Essential University Physics, 3e (Wolfson) Chapter 29 Maxwell's Equations and Electromagnetic Waves Waves
2 9. 1 Co nc e pt ua lQue s t i o ns 1) A capacitor is hooked up to a resistor and an AC voltage source as shown in the figure. The output of the source is given by V (t ) = V 0 sin t t . The plates of the capacitor are disks of radius R radius R.. !oint P !oint P is is directly between the two plates" e#uidistant fro$ the$ and a distance R distance R%& %& fro$ the center a'is. At point P point P
A) there is no $agnetic field because there is no charge $oving between the plates. ) there is a constant $agnetic field. C) there is a ti$evarying $agnetic field. Answer* C +ar* 1
&) ,hich one of the following lists is a correct representation of electro$agnetic waves fro$ longer wavelength to shorter wavelengthA) radio waves" infrared" $icrowaves" +" visible" visible" /rays" ga$$a rays ) radio waves" +" /rays" /rays" $icrowaves" infrared" visible" ga$$a rays C) radio waves" $icrowaves" visible" /rays" infrared" +" ga$$a rays ) radio waves" $icrowaves" infrared" visible" +" /rays" ga$$a rays ) radio waves" infrared" /rays" $icrowaves" +" visible" ga$$a rays Answer* +ar* 1
2) 3n an electro$agnetic wave" the electric and $agnetic fields are oriented such that they are A) parallel to one another and perpendicular to the direction of wave propagation. ) parallel to one another and parallel to the direction of wave propagation. C) perpendicular to one another and perpendicular to the direction of wave propagation. ) perpendicular to one another and parallel to the direction of wave propagation. Answer* C +ar* 1
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6) 3f the $agnetic field of an electro$agnetic wave is in the 7 xdirection and the electric field of the wave is in the 7 ydirection" the wave is traveling in the A) xy- plane. ) 7 z direction. C) z direction. ) x-direction. ) ydirection. Answer* C +ar* 1
8) An electro$agnetic wave is propagating towards the west. At a certain $o$ent the direction of the $agnetic field vector associated with this wave points vertically up. The direction of the electric field vector of this wave is A) hori9ontal and pointing south. ) vertical and pointing down. C) hori9ontal and pointing north. ) vertical and pointing up. ) hori9ontal and pointing east. Answer* A +ar* 1
5) An electro$agnetic wave propagates along the 7 y direction as shown in the figure. 3f the electric field at the origin is along the 7 z direction" what is the direction of the $agnetic field-
A) 7 z ) z C) 7 y ) 7 x ) x Answer* +ar* 1
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:) The energy per unit volu$e in an electro$agnetic wave is A) e#ually divided between the electric and $agnetic fields. ) $ostly in the electric field. C) $ostly in the $agnetic field. ) all in the electric field. ) all in the $agnetic field. Answer* A +ar* 1
;) 3f an electro$agnetic wave has co$ponents E y = E 0 sin(kx t ) and B z = B0 sin(kx t ) " in what direction is it travelingA) x ) 7 x C) 7 y ) y ) 7 z Answer* +ar* 1
<) ,hen an electro$agnetic wave falls on a white" perfectly reflecting surface" it e'erts a force F on that surface. 3f the surface is now painted a perfectly absorbing black" what will be the force that the sa$e wave will e'ert on the surfaceA) 6 F ) & F C) F ) F %& ) F %6 Answer* +ar* 1
