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lecture34 - interference two slit and diffration grating-

# lecture34 - interference two slit and diffration grating- -...

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Unformatted text preview: What you will be able to do a/er today … Explain … Calculate … •  how to recognize an interference pa8ern arising from two ­slit interference vs. diﬀrac?on gra?ng •  how to count fringes on a graph •  the y ­posi?on of the interference fringes Apply … •  knowledge of interference from two ­slit to many slits (diﬀrac?on gra?ng) •  the concept of path diﬀerence Surveys: 101 survey  Survey Monkey (emailed link) \$10 \$10 I depend on feedback from you. •  worksheets •  clickers •  pre ­reading •  general improvement \$5 as an incen?ve: STARBUCKS gi/ cards! Lo8ery on the last day of class \$20 in the pot now  for every 10 students who ﬁll in the survey, another \$5 gi/ card goes into the pot Young’s double slit interference !x = sin ! ! ! d can use small angle approxima?on because d >> λ ! ! some nm (10"9 ) d ! some mm (10"3 ) L ! some meters (1) y = tan ! ! ! L can use small angle approxima?on because L >> d bright fringes start with m = 0 then count dark fringes start with m = 0 third bright fringe m = 2 second bright fringe m = 1 ﬁrst bright fringe central bright fringe (central bright fringe) m = 0 m = 0 m = 1 m = 2 !L ybright = m d m = 0, ± 1, ± 2 … ydark ! 1\$ !L = #m + & m = 0, ± 1, ± 2 … 2% d " Young’s double slit interference m = 3 y3 m = 2 m = 1 y1 width of screen m = 0 m = 1 m = 2 Δy Δy m = 3 !L 7 bright fringes on the screen ybright = m d = 1 central (m = 0) + 6 ‘side’ fringes (m = 1, m=2, m=3) x2 m = 0, ± 1, ± 2 … worksheet A laser beam is passing through a double ­slit and produces an interference pa8ern that is captured on a screen 3.5 m behind the two slits. The wavelength of the laser is 633 nm. If a total of 181 bright fringes are captured on a 1.0m ­wide screen, what is the separa?on of the two slits? sugges?on: draw a ﬁgure! Lecture Agtivities worksheet two-slit interference & diffraction grating Name Relevant textbook sections covered: 22.2 and22.3 l. A laser beam is passing through a double-slit and produces an interference pattern that is cgpQred on a screen 3.5 m behind the two slits. The wavelength of the laser is 633 nm. If a total dSJfîigñTEiGà are captured on a 1.Om-wide screen, what is the separation of the tvvo slits? of +/,¡nh +he besl *% þ S"/ve *hfs is taV dra*^fi + yic:l*e' T a^,t L4 L/¿'.f t4e oç;U s 3=ry à= W^ U ð10 _â 35l, . 6-33Xo 'rrt , 4,o o.(\ '= 0.4 ry¡+ L.t +lv êcalut Í &tt,*¿- -à ru = O f4ø^ ymmclå t qÞ'^¿l *{+ ! fehe,h 9 2. Look at the figure. What is the total path difference between the Hint first think about how the path differs between eachruy. I't and the 4ú ruy? Many-Wave Interference •  CDs = Diffraction grating •  Diffraction (Huygen s principle) •  Multilayer thin films (beetles) 2µm 8 •  Excel: Interference of 8 waves Diffraction Gratings •  Many parallel slits (~500/mm) with constant spacing. (Or reflective bumps on CD.) •  Each slit: source for a wave •  Waves from all slits interfere. •  All waves are in phase only for a few, sharp angles: constructive interference, huge intensity enhancement. •  For all other angles, the waves (mostly) cancel each other. Worksheet 9 interference pattern from a diffraction grating because the distance between slits (1000 x10-9 m) is CLOSE to the size of a wavelength (100 x10-9 m)  can NOT use the small-angle approximation !x = sin ! d (use degree mode) y = tan ! L inθ Δx = ds Reflection Gratings •  If you shine white light on a grating, the light splits into its colored components. •  For each wavelength, constructive interference is obtained at a certain angle for each order m given by the grating equation. (same as for double slit) d sin θ = mλ interference pattern from a diffraction grating DEMO worksheet Is the pattern due to two-slit interference or a diffraction grating? How can you tell? EXPLAIN. Can you use the small-angle approximation here? Yes/No Question Is the pattern due to two-slit interference or a diffraction grating? Can you use the small-angle approximation here? A. diffraction grating, NO small angle, two-slit interference YES small angle B. diffraction grating, YES small angle, two-slit interference YES small angle C. two-slit interference, diffraction grating NO small angle, YES small angle D. two-slit interference, diffraction grating YES small angle, NO small angle worksheet 3. The figure shows the interference paffern on a screen 1.0-m away. (a) Is the paffern due to two-slit interference or a diffraction grating? ffi 89.7 f= W= € cm /\ / 43.6 cm \ 89.7 cm 43.6 cm (b) If the wavelength of the light is 600 nm, what is the slit spacing, d? L*rg = \$= ?_3.b" dsi ^6¡= G'l rr\ J^ l:4- ftlç asY"¿Lt è*a,10-- g'- 53" : - ?' [ ' ó¿ÐÀuÍ1l, sM ¿23.6:) !> += è? îzt '3\<- I ) {t'-bv'5L't fu^XzS s¡fr2.c) ¡¡nl'"s wììr^ # a= S;= 2-i?1""= r.sxrI!,- 4. The figure shows the light intensity on a screen some distance away. a) Is the pattern due to two-slit interference or a diffraction gtating? Ho* you tell? Can you use the small-angle Intensity (mV//mz) here? EXPLAIN. approximation "* -Wï'î;'#J'ä"îr"^'t^ 12 >l lY"''='^ dr'= o''t?L^ ftlç sM ¿23.6:) s¡fr2.c) ¡¡nl'"s wììr^ è*a,10-- += g'- 53" !> è? a= S;= 2worksheet -i?1""= r.sxrI!,- 4. The figure shows the light intensity on a screen some distance away. a) Is the pattern due to two-slit interference or a diffraction gtating? Ho* you tell? Can you use the small-angle Intensity (mV//mz) here? EXPLAIN. approximation "* -Wï'î;'#J'ä"îr"^'t^ q iw-s/;L Ù,lerþft"¿u siæ b;";-fu 12 +/^ø peaþc are no/ln"- hvb.&fL) ^/ n'enb 'r4 YeS Sha¿l a,g/c <fVnxìotrït ', un Ëi-"'üäf*be,< AhP= I 2.0 cm ,h.tt=t (b) If the wavelength of the light is 600 nm, and d is 0.20 mm, then how far away is the screen? (can you use the small-angle approximation here? YesÀ{o) t^^3,!4JL , d 1r d zl- 1 r |yl-^ /x/{Lw, * t" LX /ftn, L " óÐOx/o ?*, L = /. 67,," 4==- ...
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