Essential University Physics, 3e (Wolfson) 3e (Wolfson) Chapter 32 Interference and Diffraction
3 2. 1 Co nc e pt ua lQue s t i o ns 1) In a double-slit experiment, if the slit separation is increased, which o f the following happens to the interference pattern shown on the screen? A) The minima get closer together. B) The maxima sta at the same position. !) The minima and maxima sta at the same position. ") The minima sta at the same position. #) The maxima get further apart. Answer$ A %ar$ 1
&) In a single-slit diffraction experiment, the width of the slit through which light passes is reduced. 'hat happens to the width of the central bright fringe? A) It stas the same. B) It becomes narrower. !) It becomes wider. ") Its beha(ior depends on the wa(elength of the light. Answer$ ! %ar$ 1
) A single-slit diffraction diffraction pattern is formed on a distant screen. Assuming the angles in(ol(ed are small, b what factor will the width of the central bright spot on the screen change chan ge if the slit width is doubled? A) It will be cut to one-*uarter its original si+e. B) It will be cut in half. !) It will double. ") It will become four times as large. #) It will become eight times as large. Answer$ B %ar$ 1
) A light beam shines through a thin slit and illuminates a distant screen. The central bright fringe on the screen is 1. cm wide, as measured between the dar fringes that border it on either side. 'hich of the following actions would decrease the width of the central bright fringe? /There ma be more than one correct choice.) A) increase the wa(elength of the light B) decrease the wa(elength of the light !) increase the width of the slit ") decrease the width of the slit #) put the apparatus all under water Answer$ B, !, # %ar$ 1
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3) A lens is designed to wor in the (isible, near-infrared, and near-ultra(iolet. The best resolution of this lens from a diffraction standpoint is A) the same for all wa(elengths. B) in the near-ultra(iolet. ne ar-ultra(iolet. !) in the (isible. ") in the near-infrared. n ear-infrared. #) indeterminate. Answer$ B %ar$ 1
) If the diameter of a radar dish is doubled, d oubled, what happens to its resol(ing power assuming that all other factors remain unchanged? A) The resol(ing power *uadruples. B) The resol(ing power doubles. !) The resol(ing power is reduced to 14& of its original (alue. ") The resol(ing power is reduced to 14 of its original (alue. #) The resol(ing power does not change unless the focal length changes. Answer$ B %ar$ 1
3 2. 2 Pr o bl e ms ms 1) In the two-slit experiment, monochromatic light of fre*uenc 3. 5 11 6+ passes through a pair of slits separated b &.& 5 1-3 m. /c 7 . 5 18 m4s) /a) At what angle awa from the central bright spot does the third bright fringe past the central bright spot occur? /b) At what angle does the second dar fringe occur? Answer$ /a) .9: /b) &. &.: %ar$ 1
&) ;ight from a monochromatic source shines through a double slit onto a screen 3. m awa. The slits are .18 mm apart. The dar bands on the screen are measured to be 1.< cm apart. 'hat is the wa(elength of the incident light? A) 3< nm B) nm !) 9& nm ") 1& nm #) <8 nm Answer$ " %ar$ 1
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) In a two-slit experiment, the slit separation is . 5
m. The interference pattern is
recorded on a flat screen-lie detector that is &. m awa from the slits. If the se(enth bright fringe on the detector is 1. cm awa from the central fringe, what is the wa(elength of the light passing through the slits? A) 1 nm B) & nm !) &1 nm ") && nm #) & nm Answer$ ! %ar$ 3
) ;ight of wa(elength 3<3 nm passes through a double-slit and the third order bright fringe is seen at an angle of .3: awa from the central fringe. 'hat is the separation between the double slits? A) 3. =m B) 1 =m !) 13 =m ") & =m #) &3 =m Answer$ ! %ar$ 1
