is, when a burst of light
passing through opening A in 1igure 2''#' is
bloc%ed by tooth B on return# f the distance to
the mirror is ; ( m, find the speed of light#
Figure P22.2
3. n an e:periment to measure the speed of lightusing the apparatus of 1i0eau described in the
preceding problem, the distance between light
source and mirror was ))#-( %m and the wheel
had ;' notches# $he e:perimentally determined
value of c was '#66 . ) m/s# alculate the
minimum angular speed of the wheel for this
e:periment#
4. Albert A# Michelson very carefully measuredthe speed of light using an alternative version of
the techni>ue developed by 1i0eau# 5See
2roblem '#9 1igure 2''#- shows the approach he
used# 4ight was reflected from one face of a
rotating eight!sided mirror toward a stationary
mirror +(# %m away# At certain rates of rotation,
the returning beam of light was directed toward
the eye of an observer as shown# 5a9 ?hat
minimum angular speed must the rotating mirror
have in order that side A will have rotated to
position @, causing the light to be reflected to
the eye* 5b9 ?hat is the ne:t!higher angular
velocity that will enable the source of light to be
seen*
Figure P22.4
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5. 1igure 2''#( shows an apparatus used to
measure the speed distribution of gas molecules#
t consists of two slotted rotating dis%s separated
by a distance d , with the slots displaced by the
angle θ # Suppose the speed of light is measured by sending a light beam toward the left dis% of
this apparatus# 5a9 Show that a light beam will beseen in the detector 5that is, will ma%e it through
both slots9 only if its speed is given by c = d /θ ,
where is the angular speed of the dis%s and θ
is measured in radians# 5b9 ?hat is the measured
speed of light if the distance between the two
slotted rotating dis%s is '#( m, the slot in the
second dis% is displaced )/8 of one degree from
the slot in the first dis%, and the dis%s are
rotating at ( ((( rev/s*
Figure P22.5
Section 22.3 Reflection and Refraction
Section 22.4 The Law of Refraction
6. $he two mirrors in 1igure 2''#8 meet at a
right angle# $he beam of light in the vertical
plane P stri%es mirror ) as shown# 5a9 Determine
the distance the reflected light beam travels
before stri%ing mirror '# 5b9 n what direction
does the light beam travel after being reflected
from mirror '*
Figure P22.6
. An underwater scuba diver sees the Sun at an
apparent angle of -(#B from the vertical# ?hat
is the actual direction of the Sun*
!. 4ight is incident normally on a )#!cm layerof water that lies on top of a flat 4ucite plate
with a thic%ness of #( cm# 3ow much more
time is re>uired for light to pass through this
double layer than is re>uired to traverse the
same distance in air 5n4ucite = )#(69*
". A laser beam is incident at an angle of +#B
to the vertical onto a solution of corn syrup in
water# f the beam is refracted to )6#'-B to the
vertical, 5a9 what is the inde: of refraction of the
syrup solution* Suppose the light is red, with
vacuum wavelength 8+'# nm# 1ind its 5b9wavelength, 5c9 fre>uency, and 5d9 speed in the
solution#
1#. 1ind the speeds of light in 5a9 flint glass, 5b9
water, and 5c9 0ircon#
11. 4ight of wavelength C in vacuum has a
wavelength of -+ nm in water and a
wavelength of +6 nm in ben0ene# 5a9 ?hat is
the wavelength C of this light in vacuum* 5b9
sing only the given wavelengths, determine the
ratio of the inde: of refraction of ben0ene to thatof water#
12. 4ight of wavelength -+8 nm in air enters a
fishbowl filled with water, then e:its through the
crown!glass wall of the container# 1ind the
wavelengths of the light 5a9 in the water and 5b9in the glass#
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13. A ray of light is incident on the surface of a
bloc% of clear ice at an angle of -#B with the
normal# 2art of the light is reflected and part is
refracted# 1ind the angle between the reflected
and refracted light#
14. A narrow beam of sodium yellow light 5C =(6 nm9 is incident from air on a smooth surface
of water at an angle of θ ) = +(#B# Determine the
angle of refraction θ ' and the wavelength of the
light in water#
15. A beam of light, traveling in air, stri%es the
surface of mineral oil at an angle of '+#)B with
the normal to the surface# f the light travels at
'#); = ) m/s through the oil, what is the angle
of refraction*
16. A flashlight on the bottom of a -#!m!deepswimming pool sends a ray upward and at an
angle so that the ray stri%es the surface of the
water '# m from the point directly above the
flashlight# ?hat angle 5in air9 does the emergingray ma%e with the water"s surface*
1. 3ow many times will the incident beam
shown in 1igure 2''#); be reflected by each of
the parallel mirrors*
Figure P22.1
1!. A ray of light stri%es a flat, '#!cm!thic%
bloc% of glass 5n = )#(9 at an angle of +#B
with the normal 51ig# 2''#)9# $race the light beam through the glass and find the angles of
incidence and refraction at each surface#
Figure P22.1!
