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 twoslit interference & diffraction grating Name Relevant textbook sections covered: 22.2 and22.3 l. A laser beam is passing through a doubleslit 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.Omwide 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, . 633Xo '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? ManyWave 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 x109 m)
is CLOSE to the size
of a wavelength
(100 x109 m)
can NOT use the
smallangle
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 twoslit interference or a diffraction
grating? How can you tell? EXPLAIN.
Can you use the smallangle approximation here? Yes/No Question
Is the pattern due to twoslit interference or a diffraction
grating? Can you use the smallangle approximation here? A. diffraction grating,
NO small angle, twoslit interference
YES small angle B. diffraction grating,
YES small angle, twoslit interference
YES small angle C. twoslit interference, diffraction grating
NO small angle,
YES small angle
D. twoslit interference, diffraction grating
YES small angle,
NO small angle worksheet
3. The figure shows the interference paffern on a screen 1.0m away.
(a) Is the paffern due to twoslit 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;= 2i?1""= r.sxrI!, 4. The figure shows the light intensity on a screen some distance away.
a) Is the pattern due to twoslit interference or a diffraction
gtating? Ho*
you tell? Can you use the smallangle 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 twoslit interference or a diffraction
gtating? Ho*
you tell? Can you use the smallangle Intensity (mV//mz)
here? EXPLAIN.
approximation "*
Wï'î;'#J'ä"îr"^'t^ q iws/;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 smallangle approximation here? YesÀ{o) t^^3,!4JL , d 1r d zl 1 r yl^ /x/{Lw, * t" LX /ftn, L " óÐOx/o ?*, L = /. 67,,"
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 Winter '08
 BATES
 Physics, Diffraction, Wavelength, Diffraction grating, twoslit interference

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