3) In a double slit experiment, if the separation between the two slits is .3 mm and the distance from the slits to a screen is &.3 m, find the spacing between the first-order and secondorder bright fringes when coherent light of wa(elength nm illuminates the slits. A) 1.3 cm B) . cm !) .3 cm ") . cm #) 9. cm Answer$ B %ar$ 1
) In a double-slit experiment, the slit separation is &. mm, and two wa(elengths, <3 nm and 9 nm, illuminate the slits simultaneousl. A screen is placed &. m from the slits. At what distance from the central maximum on the screen will a bright fringe from one pattern first coincide with a bright fringe from the other? A) 1.3 mm B) . mm !) .3 mm ") . mm #) 9. mm Answer$ ! %ar$ 1
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<) ;ight from a nm source goes through two slits .8 mm apart. 'hat is the angular separation of the two first order maxima occurring on a screen &. m from the slits? A) .13: B) .8: !) .13: ") .<3: #) 1.<3: Answer$ B %ar$ 1
8) In a double slit experiment, the slit separation is constructed to be exactl times the wa(elength of the light passing through the slits. At what angles from the center of the pattern will the third bright fringes on both sides of the central fringe occur? A) >8.: B) ><3.: !) ><.3: ") >.9: #) >.: Answer$ A %ar$ 1
9) A double slit illuminated with light of wa(elength 388 nm forms a diffraction pattern on a screen 11. cm awa. The slit separation is & nm. 'hat is the distance between the third and fourth bright fringes awa from the central fringe? A) &.9 cm B) 3.9 cm !) 3.39 cm ") &. cm Answer$ A %ar$ 1
1) Two sources of light illuminate a double slit simultaneousl. ne has wa(elength 3< nm and the second has an unnown wa(elength. The bright fringe of the unnown wa(elength o(erlaps the bright fringe of the light of 3< nm wa(elength. 'hat is the unnown wa(elength? A) 3 nm B) & nm !) 8 nm ") <1 nm Answer$ A %ar$ 3@
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11) A pair of narrow slits, separated b 1.8 mm, is illuminated b a monochromatic light source. ;ight wa(es arri(e at the two slits in phase, an d a fringe pattern is obser(ed on a screen .8 m from the slits. If there are 3. complete bright fringes per cen timeter on the screen near the center of the pattern, what is the wa(elength of the monochromatic light? A) 33 nm B) nm !) 3 nm ") < nm #) <3 nm Answer$ # %ar$ 1
1&) At most, how man bright fringes can be formed on each side of the central bright fringe /not counting the central bright fringe) when light of & 3 nm falls on a double slit whose spacing is A) 1 B) & !) ") #) 3 Answer$ ! %ar$ 3@
1) Two radio antennas are 1& m apart on a north-south line, and the radiate in phase at a fre*uenc of . 6+. All radio measurements are made far from the antennas. If the east-west reference line passes midwa between the two antennas, what is the smallest angle from the antennas, measured north of east, at which constructi(e interference of two radio wa(es occurs? /c 7 . 5 18 m4s) A) : B) &&: !) 8: ") <: #) : Answer$ " %ar$ 1
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1) Two small forward-facing speaers are &.3 m apart. The are both emitting, in phase with each other, a sound of fre*uenc 11 6+ in a room where the speed of sound is m4s. A woman is standing opposite the midpoint between the speaers and is initiall 3. m from the midpoint. As she slowl wals parallel to the line connecting the speaers, at what ang le θ /relati(e to the centerline coming outward from the midpoint be tween the speaers) will she first hear no sound? A) .: B) .: !) <.&: ") 1.8: #) 11: Answer$ B %ar$ 1
13) !oherent monochromatic light of wa(elength &.8 nm passes through a pair of thin parallel slits. The figure shows the central portion of the pattern of bright fringes (iewed on a screen 1. m beond the slits. 'hat is the distance between the two slits?