1". ?hen the light ray in 2roblem ) passes
through the glass bloc%, it is shifted laterally bya distance d 51ig# 2''#)9# 1ind the value of d #
2#. 1ind the time re>uired for the light to pass
through the glass bloc% described in 2roblem )6#
21. $he light beam shown in 1igure 2''#')
ma%es an angle of '#B with the normal line
NN E in the linseed oil# Determine the angles θ
and θ E# 5$he refractive inde: for linseed oil is
)#-#9
Figure P22.21
22. A submarine is + m hori0ontally out from
the shore and ) m beneath the surface of the
water# A laser beam is sent from the sub so that it
stri%es the surface of the water at a point ') m
from the shore# f the beam Fust stri%es the top of
a building standing directly at the water"s edge,
find the height of the building#
23. $wo light pulses are emitted simultaneously
from a source# $he pulses ta%e parallel paths to a
detector 8#' m away, but one moves through air
and the other through a bloc% of ice# Determine
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the difference in the pulses" times of arrival at
the detector#
24. A narrow beam of ultrasonic waves
reflects off the liver tumor in 1igure 2''#'-# f
the speed of the wave is )# less in the liver
than in the surrounding medium, determine the
depth of the tumor#
Figure P22.24
25. A beam of light both reflects and refracts at
the surface between air and glass as shown in
1igure 2''#'(# f the inde: of refraction of the
glass is n g , find the angle of incidence θ ) in the
air that would result in the reflected ray and the
refracted ray being perpendicular to each other#H Hint: Iemember the identity sin56B 7 θ 9 = cos
θ #J
Figure P22.25
26. $hree sheets of plastic have un%nown
indices of refraction# Sheet ) is placed on top of
sheet ', and a laser beam is directed onto the
sheets from above so that it stri%es the interface
at an angle of '8#(B with the normal# $he
refracted beam in sheet ' ma%es an angle of
+)#;B with the normal# $he e:periment is
repeated with sheet + on top of sheet ' and, with
the same angle of incidence, the refracted beam
ma%es an angle of +8#;B with the normal# f the
e:periment is repeated again with sheet ) on topof sheet +, what is the e:pected angle of
refraction in sheet +* Assume the same angle ofincidence#
2. An opa>ue cylindrical tan% with an open top
has a diameter of +# m and is completely filled
with water# ?hen the afternoon Sun reaches an
angle of '#B above the hori0on, sunlight ceases
to illuminate the bottom of the tan%# 3ow deep
is the tan%*
2!. A cylindrical cistern, constructed below
ground level, is +# m in diameter and '# m
deep and is filled to the brim with a li>uid whoseinde: of refraction is )#(# A small obFect rests on
the bottom of the cistern at its center# 3ow far
from the edge of the cistern can a girl whose
eyes are )#' m from the ground stand and stillsee the obFect*
Section 22.5 $i%&er%ion and Pri%'%
2". $he inde: of refraction for red light in water
is )#++), and that for blue light is )#+-# f a ray
of white light enters the water at an angle of
incidence of +#B, what are the underwaterangles of refraction for the blue and red
components of the light*
3#. A certain %ind of glass has an inde: of
refraction of )#8( for blue light of wavelength
-+ nm and an inde: of )#8)( for red light ofwavelength 8 nm# f a beam containing these
two colors is incident at an angle of +#B on a
piece of this glass, what is the angle between the
two beams inside the glass*
31. A ray of light stri%es the midpoint of oneface of an e>uiangular 58B!8B!8B9 glass prism
5n = )#(9 at an angle of incidence of +B# 5a9
$race the path of the light ray through the glass,
and find the angles of incidence and refraction at