2 9 . 2 Pr o bl e ms 1) iven that the wavelengths of visible light range fro$ 600 n$ to :00 n$" what is the highest fre#uency of visible light- (c = 2.0 ' 10; $%s) A) 2.1 > 10; ?9 ) :.8 > 1016 ?9 C) &.2 > 10&0 ?9 ) 6.2 > 1016 ?9 ) 8.0 > 10; ?9 Answer* +ar* 1
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&) The $agnitude of the electric field at a point P for a certain electro$agnetic wave is 8:0 @%C. ,hat is the $agnitude of the $agnetic field for that wave at P - (c = 2.0 ' 10; $%s) A) &.<1 T ) 1.<0 T C) 1.10 T ) 1.61 T ) &.61 T Answer* +ar* 1
2) The $agnitude of the $agnetic field at point P for a certain electro$agnetic wave is &.1& BT. ,hat is the $agnitude of the electric field for that wave at P - (c = 2.0 ' 10; $%s) A) 525 @%C ) :68 @%C C) 8.&2 @%C ) 5.25 @%C ) :.68 @%C Answer* A +ar* 1
6) 3f the electric field and $agnetic field of an electro$agnetic wave are given by E = E 0 sin(kx ωt ) and B = B0 sin(kx ωt )" and if the value of E 0 is 81 +%$" what is the value of B0- (c = 2.0 ' 10; $%s) A) 1.: > 1016 T ) 1.: > 102 T C) 1.: > 1016 T ) 1.: > 106 T ) 1.: > 1012 T Answer* +ar* 1
8) A planar electro$agnetic wave is propagating in the 7 x direction. At a certain point P and at a given instant" the electric field of the wave is given by
= (0.0;& +%$) . ,hat is the $agnetic
vector of the wave at the point P at that instant- (c = 2.0 ' 10; $%s) A) 0.&: nT ) 0.&: nT C) 0.&: nT ) 5.; nT ) 5.; nT Answer* A +ar* 1
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5) 3f the z co$ponent of the $agnetic field of an electro$agnetic wave traveling in the 7 x direction through vacuu$ obeys the e#uation B z ( x" t ) = (1.&8 BT) cos(2;00 $1) x (1.16 > 10 1& rad%s)t D" what is the largest that the y co$ponent of the electric field can be- (c = 2.0 ' 10; $%s) A) 2:8 @%C ) 6.1: > 1018 @%C C) 2.:8 > 10; @%C ) 6.1: > 10< @%C ) 1.&8 > 105 @%C Answer* A +ar* 1
:) The y co$ponent of the electric field of an electro$agnetic wave traveling in the 7 x direction through vacuu$ obeys the e#uation E y = (2:8 @%C) coskx (&.&0 > 1016 rad%s)t D. ,hat is the wavelength of this electro$agnetic wave- (c = 2.0 ' 10; $%s) A) 0.&:& $ ) 1.25 $ C) &.:& $ ) ;.8: $ ) 1:.1 $ Answer* +ar* 1
;) The yco$ponent of the electric field of an electro$agnetic wave traveling in the 7 x direction through vacuu$ obeys the e#uation E y = (2:8 @%C) coskx (&.&0 > 1016 rad%s)t D. (c = 2.0 ' 10; $%s) (a) ,hat is the largest that the x-co$ponent of the wave can be(b) ,hat is the largest that the z-co$ponent of the wave can beAnswer* (a) 9ero (b) 1.&8 T +ar* 1
<) A planar electro$agnetic wave is propagating in the 7 x direction. At a certain point P and at a given instant" the electric field of the wave is given by
= (0.0;& +%$) . ,hat is the !oynting
vector at the point P at that instant- (c = 2.0 ' 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 10 1& C&%@ E $&) A) 1; ,%$& ) 1; ,%$& C) <.0 ,%$& ) <.0 ,%$& ) 1; ,%$& Answer* A +ar* 1
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10) The $agnitude of the !oynting vector of a planar electro$agnetic wave has an average value of 0.:&6 ,%$&. ,hat is the $a'i$u$ value of the $agnetic field in the wave- (c = 2.0 ' 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) ::.< nT ) 88.1 nT C) 2;.< nT ) 10; nT ) 185 nT Answer* A +ar* 1