A) .< mm B) .11 mm !) .&81 mm ") .3& mm #) . mm Answer$ ! %ar$ 1
1) ;ight of wa(elength 319 nm passes through two slits. In the interference pattern on a screen . m awa, adacent bright fringes are separated b 3.& mm in the general (icinit of the center of the pattern. 'hat is the separation of the two slits? Answer$ . mm %ar$ 3@
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1<) onochromatic laser light of fre*uenc 3.& 5 11 6+ is shown on a pair of thin parallel slits, and the pattern is (iewed on a screen 1.& m awa. The fifth bright fringes /not counting the central fringe) occur at >&.1& cm on either side of the central bright fringe. The entire apparatus is now immersed in a transparent li*uid. 'hen the experiment is repeated, the fifth bright fringes now occur at >1. cm from the central bright fringe. /c 7 . 5 18 m4s) /a) 6ow far apart are the slits? /b) 'hat is the index of refraction of the li*uid? Answer$ /a) .1 mm /b) 1.8 %ar$ 1
18) In a double slit experiment, the intensit of light at the center of the central bright fringe is measured to be .& ='4m&. 'hat is the intensit halfwa between the center of this fringe and the first dar band, assuming that the small-angle approximation is (alid? A) .& ='4m& B) .1 ='4m& !) .< ='4m& ") 1. ='4m& #) .1& ='4m& Answer$ B %ar$ 1
19) ;ight passes through a pair of (er thin parallel slits. The resulting interference pattern is (iewed far from the slits at (arious angles θ relati(e to the centerline coming outward from the midpoint between the slits. The central bright fringe is at θ 7 :. If the central bright fringe has intensit I , what is the intensit of the next bright fringe on either side of it? A) I B) I 4 !) I 4& ") I cos 13: #) I cos& 13: Answer$ A %ar$ 1
&) ;ight of wa(elength 3&3 nm passes through two slits separated b .3 mm and produces an interference pattern on a screen <.8 m awa. The intensit at the central maximum is I . 'hat is the distance on the screen from the center of this central maximum to the point where the intensit due to double-slit interference has fallen to 14& I ? Answer$ &.3 mm %ar$ 1
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&1) ;ight of fre*uenc . 5 11 6+ illuminates a soap film /n 7 1.) ha(ing air on both sides of it. 'hen (iewing the film b reflected light, what is the minimum thicness of the film that will gi(e an interference maximum when the light is incident normall on it? /c 7 . 5 18 m4s) A) &. nm B) 9. nm !) 188 nm ") &<9 nm #) < nm Answer$ B %ar$ 1
&&) A thin laer of oil /n 7 1.&3) is on top of a puddle of water /n 7 1.). If normall incident 3-nm light is strongl reflected, what is the minimum non+ero thicness of the oil laer? A) & nm B) &3 nm !) 1 nm ") nm #) 13 nm Answer$ A %ar$ 1
&) 'hite light is incident normall on a thin soap film ha(ing an index of refraction of 1.. It reflects with an interference maximum at 8 nm and an interference minimum at 3< nm with no minima between those two (alues. The film has air on both sides of it. 'hat is the thicness of the soap film? A) < nm B) &< nm !) 8 nm ") 89 nm #) 31 nm Answer$ ! %ar$ 1
&) A coating is being applied to reduce the reflecti(it of a pane of glass to light with a fre*uenc of 3.<3 5 11 6+ that is incident normall on the pane. If the material has an index of refraction of 1.<3 and the glass has an index of refraction of 1.3<, what is the minimum thicness the coating should ha(e? /c 7 . 5 18 m4s) A) . nm B) 9.9 nm !) 13 nm ") 3.& nm #) 8.1 nm Answer$ B %ar$ 1
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&3) Two extremel flat glass plates, 1. cm wide, touch at one end but are separated b a thin wire at the other end, forming a wedge. ;ight with a wa(elength of 3 nm shines almost perpendicularl on the glass and forms fringes which are 1.8 mm apart. 'hat is the diameter of the wire? A) &3. =m B) 1<.3 =m !) &. =m ") 1&.3 =m #) 1. =m Answer$ " %ar$ 1
&) A puddle of water has a thin film of gasoline floating on it. A beam of light is shining perpendicular on the film. If the wa(elength of light incident on the film is 3 nm and the indices of refraction of gasoline and water are 1. and 1., respecti(el, what is the minimum thicness of the film to see a bright reflection? A) 1 nm B) & nm !) nm ") nm #) 3 nm Answer$ A %ar$ 1
&<) A piece of glass has a thin film of gasoline floating on it. A beam of light is shining perpendicular on the film. If the wa(elength of light incident on the film is 3 nm and the indices of refraction of gasoline and glass are 1. and 1.3, respecti(el, what is the minimum non+ero thicness of the film to see a bright reflection? A) 3 nm B) nm !) nm ") & nm #) 1 nm Answer$ " %ar$ 1
&8) A -nm thic oil film floats on the surface of the water. The indices of refraction of the oil and the water are 1.3 and 1., respecti(el. The surface of the oil is illuminated from abo(e at normal incidence with white light. 'hat T' wa(elengths of light in the -nm to 8-nm wa(elength band are most strongl reflected? A) 1 nm and < nm B) nm and <& nm !) 3 nm and < nm ") < nm and < nm #) 9 nm and <8 nm Answer$ B %ar$ 1
&9) ;ight of wa(elength &3. nm in air falls at normal incidence on an oil film that is 83. nm 9 !opright 0 &1 2earson #ducation, Inc.
