lecture29 - light waves and refraction

lecture29 - light waves and refraction - What you will...

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Unformatted text preview: What you will be able to do a/er today … Explain … Calculate … •  the proper3es of light vs. sound •  what proper3es of light change when moving through a medium •  what a refrac3ve index is •  the refrac3ve index •  the new wavelength of a light wave traveling in a medium Apply … knowledge of sound waves to light waves. Think about how a medium changes a situa3on Worksheet: review •  •  A.  B.  C.  D.  E.  A piano tuner strikes his tuning fork (f = 523.3 Hz) and strikes a C-note at the same time. The two have nearly the same frequency and he hears 3.0 beats per second. As he tightens the piano string, the beat frequency decreases to 2.0 beats per second. What is the frequency of the piano string after tightening the string? 520.3 Hz 521.3 Hz 523.3 Hz 525.3 Hz 526.3 Hz Lecture Activities beats & standing waves Relevant textbook sections covered: 21.8 Worksheet 1(a) & 1(b) 1. A piano tuner strikes his tuning fork (f = 523.3 Hz) and strikes a C-note (2"d halmonic) at the same time. The two have nearly the same frequency and he hears 3.0 beats per second. As he tighlens the piano string, the beat frequency decreases to 2.0 beats per second. The length of the piano string is 1.8 m and a linear mass density (¡r) of 8.3 x 10-a kg/m. (a) What are the TWO OPTIONS for the frequency of the piano string beþre tightening? al^^r-r"'-__r {o*r, = Z.o Hz= la,(L"o f, | à {,= szz.e¡z't Z It+ =laz",z l,= l¿.";^¡€-.r. = ça8." rì¿) lt (b) What is the frequency of the piano string beþre and after tightening? Hint: Use the information about the change in tension and the change in beat frequency. -Ll¡ç.n"', t*+\ =L6'z vtâl + q þlx1o!.r* t".t.= Z.ôüz= l€,-f,,**i :> f,,^"*= Szz,zwzLzHz = 571,1 Ylz oR 5 z5 '7\\e kn"w, Ç._0."* > f , (o.: "";.n"ll5) ì+ 6.u'5¡ ho,^ ! o uu., Gzo ZU*l onot ìntvc:'J'r'J +" ^+ TqãA'i*^f is rhe rension in the srring belure tightening, Y tin.<- ,nre (c.) whar V=}'{ [-:-r- ,'./=Å-i t+ ,'¡2 c L n -.s- ,\. r - ,rlI -.:i. ----/-'1--r -7 .# -: t, -r' -l a 3 = 571,1 Ylz oR 5 z5 '7\\e Worksheet Y tin.<- ,nre k1(d)._0."* > f , (o.: "";.n"ll5) 1(c) & n"w, Ç (c.) whar ì+ 6.u'5¡ ho,^ ! o uu., Gzo ZU*l onot ìntvc:'J'r'J +" ^+ TqãA'i*^f is rhe rension in the srring belure tightening, V=}'{ 2ü !r^.*,,. ^; e. t+ [-:-r- ,'¡2 c L n -.s- ,\. r - ,rlI -.:i. ----/-'1--r -7 .# -: t, -r' -l a ,'./=Å-i t f--/ .\ I _ //\ _ I.¿)fi\' /-." <> t-- -t -__, _'/ L + T,= (r,2"\õ+#)(r.B =f+zu q )f (szo'27$ =à % .\.-^3. = ( tu'?\---tT n \.,oo, = E\ .ì \ 428rt I J I 4 Conditions for Constructive and Destructive Interference Constructive Interference path difference (in meters) phase difference (in radians) !x = m! !! = m ! 2" Destructive Interference 1 !x = (m + )! 2 1 !! = (m + ) ! 2" 2 !x !! = 2" + !!0 # EXAMPLE: Sound waves of 40.0 cm wavelength enter the tube shown in the figure. What must be the smallest radius R so that a minimum in the sound level will be heard at the detector at the other end of the tube? GOAL conditions: destructive 1 !x = (m + )! 