each surface# 5b9 f a small fraction of light is
also reflected at each surface, find the angles of
reflection at these surfaces#
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32. $he inde: of refraction for violet light in
silica flint glass is )#88 and that for red light is
)#8'# ?hat is the angular dispersion of visible
light passing through an e>uilateral prism of
ape: angle 8#B if the angle of incidence is(#B* 5See 1ig# 2''#+'#9
Figure P22.32
Section 22.! Total (nternal Reflection
33. alculate the critical angles for the following
materials when surrounded by airK 5a9 0ircon, 5b9
fluorite, 5c9 ice# Assume that C = (6 nm#
34. 1or (6!nm light, calculate the critical angle
for the following materials surrounded by airK5a9 diamond and 5b9 flint glass#
35. Iepeat 2roblem +- when the materials are
surrounded by water#
36. A beam of light is incident from air on the
surface of a li>uid# f the angle of incidence is
+#B and the angle of refraction is ''#B, find
the critical angle for the li>uid when surrounded
by air#
3. A light pipe consists of a central strand of
material surrounded by an outer coating# $he
interior portion of the pipe has an inde: of
refraction of )#8# f all rays stri%ing the interior
walls of the pipe with incident angles greater
than (6#(B are subFect to total internal reflection,what is the inde: of refraction of the coating*
3!. Determine the ma:imum angle θ for which
the light rays incident on the end of the light
pipe in 1igure 2''#+ are subFect to total internal
reflection along the walls of the pipe# Assume
that the light pipe has an inde: of refraction of
)#+8 and that the outside medium is air#
Figure P22.3!
3". onsider a common mirage formed by
super!heated air Fust above a roadway# A truc%
driver whose eyes are '# m above the road,
where n = )# +, loo%s forward# She has the
illusion of seeing a patch of water ahead on the
road, where her line of sight ma%es an angle of)#'B below the hori0ontal# 1ind the inde: of
refraction of the air Fust above the road surface#
5 Hint: $reat this as a problem in total internal
reflection#9
4#. A Fewel thief hides a diamond by placing iton the bottom of a public swimming pool# 3e
places a circular raft on the surface of the water
directly above and centered on the diamond, as
shown in 1igure 2''#-# f the surface of the
water is calm and the pool is '# m deep, find
the minimum diameter of the raft that would prevent the diamond from being seen#
Figure P22.4#
41. A room contains air in which the speed ofsound is +-+ m/s# $he walls of the room aremade of concrete, in which the speed of sound is
) ( m/s# 5a9 1ind the critical angle for total
internal reflection of sound at the concrete!air
boundary# 5b9 n which medium must the sound
be traveling in order to undergo total internal
reflection* 5c9 LA bare concrete wall is a highly
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8/15/2019 Chapter 22 Problems
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first day of spring, light from the rising Sun
enters a rectangular window in the eastern wall#
$he light traverses '#+; m hori0ontally to shine
perpendicularly on the wall opposite the
window# A prisoner observes the patch of lightmoving across this western wall and for the first
time forms his own understanding of the rotationof the &arth# 5a9 ?ith what speed does the
illuminated rectangle move* 5b9 $he prisoner
holds a small s>uare mirror flat against the wall
at one corner of the rectangle of light# $he
mirror reflects light bac% to a spot on the eastern
wall close beside the window# 3ow fast does the
smaller s>uare of light move across that wall*
5c9 Seen from a latitude of -#B north, the rising