thic. The oil is floating on a water laer 13 cm thic. The refracti(e index of water is 1., and that of the oil is 1.. Cou want to add oil so that light reflected off of the top of the oil film will be canceled. 'hat is the minimum distance that ou should ID!E#AF# the oil film? A) .< nm B) <3.9 nm !) 1 nm ") 1&1 nm #) 13& nm Answer$ A %ar$ 1
) Two opticall flat glass plates, 1. cm long, are in contact at one end and separated b .& mm at the other end. The space between the plates is occupied b oil with index of refraction 1.3. The index of refraction of the glass plates is 1.33. The plates are illuminated at normal incidence with monochromatic light, and fringes are obser(ed. If the dar fringes are spaced &. mm apart, what is the wa(elength of the monochromatic light? A) &3 nm B) <3 nm !) 3&3 nm ") <3 nm #) <&3 nm Answer$ # %ar$ 1
1) ;ight is incident normall from air onto a li*uid film that is on a glass plate. The li*uid film is 1 nm thic, and the li*uid has index of refraction 1.. The glass has index of refraction n 7 1.3. !alculate the longest (isible wa(elength /as measured in air) of the light for which there will be totall destructi(e interference between the ras reflected from the top and bottom surfaces of the film. /Assume that the (isible spectrum lies between and < nm.) Answer$ 3&3 nm %ar$ 3@
&) A soap bubble, when illuminated with light of fre*uenc 3.11 5 11 6+, appears to be especiall reflecti(e. If it is surrounded b air and if its index of refraction is 1.3, what is the thinnest thicness the soap film can be? /c 7 . 5 18 m4s) Answer$ 19 nm %ar$ 1
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) A single slit forms a diffraction pattern, with the first minimum at an angle of .: from central maximum, when monochromatic light of -nm wa(elength is used. The same slit, illuminated b a new monochromatic light source, produces a diffraction pattern with the second minimum at a .: angle from the central maximum. 'hat is the wa(elength of this new light? A) &3 nm B) 3 nm !) <3 nm ") 3 nm #) 3&3 nm Answer$ A %ar$
) A single slit forms a diffraction pattern, with the first minimum at an angle of .: from central maximum, using monochromatic light of 9-nm wa(elength. 'hat is the width of the slit? A) <& nm B) <1 nm !) < nm ") 8 nm #) < nm Answer$ A %ar$
3) A slit of width .1 mm has light of fre*uenc 3. 5 11 6+ passing through it onto a screen cm awa. 6ow wide is the central maximum? /c 7 . 5 18 m4s) A) .1& cm B) <.& cm !) 1.8 cm ") . cm #) .9 cm Answer$ B %ar$ 1
) A single slit, which is .3 mm wide, is illuminated b light of 33 nm wa(elength. 'hat is the angular separation between the first two minima on either side of the central maximum? A) .: B) .<: !) .3: ") .: #) .<: Answer$ " %ar$ 1
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<) ;ight of wa(elength 8< nm is incident on a single slit .<3 mm wide. At what distance from the slit should a screen be placed if the second dar fringe in the diffraction pattern is to be 1.< mm from the center of the diffraction pattern? A) .9 m B) .< m !) .9 m ") 1.1 m #) 1.9 m Answer$ ! %ar$ 1
8) If the fifth order minimum in the diffraction pattern due to a thin slit is at : from the central maximum, at what angle does the first order minimum occur? A) 8.: B) .: !) .: ") <.: #) 1.<: Answer$ " %ar$ 1
9) If the fifth order minimum in the diffraction pattern of a thin slit is at : from the central maximum, what is the highest order minimum in the p attern? A) B) 11 !) 8 ") < #) 9 Answer$ " %ar$ 1
) A single slit illuminated with a 3 nm light gi(es a diffraction pattern on a far screen. The 3th minimum occurs at <.: awa from the central maximum. At what angle does the 18th minimum occur? A) &.: B) 1.9: !) 3.3: ") .: Answer$ A %ar$ 1