2 GOAL conditions: smallest radius  m = 0 Worksheet The diagram below shows a snapshot of sound waves continuously emitted from two speakers. a)  What can you say about the type of interference (constructive, destructive, or something in between) occurring at points A, B, and C? A B C Question: combining power & interference The diagram below shows a snapshot of sound waves continuously emitted from two speakers. Rank the intensity at points A to C from the highest to the lowest intensity. A.  B.  C.  D.  E.  B=C>A B>C>A C>A>B B>A>D cannot determine Remember: intensity changes as 1/r2. For a wave, this is represented as a change in amplitude  I ~ A2 A B C Is light a wave? •  Everyday phenomena: Which ones indicate that light might be a wave? Which ones make this hard to believe? 9 We know that sound waves and light waves can pass through a medium (air, water, etc), but can they pass through vacuum ? A.  Neither will move through vacuum, as they need atoms to move up and down (wave on a string) B.  A light wave can pass through vacuum, but a sound wave cannot C.  A sound wave can pass through vacuum, but a light wave cannot D.  Both will move through a vacuum, as there is nothing blocking their propaga3on DEMO Light as a Wave •  Young s two source interference experiment proved that light is a wave. video •  Light usually moves along straight lines but it spreads out when passing through a narrow slit or a small hole ( diffraction ). •  Light has other wave effects: interference, refraction, Doppler effect, shock waves, etc. •  Light also has particle properties, like momentum (recoil of atoms, radiation pressure) •  Duality of light. Quantum physics: particles like protons and electrons possess wave-like properties. 11 The amplitude and frequency of 4 E&M waves are shown below. The waves are representa3ve of one instant in 3me and are all travelling in vacuum. Which wave travels the fastest? (A) (B) (C) (D) (E) All the same The Electromagnetic Spectrum •  All electromagnetic waves have the same properties and show the same effects. •  Just different frequency and energy. Simulation 13 Worksheet •  •  Light is passing through a glass window. True or false? (A: True, B: False) 1.  The wave speed ( speed of light ) is the same in glass and in air. 2.  The frequency is the same in glass and in air. 3.  The wavelength is the same in the glass and in air. 14 Speed of Light and Refractive Index •  c0 = 3.0 x 108 m/s (in vacuum, air) •  Inside glass: different medium so different speed (light interacts with the electrons). •  The refractive index is defined as: n = c0/v Speed of light in a medium   Speed of light in a medium (through which it can pass through, e.g. water, plastic, glass, etc.) is ALWAYS SLOWER than its speed in vacuum (c) c v= n For vacuum n = 1 cvacuum = c ≈ 3.0 × 108 m/s For water n = 1.33 cwater ≈ 2.25 × 108 m/s Medium Index of refraction (n) Vacuum Air Water Alcohol Glycerin Glass Diamond 1 1.000293 1.33 1.36 1.47 1.52 2.42 Wavelength of light in a medium   Frequency does not change as a wave enters from one medium to another   the wave “hits” the medium at the same repetition rate frequency in vacuum = frequency in a medium   As the speed of light is slower in a medium, compared to it’s speed in vacuum, the wavelength of light in a medium is smaller than its wavelength in vacuum. c=!f c !f n= = v !n f ⇒ λn = λ n Worksheet You have an instrument that gives you limited