Unformatted text preview: What you will be able to do a/er today … Explain … Calculate … • the path diﬀerence for light interference in a 2
slit experiment • what are dark and bright ‘fringes’ • the y
posiAon of interference fringes Apply … • knowledge of interference from sound to light • the concept of path diﬀerence Surveys • UBC teaching evaluaAon (email sent out) • CLASS survey on VISTA worth 0.5% BONUS marks (by DEC 10) Surveys: 101 survey I depend on feedback from you. • worksheets • clickers • pre
reading • general improvement as an incenAve: STARBUCKS gi/ cards $10 EACH! Lo\ery on the last day of class $20 in the pot now for every 10 students who ﬁll in the survey another $5 goes into the pot $10 Interference from a Soap Film
• Ray 1 undergoes a phase change of
180° with respect to the incident ray
• Ray 2, which is reflected from the
lower surface, undergoes no phase
change with respect to the incident
wave 1 2
Air initial phase difference
path difference Soap Film
n = 1.35 t Air
3 4 The initial phase difference between the two reflected
rays, 1 and 2, is:
incident A. zero radians
B. π/2 radians
C. π radians
D. 3π/2 radians
E. 2π radians 1 2
n=1
n=2
n = 1.5 Worksheet
A thin film with n = 2 is located on material with a
refractive index of n = 1.5. When viewed straight on
(perpendicular), the film appears blue (λ=512nm)
and has no red (λ= 640nm) color.
What is the minimum thickness of the film?
Ans. 320 nm
incident 1 2
n=1
n=2
n = 1.5 ‘thin film’ applied to an air gap
air gap increases in width
from center to edge
changing path
difference
At the center, where the
path difference is 0, there
is only a difference in
phase
At a given radius, there will
be either destructive or
constructive interference Young s Double Slit Experiment, Setup
The light passing through
two slits form a visible
pattern on a screen
The pattern consists of a
series of bright and dark
bands called fringes
Constructive interference
occurs where a bright
fringe occurs
Destructive interference
results in a dark fringe S1
S2 d L equally spaced
(path difference change of λ) Interference Patterns
• Constructive
interference occurs at
the center point
• The two waves travel
the same distance
therefore, they arrive in
phase Interference Patterns
• At R, The upper wave travels
onehalf of a wavelength
farther than the lower wave.
The trough of the bottom
wave overlaps the crest of the
upper wave. This is
destructive interference
A dark fringe occurs
At Q, The upper wave travels
one wavelength farther than
the lower wave. Therefore,
the waves arrive in phase.
A bright fringe occurs Young’s double slit interference !x
= sin ! ! !
d ! ! some nm (10"9 )
d ! some mm (10"3 )
L ! some meters (1) y
= tan ! ! !
L
can use small angle approximaAon Δx Δx = d sinθ Δx = r2 − r1 = d sin(θ )
This assumes that the paths are parallel
Not exactly, but a very good approximation (L >> d)
The positions of a point on the screen can be given by:
(1) the angle that the point makes with respect to the central axis
(2) or the vertical distance of the point from the central axis y = L tan(θ )
! ! some nm (10"9 )
d ! some mm (10"3 )
L ! some meters (1)
can use small angle approximaAon !x
= sin ! ! !
d y
= tan ! ! !
L 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 ybright = m λL
d m = 0, ± 1, ± 2 K 1 ȹ λ L
ȹ ydark = ȹ m + ȹ
m = 0, ± 1, ± 2 K
2 Ⱥ d
ȹ Interference Equations: final
• For bright fringes
sources in phase: constructive Δx = mλ
ybright = m λL
d m = 0, ± 1, ± 2 K • For dark fringes
ydark 1 ȹ λ L
ȹ = ȹ m + ȹ
m = 0, ± 1, ± 2 K
2 Ⱥ d
ȹ sources in phase: destructive Δx = (m+ ½)λ Examples
• Red light (λ=664 nm) is used in Young s experiment according to
the drawing. Find the distance y on the screen between the central
bright and the thirdorder bright fringe. Ans y = 0.046 m In the previous example, what is the total phase difference
between the waves from the two sources at the location of the
third (m = 3) bright fringe? A. zero radians
B. π radians
C. 2π radians
D. 4π radians
E. 6π radians
one wavelength is 2π, so m = 3 has three wavelengths,
or 6π, separation from the central fringe worksheet
A gas mixture is used as a light source in a double
slit experiment. The source emits light at 550 nm
and 400 nm.
(a) What is the lowest order 550 nm bright fringe
that will fall on a 400 nm dark fringe? Ans. m = 4
(b) What is the order for the 400 nm dark fringe? Is it
Ans. m = 5, m values are NOT the same
the same? worksheet !"#$%&'()
Young’s double slit experiment is*( performed with a NdYAG
+#,./0( measured carefully on a
laser (λ= 1064 nm). Fringes are1#,$%&(0%23(&45&"2'&3(20(5&"6#"'&1(,1&"(783&"(7239(%2.93(6"#'
@ABC from the double slit. You insert
screen some distance L away ('DE(F"2.&0(8"&('&80,"&1(G8"&6,%%H(#(8(0G"&&(@E)A('(878H(6"#'
J"1(18"K(6"2.&(20(6#,1(3#($&(J(''(6"#'(39&(G&3&"(#6(39&(G&3"8%($"2.93
a small piece of glass (n=1.5) into the lower slit. What 0'8%%(52&G&(#6(.%800(7
is the
9#7(',G9(1#&0(39&(G&3"8%($"2.93(6"2.&('#M&(26(8(
minimum thickness of the glass;B(needed2(39&(%#7&"(0%23(>80(09#7(2(39&(62.,"&DN((
@EB(4(@A '(20(20&"3&1( to turn the central
+#,(G8(800,'&(8(21&4(#6("&6"8G32#(#6(?OEBB(6#"(39&(52&G&(#6(.%800(8bright fringe to a dark fringe? (Remember: we’re dealing
a phase change?) 6#"(783&"E(
>!2GK(39&(G%#0&03(807&"D(
with TRANSMITED light;
(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( is there 19 worksheet
Light traveling in different medium
will changes its wavelength (and
its speed, but NOT its frequency).
So a different number of wavelengths will fit in the glass as
compared to the air.
We want the fit some (m+1/2)λ in
the film to cause destructive
interference = 1064 nm QUESTION In a two
slit interference experiment, the slits are 0.200 mm apart, and the screen is at a distance of 1.00 m. The third bright fringe (not counAng the central bright fringe straight ahead from the slits) is found to be displaced 9.49 mm from the central fringe. Find the wavelength of the light used. (Pick closest answer) (A) 375nm (B) 486nm (C) 512nm (D) 632nm (E) 750nm In a two
slit interference experiment, the slits are 0.200 mm apart, and the screen is at a distance of 1.00 m. The third bright fringe (not counAng the central bright fringe straight ahead from the slits) is found to be displaced 9.49 mm from the central fringe. Find the wavelength of the light used. Path diﬀerence is: , and . Thus, (A) 375nm (B) 486nm (C) 512nm (D) 632nm (E) 750nm Y= ...
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 Winter '08
 BATES
 Physics, Light, Wavelength, Δx, Thomas Young, air gap

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