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1) A single slit forms a diffraction pattern with monochromatic light. The th minimum of the pattern occurs at an angle of 3: from the central maximum. 6ow man bright bands are on each side of the central maximum? A) 3 B) !) ") < #) 8 Answer$ A %ar$ 3@
&) A laser beam passes through a thin slit. 'hen the pattern is (iewed on a screen 1.&3 m past the slit, ou obser(e that the fifth-order dar fringes occur at >&.1 cm from the central bright fringe. The entire experiment is now performed within a li*uid, and ou obser(e that each of the fifth-order dar fringes is .<9 cm closer to the central fringe than it was in air. 'hat is the index of refraction of this li*uid? A) 1. B) 1. !) 1.9 ") 1.& #) .3 Answer$ ! %ar$ 1
) In the figure, a slit . mm wide is illuminated b light of wa(elength & nm. A diffraction pattern is seen on a screen &.8 m from the slit. 'hat is the linear distance on the screen between the first diffraction minima on either side of the central diffraction maximum?
Answer$ 8. mm %ar$ 1
) If the central maximum in a single slit diffraction pattern has intensit I , the intensit of the secondar maximum that is nearest to it is closest to A) .3 I . B) I 4. !) I 4&. ") I . #) & I . Answer$ A %ar$ 1 1 !opright 0 &1 2earson #ducation, Inc.
3) A slit of width &. Gm is used in a single slit experiment with light of wa(elength 3 nm. If the intensit at the central maximum is I , what is the intensit 1: from the center? A) .3 I B) . I !) . I ") .3 I #) .3 I Answer$ # %ar$ 1
) A single slit that is &1 nm wide forms a diffraction pattern when illuminated b monochromatic light of 8-nm wa(elength. At an angle of 1: from the central maximum, what is the ratio of the intensit to the intensit of the central maximum? A) I 4 I 7 .3 B) I 4 I 7 .9 !) I 4 I 7 . ") I 4 I 7 .< #) I 4 I 7 .31 Answer$ A %ar$ 3@
<) A thin beam of light of wa(elength &3 nm goes through a thin slit and falls on a screen . m past the slit. Cou obser(e that the first completel dar fringes occur on the screen at distances of >8.& mm from the central bright fringe, and that the central bright fringe has an intensit of &. '4m& at its center. /a) 6ow wide is the slit? /b) 'hat is the intensit of light at a point on the screen that is one-*uarter of the wa from the central bright fringe to the first dar fringe? Answer$ /a) .&&8 mm /b) 1.& '4m& %ar$ 1
8) 'hen monochromatic light illuminates a grating with < lines per c entimeter, its second order maximum is at &.:. 'hat is the wa(elength of the light? A) nm B) nm !) 3& nm ") nm #) <3& nm Answer$ " %ar$ 1
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9) onochromatic light is incident on a grating that is <3 mm wide and ruled with 3, lines. The second-order maximum is seen at &.3:. 'hat is the wa(elength of the incident light? A) && nm B) nm !) 3& nm ") 3 nm #) 8 nm Answer$ B %ar$ 1
3) In a diffraction grating experiment, light of nm wa(elength produces a first-order maximum .3 mm from the central maximum on a distant screen. A second monochromatic source produces a third-order maximum .8< mm from the central maximum when it passes through the same diffraction grating. 'hat is the wa(elength of the light from the second source? A) <9 nm B) 9< nm !) 3< nm ") <9 nm #) <9 nm Answer$ B %ar$ 1
31) A diffraction grating has lines per mm. If light of fre*uenc . < 5 11 6+ is sent through this grating, at what angle does the first order maximum occur? /c 7 . 5 18 m4s) A) 3: B) : !) &&: ") 11: #) &8: Answer$ " %ar$ 1
3&) A diffraction grating has lines per mm. If light of wa(elength nm is sent through this grating, what is the highest order maximum that will appear? A) 8 B) & !) ") 3 #) 3. Answer$ " %ar$ 1