11) The $agnitude of the !oynting vector of a p lanar electro$agnetic wave has an average value of 0.<2< ,%$&. The wave is incident upon a rectangular area" 1.8 $ by &.0 $" at right angles. ?ow $uch total electro$agnetic energy falls on the area during 1.0 $inute- (c = 2.0 ' 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 1:0 F ) &10 F C) &80 F ) 200 F ) 260 F Answer* A +ar* 1
1&) The $agnetic field of an electro$agnetic wave has a peak value of 8.0 > 1010 T. ,hat is the intensity of the wave- (c = 2.0 ' 10; $%s" c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 1.0 > 1012 ,%$& ) 1.8 > 108 ,%$& C) 2.0 > 108 ,%$& ) &.0 > 1012 ,%$& ) :.8 > 108 ,%$& Answer* C +ar* 1
12) A sinusoidal electro$agnetic wave in vacuu$ delivers energy at an average rate of 8.00 ,%$&. ,hat are the a$plitudes of the electric and $agnetic fields of this wave- (c = 2.0 ' 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) Answer* $a' = 0.0516 +%$" B$a' = 0.&08 nT +ar* 1
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16) 3f the intensity of an electro$agnetic wave is ;0 G,%$&" what is the a$plitude of the $agnetic field of this wave- (c = 2.0 ' 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 0.;& $T ) 0.22 T C) 10 T ) 16 T ) 0.8; $T Answer* A +ar* 1
18) A laser with a power of 1.0 $, has a bea$ radius of 1.0 $$. ,hat is the peak value of the electric field in that bea$- (c = 2.0 ' 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 6<0 +%$ ) ;60 +%$ C) 58 +%$ ) 1&0 +%$ ) && +%$ Answer* A +ar* 1
15) 3f a bea$ of electro$agnetic radiation has an intensity of 1&0 ,%$&" what is the $a'i$u$ value of the electric field- (c = 2.0 ' 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 1.8 k+%$ ) 1.0 T C) 1.0 +%$ ) 0.20 k+%$ ) 0.002& +%$ Answer* +ar* 1
1:) @ear the earth the intensity of radiation fro$ the sun is 1.28 k,%$&. ,hat volu$e of space in this region contains 1.0 F of electro$agnetic energy- (c = 2.0 ' 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 6.8 ' 105 $2 ) 2200 $2 C) :.6 ' 106 $2 ) 1600 $2 ) &&0"000 $2 Answer* +ar* 1
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1;) An electro$agnetic wave has a peak electric field of 2.0 k+%$. ,hat is the intensity of the wave- (c = 2.0 ' 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) &6 k,%$& ) 1& k,%$& C) ;.0 k,%$& ) 6.0 k,%$& Answer* +ar* 1
1<) An ;00k?9 radio signal is detected at a point 6.8 k$ distant fro$ a trans$itter tower. The electric field a$plitude of the signal at that point is 0.52 +%$. Assu$e that the signal power is radiated unifor$ly in all directions and that radio waves incident upon the ground are co$pletely absorbed. ,hat is the $agnetic field a$plitude of the signal at that point- (c = 2.0 ' 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) &.1 nT ) 1.: nT C) 1.2 nT ) &.8 nT ) &.< nT Answer* A +ar* 1
&0) An ;00k?9 radio signal is detected at a point ;.8 k$ distant fro$ a trans$itter tower. The electric field a$plitude of the signal at that point is 0.<0 +%$. Assu$e that the signal power is radiated unifor$ly in all directions and that radio waves incident upon the ground are co$pletely absorbed. ,hat is the average electro$agnetic energy density at that point- (c = 2.0 ' 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 2.5 pF%$2 ) 8.1 pF%$2 C) :.& pF%$2 ) 10 pF%$2 ) 16 pF%$2 Answer* A +ar* 1