informa3on about light waves travelling through 4 different materials. It gives you a snapshot in 3me and tells you Δd, the distance between two points along the wave in the medium. It also gives you Δt, the 3me it takes for the A ­B wave segment to pass by (or fly by) a sta3onary observer. You want to chose a material through which the light will travel the fastest. Rank the materials, and find the n ­value of each medium B B x Medium 1 A Medium 2 A A Δd = 120 nm B A x Medium 3 x B x Medium 4 Worksheet 3. You have an instrument that gives you limited information about light waves travelling through 4 different materials. gives you a snapshot in time and tells you the distance ^d, between two points along the wave in the medium. It also gives you Àt, the time it takes for that section (A-B) to past a stationary observer. It 1) lT > at = toxto ''s move 61=16¡16t5 t* = ll 3) Àl=2.5x10'ßFf Àt=20¡10,.s (a) Determine the wavelength and frequency for the wave IN each medium r) ¡d--s***r = $.À^ \,.3i3 'rh LÍ :-) Aâ' Ço)o* " '},n IJ " *.C: nvt-, {b P' = ic -- l2xtÙ ,s Ê .-Sxl¡r" it¿ ' ¡óxlo-rbg ff å#r?lrk'; " l?o,¡*" á 1À 6dtnu* .I . Ad " ZËon"'' r IÀn 67'ån"" È ,,\n ,T'f,. z,e rro-tes (b) Find rhe n-value of each mediur ¿a sxro'\r't'e -Ð 't T) , ÞÌ'2-s'\lü p+ ,lÀ r ï.k tds tt" of the lishr passins through each --'Ï Ê .-Sxl¡r" it¿ ' 't Worksheet (b) Find rhe n-value of each mediur ¡¡ .Esdi!!o*'*q-r "[m ê--rr n'3 À"0 *l¡ 3 x rr¡t ñ¡,oq*. \l"'"- 5¡lu'nrb t).fr= 3¡lù*'À ff å#r?lrk'; ^ 3 ¿/) # A 3À lO8*ft xtui "rlt i øoo"rru'^--- grn* ? 6t)on- '/ '' "* Z) fcron* , ì.2 1,8,,* 333t'nu, Ð 6?.5" 60 ï.k tds tt" ?,Jùre*-;¡-r;rr*" r" l, )* ù L,) p+ of the lishr passins through each ãÃFìrirrd't¡* n= l.Z l) l,&ü' , Ad " ZËon"'' r IÀn 67'ån"" È ,,\n ,T'f,. z,e rro-tes -Ð "- n¡* x l.? ' Tlno x l"xe> a ?f ^n^ l,lcr,.rJnoxl\ ('¡ ,* vø(ur,r* ) Worksheet B B x Medium 1 A A Medium 2 x Medium 1 A B From the drawing we know the length of 1.5 wavelengths = 500nm. A B So the wavelength inside the medium is: x =333nm λ x Medium 3 Medium 4 It takes 10 ­15 sec f or half a cycle to pass by (one cycle =T) . 0.5 T = 10 ­15 sec So f= 1/T = 0.5 x 1015 Hz . Speed of the wave is c/n=λ f= 1.66 x 108 m/s; nmedium1 =1.8 Medium 2 From the drawing we know the length of 1.0 wavelengths = 500nm. So the wavelength inside the medium is: λ =500nm It takes 10 ­15 sec for half a cycle to pass by (one cycle =T) . 0.5 T = 10 ­15 sec So f= 1/T = 0.5 x 1015 Hz . Speed of the wave is c/n=λ f= 2.5 x 108 m/s; nmedium 2 =1.2 Medium 3 From the drawing we know the length of 4 wavelengths = 250nm. So the wavelength inside the medium is: λ =62.5nm It takes 0.25 x 10 ­15 sec for a full cycle to pass by (one cycle =T) . T = 0.25 x10 ­15 sec So f= 1/T = 4 x 1015 Hz . Speed of the wave is c/n=λ f= 2.5 x 108 m/s; nmedium 3 =1.2 Medium 4 B From the drawing we know the length of 2 wavelengths = 120 nm. B x x So the wavelength inside the medium is: λ =60 nm A A Medium  ­ Medium 2 It takes 0.25 x 10115 sec for a full cycle to pass by (one cycle =T) . T = 0.25 x 10 ­15 sec So f= 1/T = 4 x 1015 Hz . Speed of the wave is c/n=λ f= 2.4 x 108 m/s; nmedium 4 =1.25 A Δd = 120 nm B x Medium 3 A B x Medium 4 Nmedium 1 =1.8 , nmedium 2 =1.2, nmedium 3 =1.2 , nmedium 4 =1.25 ...
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