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3) A 6e-De laser, which produces light of wa(elength &.8 nm, is u sed to calibrate a diffraction grating. If the first-order maximum occurs at &.3: from the central spot, what is the distance between the slits of the grating? A) .93 =m B) 1.81 =m !) &.& =m ") .& =m #) .3& =m Answer$ B %ar$ 1
3) onochromatic light of wa(elength 3 nm is incident normall on a diffraction grating. If the third-order maximum of the diffraction pattern is obser(ed at &.: from the central spot, how man TTA; number of maxima can be seen? A) 3 B) < !) 1 ") 11 #) 1 Answer$ " %ar$ 1
33) 'hat is the angular separation of the two second -order spectral lines ha(ing wa(elengths 1< nm and 88 nm using a diffraction grating ha(ing 3 lines4mm? A) 1.: B) 1.3&: !) .813: ") .&: Answer$ A %ar$ 1
3) An 18-mm wide diffraction grating has rulings of 88 lines per mm. onochromatic light of 39 nm wa(elength is incident normall on the grating. 'hat is the largest angle, measured from the central bright spot, at which an intensit maximum is formed? A) 1: B) &9: !) &<: ") &3: #) &: Answer$ A %ar$ 3@
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3<) A diffraction grating has rulings of 89 lines4mm. 'hen white light is incident normall on the grating, what is the longest wa(elength that forms an intensit maximum in the fifth order? A) &&3 nm B) & nm !) &3 nm ") &<3 nm #) nm Answer$ A %ar$ 1
38) A metallic sheet has a large number of slits, 3. mm wide and & cm apart, and is used as a diffraction grating for microwa(es. A wide parallel beam of microwa(es is incident normall on the sheet. If the microwa(e wa(elength is . cm, what is the largest angle awa from the central maximum at which an intensit maximum occurs. A) : B) 9: !) <: ") <9: #) 8: Answer$ A %ar$ 1
39) A metallic sheet has a large number of slits, 3. mm wide and & cm apart, and is used as a diffraction grating for microwa(es. A wide parallel beam of microwa(es is incident normall on the sheet. 'hat is the smallest microwa(e fre*uenc for which onl the central maximum occurs? /c 7 . 5 18 m4s) A) .3 H6+ B) .< H6+ !) 1. H6+ ") 1.3 H6+ #) &. H6+ Answer$ " %ar$ 1
) A diffraction grating has 3 lines per mm. 'hat is the highest order m that contains the entire (isible spectrum from nm to < nm? A) m 7 & B) m 7 !) m 7 ") m 7 3 #) m 7 Answer$ B %ar$ 1
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1) A thin beam of laser light of wa(elength 31 nm passes through a diffraction grating ha(ing 93& lines4cm. The resulting pattern is (iewed on a distant cur(ed screen that can show all bright fringes up to and including >9.: from the central spot. 'hat is the TTA; number of bright fringes that will show up on the screen? A) B) 3 !) 8 ") 9 #) 1 Answer$ " %ar$ 1
&) A thin beam of laser light of wa(elength 31 nm passes through a diffraction grating ha(ing 93& lines4cm. The resulting pattern is (iewed on a distant cur(ed screen that can show all bright fringes up to and including >9.: from the central spot. If the experiment were performed with all of the apparatus under water /which has an index of refraction of 1.), what would be the TTA; number of bright spots that would show up on the screen? A) B) < !) 1& ") 1 #) 1 Answer$ " %ar$ 1
) A diffraction grating is to be used to find the wa(elength of the light in the emission spectrum of a gas. The grating spacing is not nown, but a light ha(ing a nown wa(elength of &.8 nm is deflected b .&: awa from the central maximum in the second order b this grating. ;ight of the wa(elength to be measured is deflected b 8.&: awa from the central maximum in the second order. 'hat is the wa(elength of this light? Answer$ 89 nm %ar$ 3@
) If an x-ra beam of wa(elength 1. 5 1-1 m maes an angle of : with a set of planes in a crstal causing first order constructi(e interference, what is the plane spacing? A) .&8 nm B) .< nm !) .& nm ") .1 nm #) .1 nm Answer$ # %ar$ 1