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&1) An ;00k?9 radio signal is detected at a point &.: k$ distant fro$ a trans$itter tower. The electric field a$plitude of the signal at that point is 0.25 +%$. Assu$e that the signal power is radiated unifor$ly in all directions and that radio waves incident upon the ground are co$pletely absorbed. ,hat is the intensity of the radio signal at that point- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 1:0 ,%$& ) &60 ,%$& C) 260 ,%$& ) 1&0 ,%$& ) ;5 ,%$& Answer* A +ar* 1
&&) An ;00k?9 radio signal is detected at a point <.1 k$ distant fro$ a trans$itter tower. The electric field a$plitude of the signal at that point is 0.66 0 +%$. Assu$e that the signal power is radiated unifor$ly in all directions and that radio waves incident upon the ground are co$pletely absorbed. ,hat is the average total power radiated b y the trans$itter- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 0.&: G, ) 0.2& G, C) 0.2; G, ) 0.68 G, ) 0.80 G, Answer* A +ar* 1
&2) A radio$eter has two s#uare vanes (each $easuring 1.0 c$ by 1.0 c$)" attached to a light hori9ontal cross ar$" and pivoted about a vertical a'is through the center" as shown in the figure. The center of each vane is 5.0 c$ fro$ the a'is. Hne vane is silvered and it reflects all radiant energy incident upon it. The other vane is blackened and it absorbs all incident radiant energy. An electro$agnetic wave with an intensity of 0. 20 k,%$& is incident nor$ally upon the vanes. ,hat is the electro$agnetic power absorbed by the blackened vane- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&)
A) 0.020 , ) 0.060 , C) 0.080 , ) 0.050 , ) 0.0<0 , Answer* A +ar* 1 < Copyright 4 &015 !earson ducation" 3nc.
&6) A $icrowave oven operates with sinusoidal $icrowaves at a fre#uency of &600 G?9. The height of the oven cavity is &8 c$ and the base $easures 20 c$ by 20 c$. Assu$e that $icrowave energy is generated unifor$ly on the up per surface of the cavity and propagates directly downward toward the base. The base is lined with a $aterial that co$pletely absorbs $icrowave energy. The total $icrowave energy content of the cavity is 0.80 F. ,hat is the a$plitude of the electric field- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 1500 +%$ ) 1<00 +%$ C) &&00 +%$ ) &800 +%$ ) &;00 +%$ Answer* C +ar* 1
&8) A $icrowave oven operates with sinusoidal $icrowaves at a fre#uency of &600 G?9. The height of the oven cavity is &8 c$ and the base $easures 20 c$ by 20 c$. Assu$e that $icrowave energy is generated unifor$ly on the up per surface of the cavity and propagates directly downward toward the base. The base is lined with a $aterial that co$pletely absorbs $icrowave energy. The total $icrowave energy content of the cavity is 0.80 F. ,hat is the power output of the oven- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 0.80 k, ) 0.88 k, C) 0.50 k, ) 0.58 k, ) 0.:0 k, Answer* C +ar* 1
&5) A $icrowave oven operates with sinusoidal $icrowaves at a fre#uency of &600 G?9. The height of the oven cavity is &8 c$ and the base $easures 20 c$ by 20 c$. Assu$e that $icrowave energy is generated unifor$ly on the up per surface of the cavity and propagates directly downward toward the base. The base is lined with a $aterial that co$pletely absorbs $icrowave energy. The total $icrowave energy content of the cavity is 0.80 F. ,hat is the intensity of the $icrowave bea$- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 10 1& C&%@ E $&) A) 8.& k,%$& ) 8.: k,%$& C) 5.& k,%$& ) 5.: k,%$& ) :.& k,%$& Answer* +ar* 1 10 Copyright 4 &015 !earson ducation" 3nc.