Sun moves through the s%y along a line ma%ing
a (#B angle with the southeastern hori0on# n
what direction does the rectangular patch of
light on the western wall of the prisoner"s cellmove* 5d9 n what direction does the smaller
s>uare of light on the eastern wall move*
4". As shown in 1igure 2''#-6, a light ray isincident normally on one face of a +B!8B!6B
bloc% of dense flint glass 5a prism9 that is
immersed in water# 5a9 Determine the e:it angle
θ - of the ray# 5b9 A substance is dissolved in the
water to increase the inde: of refraction# At what
value of n' does total internal reflection cease at
point P *
Figure P22.4"
5#. A narrow beam of light is incident from air
onto a glass surface with inde: of refraction)#(8# 1ind the angle of incidence for which the
corresponding angle of refraction is one half theangle of incidence# 5 Hint: Oou might want to use
the trigonometric identity sin 'θ = ' sin θ cos θ #9
51. Nne techni>ue to measure the angle of a prism is shown in 1igure 2''#()# A parallel
beam of light is directed on the ape: of the
prism so that the beam reflects from opposite
faces of the prism# Show that the angular
separation of the two reflected beams is given by
B = ' A#
Figure P22.51
52. A -#!m!long pole stands vertically in a
la%e having a depth of '# m# ?hen the Sun is-#B above the hori0ontal, determine the length
of the pole"s shadow on the bottom of the la%e#
$a%e the inde: of refraction for water to be )#++#
53. A piece of wire is bent through an angle θ #
$he bent wire is partially submerged in ben0ene
5inde: of refraction = )#(9 so that to a person
loo%ing along the dry part, the wire appears to
be straight and ma%es an angle of +#B with the
hori0ontal# Determine the value of θ #
54. ?hen you loo% through a window, by howmuch time is the light you see delayed by having
to go through glass instead of air* Ma%e an
order!of!magnitude estimate on the basis of data
you specify# @y how many wavelengths is it
delayed*
55. A transparent cylinder of radius R = '# m
has a mirrored surface on its right half, as shown
in 1igure 2''#((# A light ray traveling in air is
incident on the left side of the cylinder# $heincident light ray and the e:iting light ray are
parallel and d = '# m# Determine the inde: ofrefraction of the material#
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Figure P22.55
56. A laser beam stri%es one end of a slab ofmaterial, as in 1igure 2''#(8# $he inde: of
refraction of the slab is )#-# Determine the
number of internal reflections of the beam
before it emerges from the opposite end of theslab#
Figure P22.56
5. 1or this problem, refer to 1igure ''#)(# 1or
various angles of incidence, it can be shown that
the deviation angle δ is a minimum when the ray
passes through the glass so that the interior ray
is parallel to the base of the prism# A
measurement of this minimum angle of
deviation enables one to find the inde: ofrefraction of the prism material# Show that n is
given by the e:pression where A is the ape:
angle of the prism#
n =
+
'sin
9J5'
)Hsin min
A
A δ
5!. A hi%er stands on a mountain pea% near
sunset and observes a rainbow caused by water
droplets in the air about # %m away# $he
valley is '# %m below the mountain pea% andentirely flat# ?hat fraction of the complete
circular arc of the rainbow is visible to thehi%er*
5". A light ray is incident on a prism and
refracted at the first surface, as shown in 1igure
2''#(6# 4et φ represent the ape: angle of the
prism and n its inde: of refraction# 1ind, in
terms of n and φ, the smallest allowed value of
the angle of incidence at the first surface for
which the refracted ray will not undergo internal
reflection at the second surface#
Figure P22.5"