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3) If an x-ra beam of wa(elength 1. 5 1-1 m maes an angle of &: with a set of planes in a crstal causing first order constructi(e interference, at what angle will the second order line appear? A) : B) &: !) : ") .: #) 11: Answer$ ! %ar$ 1
) !ertain planes of a crstal of halite ha(e a spacing of .99 nm. The crstal is irradiated b a beam of x-ras. irst order constructi(e interference occurs when the beam maes an angle of &: with the planes. 'hat is the wa(elength of the x-ras? A) .1 nm B) .1< nm !) .&1 nm ") .& nm #) .&< nm Answer$ # %ar$ 1
<) A researcher is in(estigating a cubic crstal with x-ras. 6e is looing at Bragg reflection from the planes parallel to the cube faces. 6e finds that when using x-ras of .13 nm a strong first maximum occurs when the beam maes an angle of &.3: with the planes. 'hat is the spacing of adacent atoms in the crstal? Answer$ .&< nm %ar$ 1
8) ;ight of wa(elength 3 nm illuminates a round .3-mm diameter hole. A screen is placed . m behind the slit. 'hat is the diameter of the central bright area on the screen? A) 13 mm B) &< Gm !) <.< mm ") 8 Gm Answer$ A %ar$ 3@
9) ;ight of wa(elength nm from a 6e-De laser passes through a circular aperture and is obser(ed on a screen . m behind the aperture. The diameter of the central bright area is 3. cm. 'hat is the diameter of the aperture? A) 11 Gm B) &. Gm !) Gm ") 9 Gm Answer$ A %ar$ 3@
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<) A radio telescope & m in diameter is used to in(estigate sources emitting a &1-cm wa(elength wa(e. 'hat is the minimum angular separation of the sources that can be resol(ed b this sstem? A) .<: B) .: !) .1: ") .13: #) .&: Answer$ A %ar$ 1
<1) A certain astronomical telescope has a diameter of 3. m. !onsidering onl the limitation due to diffraction, what is the minimum angle of resolution for this telescope at a wa(elength of & nm? A) .111 =rad B) .11 =rad !) .&< =rad ") .13 =rad #) .3 =rad Answer$ " %ar$ 1
<&) A 1-inch telescope /&3. cm in diameter) is used to determine if what appears to be one star is actuall two stars. Ftars are so far awa that the are essentiall point sources. 6ow close /in angle) can the two stars be and still be resol(ed b this telescope if it is focusing light of wa(elength of 33 nm? /!onsider onl the limitation due to diffraction.) A) .& 5 1-8 degree B) &. 5 1- degree !) . 5 1- degree ") 1.3 5 1- degree #) . 5 1-8 degree Answer$ " %ar$ 1
<) If the headlights on a car are separated b 1. m, how far down the road can the be resol(ed if the angular resolution of the ee is 3. 5 1- rad and the person has excellent (ision? A) 1. m B) 3. m !) .8 m ") .3 m #) &. m Answer$ # %ar$ 1
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<) 'hat is the limiting angle of resolution for the ee if the pupil diameter of the ee is . mm, the wa(elength of the light is nm, and index of refraction of the li*uid in the ee is 1.? A) .& mrad B) .&1 mrad !) .1 mrad ") .11 mrad #) .& mrad Answer$ ! %ar$ 1
<3) A camera used for aerial sur(eillance has a lens with a -cm maximum aperture and a &cm focal length. Assume light of 33-nm wa(elength is used and that the resolution of the camera is limited solel b diffraction. 'hat is the angular resolution of the camera at maximum aperture? A) 1. =rad B) &.& =rad !) .& =rad ") .3 =rad #) . =rad Answer$ B %ar$ 1
<) Treat each of our ees as a circular aperture of diameter .3 mm. ;ight of wa(elength 3 nm is used to (iew two point sources that are 89 m distant from ou. 6ow far apart must these two point sources be if the are to be ust resol(ed b our ee? Assume that the resolution is diffraction limited and use EaleighJs criterion. Answer$ 1 cm %ar$ 1
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