&:) A :.8 × 1016 ?9 laser e$its a :.:Bs pulse" 8.0 $$ in dia$eter" with a bea$ energy density of 0.81 F%$2. ,hat is the a$plitude of the electric field of the e$itted waves- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 260 k+%$ ) 6;0 k+%$ C) &60 k+%$ ) 180 k+%$ ) 1&0 k+%$ Answer* A +ar* 1
&;) &;)A sinusoidal electro$agnetic wave is propagating in vacuu$. At a given point P and at a particular ti$e" the electric field is in the 7 x direction and the $agnetic field is in the y direction. (a) ,hat is the direction of propagation of the wave(b) 3f the intensity of the wave at point P is
what is the electric field a$plitude at
that point- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) Answer* (a) z direction (b) 15 +%$ +ar* 807
&<) A very s$all source of light that radiates unifor$ly in all directions produces an electric field a$plitude of &.<5 +%$ at a point 22.0 $ fro$ the source. ,hat is the power output fro$ the source- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) Answer* 18< , +ar* 807
20) The average intensity of the sunlight in Gia$i" Ilorida" is 1. 06 k,%$&. Ior surfaces on which the light is all absorbed" what is the average value of the radiation pressure due to this sunlight in Gia$i- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) &.&; !a ) 1.:2 !a C) 5.<2 !a ) 2.6: !a ) <.:; !a Answer* +ar* 1
21) The intensity of solar radiation near the earth is 1.6 k,%$&. ,hat force is e'erted by solar radiation i$pinging nor$ally on a 8.0 $& perfectly reflecting panel of an artificial satellite orbiting the earth- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 16 k@ ) <6 @ C) 160 @ ) &2 @ ) 6: @ Answer* +ar* 1 11 Copyright 4 &015 !earson ducation" 3nc.
2&) The total electro$agnetic power e$itted by the sun is 2.; > 10&5 ,. ,hat is the radiation pressure on a totally absorbing satellite at the orbit of Gercury" which has an orbital radius of 8.; > 1010 $- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 20 !a ) 0.20 !a C) 0.020 !a ) 200 !a ) 2.0 !a Answer* A +ar* 1
22) A &&.0kg $irror with a surface area of 1.0 $& and a reflectivity is bo$barded by light of average intensity at an angle of to the nor$al of its surface. 3f the light has a duration of how $uch does the velocity of the $irror change during that ti$e- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 1&0 n$%s ) 6.& n$%s C) 2.5 n$%s ) &.1 n$%s Answer* A +ar* 807
26) A radio$eter has two s#uare vanes (1.0 c$ by 1.0 c$)" attached to a light hori9ontal cross ar$" and pivoted about a vertical a'is through the center" as shown in the figure. The center of each vane is 5.0 c$ fro$ the a'is. Hne vane is silvered and it reflects all radiant energy incident upon it. The other vane is blackened and it absorbs all incident radiant energy. An electro$agnetic wave with an intensity of 0.20 k,%$& is incident nor$ally upon the vanes. ,hat is the radiation pressure on the blackened vane- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&)
A) 1.0 > 1010 !a ) 1.0 > 10< !a C) 1.0 > 10; !a ) 1.0 > 10: !a ) 1.0 > 105 !a Answer* +ar* 1
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28) A radio$eter has two s#uare vanes (1.0 c$ by 1.0 c$)" attached to a light hori9ontal cross ar$" and pivoted about a vertical a'is through the center" as shown in the figure. The center of each vane is 5.0 c$ fro$ the a'is. Hne vane is silvered and it reflects all radiant energy incident upon it. The other vane is blackened and it absorbs all incident radiant energy. An electro$agnetic wave with an intensity of 0.20 k,%$& is incident nor$ally upon the vanes. ,hat is the tor#ue due to radiation pressure on the vane asse$bly about the vertical a'is- (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&)
A) &.6 > 101& ) 5.0 > 101& C) 1.& > 1011 ) 1.; > 1011 ) &.6 > 1011 Answer*
@E$ @E$ @E$ @E$ @E$
