8)_Interference_and_Diffraction_230607_132506

pdf

School

University of Notre Dame *

*We aren’t endorsed by this school

Course

43900

Subject

Physics

Date

Jan 9, 2024

Type

pdf

Pages

Uploaded by UltraLemur862

Deckruckive Wtertevence for asingle Slit: Dsinb=mX firm=,£2.43,.. Mol phase dngle : B=2="050 Ficld amplitvde 1 ine diffractin patieen : E=NaE 52 TitenSity W 4ie diefraction pattern - =1, (SHE): Payleigh Griterion for Giroular apertures : =125 Eroqq equation ‘wh=2dsing, m=12,3,.. A= p=1n 3 dsinG=m) | T=TI,c0s*(6) dsing=(m+5)2 | tan(6e)= 2

Question 1 (1 points) What is the wavelength of light falling on double slits separated by Zfifi_umdthemu:d.mder_mamn is at an angle of 55.2° ”0 A= dSING — 2 bbSin(55.22) x 1000 nm =128 nm m 3 I pm Question 2 (1 points) What is the smf f%t se??[a ion be een two slits that will produce a ed ||ght7 mA Z(bOSxIO“) I: I d‘ Sih = Sin(40°) 1000 nm ”Mo |2tf'“ I Question 3 (1 points) Shown below is a double slit located a distance z from a screen, with the distance from the center of the screen given by y. When the distance d between the slits is relatively large, numerous bright spots appear, called fringes. For small angles (where sin 8 =~ 6, with 6 in radians), the distance between fringes is given by Ay = z/\fd (try prove this yourself). Calculate the distance between fringes for 630-nm light falling on double slits separated by 0.0800 mm, located 3.22 m from a screen d X Image size: s m L Max Screen T XA _ 322030007 | e AY=d 000> | 2dom Question 4 (1 points) Calculate the minimum thickness of an oil slick on water that appears blue when illuminated by white light perpendicular to its surface. Take the specific shade of blue wavelength to be 460 nm and the index of refraction of the oil to be 1.58. {1y;} bve 5= A AnT N Aair "|50 Dair= sy gy - Linm 2+°-_ = I Xm_ 2¢1| {12.9mm |

Question 5 (1 points) Wn’\v" A thin film with . :“1.32 is surrounded by _air. What is the minimum thickness of this film such that the reflection of normally incident light with A = 587%1111 is minimized? Question 6 (1 points) A film of oil on water will appear dark when it is very thin, because the path length difference becomes small compared with the wavelength of light and there is a phase shift at the top surface. If it becomes (@rk when the path length difference is less than one-fourth the wavelengthqwhat is the thic i isi ? This particular type of oil has an index of refraction of 1.46, Take u%m-n to be the shortest visible wavelength in air n Path lengin diff : P=24, = Ami ! ﬂV\d. 2"’"\”“"—":*“_ 3 Amin _ 313%070 " twax=_ 8N~ 8(14L) = 318 x157%= 219 x1079={319nm Question 7 (1 points) The thickness of an aluminum foil is measured using a Michelson interferometer that has its movahle mirror mounted on a micrometer. There is a difference of 27 fringes In the observed interference pattern when the micrometer clamps down on the foil compared to when the micrometer is empty. Calculate the thickness of the foil assuming that the light source He Ne laser used has a wavelength of 629 nre. mlo_ 27629 x10-3) _; 4d=.—z?—_#’_—)~_&t\°|pm Question 8 (1 points) n A soap bybble with index of refraction n.=_1.3 and a thickness of 325nm*When illuminated by white light and \iewed directly (perpendicular to the surface), what wavelength'in the visible spectrum (375nm to 725nm) will be strongly reflected? Tym= A q(g—u;)(\_g).: 1690 > 125 nm 2d=MmX a=4dn _4EBBN3) TVt n M ? ™YWM=2, AR - gyg > 726 wm 2 m=3 2B29013). [563]< 126 mm |

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Question 9 4 (1 points) A diffraction.qrating has 3.20e+3 lines_per centimeter. At what angle will the ﬂrst—o”«a’r maximum be for 520-nmtwavelength green light? . -|‘[v_nl]_' [ 15200 7 B=sinL T 1780 | Zao0me 935" Question 10 (1 points) The characters of a stadium scoreboard are formed with closely spaced lightbulbs that radiate primarily yellow light. (Use A =587 nm.) How closely must the bulb aced so that an observer 39.2 m away sees a display of continuous lines rather than the individual bulbs? Assume that the pupil of the observer’s eye has a diameter of 5.65 mm. A X 1.222d _ 1.22(587x10 N33.2%10%) _—— gy =i s=3 —~x=" S0t [0M97 o] Goser Xedist blw 2 oljects pX Waveleng’rh of h'gh‘r D dlitimeter of observing lens ol distaince biw 0USETVeY iens andojeot Question 11 (1 points) The structure of the NaCl rysta!_{Trms reflecting planes 0.541 nm apart. What is the smallest angl ,Pfi@sfi ed from these planes, at which X-ray diffraction can be observed, if X-rays of wavelength 0.0846 nm are used? . A a8 ] 2d81h9=m>\—?9=31n! 2d -.swl'[ .2‘(0—._5q‘|)_] H4%' Question 12 (1 points) The structure of the NaCl crystal forms reflecting planes 0.541 nm apart. What is the smallest angle, measured from these planes, at which X-ray diffraction can be observed, if X-rays of wavelength 0.0846 nm are used? AW aS |, (oL | Question 13 (1 points) Calculate the wavelength of light that has its seconmaer maximum at 45.0° ehen falling on a diffraction grating that has 6.07e+3 lines per centimeter. 4 . dSInD _ 147 sinlys®) _ i dSnp=mA—> A=—m =" =2 [582nm d=_tem 7 am_ 47 nm LOTxp® ltm o lines

Question 14 (1 points) Find the waveleg\gth of light that has its thlLd.u!l“nllmm at an angle of 42.8"@hen it falls on a single slit of width 3.06 glnd . A SInG _ 3060 Sin(42.3%) dsinb=mA—=> A=~ "3 W% mm d=30bpmy 10> nm — ed hm T pm Question 15 (1 points) In Young's double slit experiment, the bright spots correspond to Select the correct answer Q there are no bright spots in the double slit experiment Q regions of either constructive or destructive interference QO regions of destructive interference @ regions of constructive interference Question 16 (1 points) As the width of the slit producing a single-slit diffraction pattern is reduced, how will the diffraction pattern produced change? Select the correct answer @ _The diffraction pattern becomes wider. QO The diffraction pattern becomes narrower. Q The diffraction pattern does not change. QO cCannot be determined without more information. Question 17 (1 points) In Young's double slit experiment, the dark spots correspond to Select the correct answer Q there are no dark spots in the double slit experiment @ regions of destructive interference QO regions of constructive interference QO regions of either constructive or destructive interference Question 18 (1 points) For a single slit, the path difference A is related to the angle between the point on the screen and the slit # and the width of the slit D by the following equation. Select the correct answer QO The path difference is constant for a single slit | O Dcos(f) @ Dsin®) QO sin@@) /D O D%sin(d)

8)_Interference_and_Diffraction_230607_132506

Related Documents