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25) A $icrowave oven operates with sinusoidal $icrowaves at a fre#uency of &600 G?9. The height of the oven cavity is &8 c$ and the base $easures 20 c$ by 20 c$. Assu$e that $icrowave energy is generated unifor$ly on the up per surface of the cavity and propagates directly downward toward the base. The base is lined with a $aterial that co$pletely absorbs $icrowave energy. The total $icrowave energy content of the cavity is 0.80 F. ,hat $agnitude force does the $icrowave bea$ e'ert on the base of the oven- (c = 2.00 > 10; $%s" μ0 = 6π > 10 : T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) A) 1.5 @ ) &.0 @ C) &.8 @ ) 2.0 @ ) 2.8 @ Answer* +ar* 1
2:) A totally absorbing surface having an area of :.: c$& faces a s$all source of sinusoidal electro$agnetic radiation that is &.6 $ away. At the surface" the electric field a$plitude of the radiation is ;6 +%$. (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) (a) ,hat is the radiation pressure e'erted on the surface(b) ,hat is the total power output of the source" if it is assu$ed to radiate unifor$ly in all directionsAnswer* (a) 0.021 !a (b) 5;0 , +ar* 1
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2;) A laser bea$ has a wavelength of 522 n$ and a power of 0.800 $, spread unifor$ly over a circle 1.&0 $$ in dia$eter. This bea$ falls perpendicularly on a perfectly reflecting piece of paper having twice the dia$eter of the laser bea$ and a $ass of 1.80 $g. (c = 2.00 > 10; $%s" μ0 = 6π > 10: T E $%A" ε0 = ;.;8 > 101& C&%@ E $&) (a) ,hat are the a$plitudes of the electric and $agnetic fields in this laser bea$(b) ,hat acceleration does the laser bea$ give to the paperAnswer* (a) 8:: @%C" 1.<& T (b) &.&& $%s& +ar* 1
2<) Jight of intensity I 0 and polari9ed hori9ontally passes through three polari9es. The first and third polari9ing a'es are hori9ontal" but the second one is oriented &0.0K to the hori9ontal. 3n ter$s of I 0" what is the intensity of the light that passes through the set of polari9ersA) 0.:;0 I 0 ) 0.1;0 I 0 C) 0.66& I 0 ) 0.;;2 I 0 Answer* A +ar* 1
60) !olari9ed light passes through a polari9er. 3f the electric vector of the polari9ed light is hori9ontal what" in ter$s of the initial intensity I 0" is the intensity of the light that passes through a polari9er if the polari9er is tilted &&.8K fro$ the h ori9ontalA) 0.;86 I 0 ) 0.16: I 0 C) 0.1<1 I 0 ) 0.011 I 0 Answer* A +ar* 1
61) npolari9ed light is incident upon two polari9ation filters that do not have their trans$ission a'es aligned. 3f of the light passes through this co$bination of filters" what is the angle between the trans$ission a'es of the filtersA) 82K ) :2K C) ;8K ) ;0K Answer* A +ar* 21
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6&) npolari9ed light passes through three polari9ing filters. The first one is oriented with a hori9ontal trans$ission a'is" the second filter has its trans$ission a'is &8.:K fro$ the hori9ontal" and the third one has a vertical trans$ission a'is. ,hat percent of the light gets through this co$bination of filtersA) :.5L ) <&.6L C) 80.0L ) 0.00L Answer* A +ar* 1
62) 3n the figure" the orientation of the trans$ission a'is for each of three polari9ing sheets is labeled relative to the vertical direction. A bea$ of light" polari9ed in the vertical direction" is incident on the first polari9ed with an intensity of 1000 ,%$&. ,hat is the intensity of the bea$ after it has passed through the three polari9ing sheets when θ 1 = 20K" θ & = 20K and θ 2 =50K-
A) 161 ,%$& ) 215 ,%$& C) 622 ,%$& ) 852 ,%$& ) 1;; ,%$& Answer* +ar* 1
66) The following are positioned in se#uence* A source of a bea$ of natural light of intensity I 0M three ideal polari9ers A" B" and C M and an observer. !olari9er a'is angles are $easured clockwise fro$ the vertical" fro$ the perspective of the observer. The a'is angle of polari9er A is set at 0K (vertical)" and the a'is angle of polari9er C is set at 80K. !olari9er B is set so that the bea$ intensity is 9ero at the observer. ,hich of the following pairs of angles are possible a'is angle settings of polari9er BA) 60K and <0K ) 60K and 120K C) 60K and 160K ) <0K and 120K ) <0K and 160K Answer* +ar* 1
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