Upload
jean
View
47
Download
0
Embed Size (px)
DESCRIPTION
Announcements 11/9/12. Prayer Clement sick today, no office hours Lab 8 going on, due on Sat Nov 17 Lab 9 starts tomorrow, due on Sat Nov 17 Lab 10 starts tomorrow, due on Tues Nov 20 Exam 3 starts day after break. Two facts you should know:. (They follow quickly from - PowerPoint PPT Presentation
Citation preview
Announcements 11/9/12 Prayer Clement sick today, no office hours Lab 8 going on, due on Sat Nov 17 Lab 9 starts tomorrow, due on
Sat Nov 17 Lab 10 starts tomorrow, due on
Tues Nov 20 Exam 3 starts day after break
cos2
ix ixe ex
sin
2
ix ixe ex
i
Two facts you should know:
(They follow quickly from eix = cosx + i sinx)
From warmup
Extra time on?a.(nothing in particular)
Other comments?a.(nothing in particular)
Double slit diffraction
Two slit interference
From Wikipedia
http://en.wikipedia.org/wiki/Double-slit_experiment
From warmup
What is the purpose of S1 in the right figure? Some good thoughts:
a. To make sure that the light sources at b and c are identicalb. Is it to make sure that the point source of light is centered
exactly between b and c and to make sure that b and c are coherent?
c. That is the original ray. The two slits b and c split it up like a speaker splits up a single sound wave.
Reminder: How did we do it with sound? An alternate method: Use a laser, then S1 not needed
Double slit experiment
Essentially the same as the two speaker demo
Goal: what’s the shape of that curve? How can we predict where the maxima & minima will be?
aka “Young’s Double Slit”
screen here
max
min
max
min
inte
nsity
Wait, which is correct?
The Easy Part
Maxima/minima
Maxima: PL = ?
Minima: PL = ?
sind m
12sind m
Approximation #1: d is small enough that the two rays are parallel. Requires d << L.
From warmup
Consider a two-slit interference pattern like those above. What do you suppose would happen if the entire setup were immersed in water?
a. The bars would move together and get smaller because the wavelength decreases when you immerse it in water, therefore the distance between the bars is decreased.
How to solve the problem
Complex numbers!! The light from each slit travels a different
distancea. This creates a phase shiftb. Incorporate the phase shift into eifactors
First: what’s the phase shift for two waves oscillating in phase with a known PL?
Quick writing (w/o Approx. 1)
= ( PL / ) 360
= 2PL /
3.2 m
3.0 m
two sourcesof sound, =1.2m
(in phase)
what is relative phase shift, here?
( , ) cos( ) cos( 60 )f x t A kx t A kx t
Intensity?How to add?
What’s PL?
Clicker Vote: What should we measure the phase shift relative to?
a. The top slitb. The bottom slitc. Halfway between
the two slits
= 2PL /
The Full Answer
Etot = Etop slit + Ebottom slit
= [use whiteboard]
I ~ |E|2
I = [use whiteboard]
Plot of I(y) for I0=1, =500 nm, L=1 m, d=1
m
How did I turn into y?
Approximation #2: sometimes (not here!) is small enough that y/L. Requires y << L.
= 2PL /
20
2cos sin
2
dI I
Plots
20
1
2cos sin
2
tan /
dI I
y L
2
0 cosdy
I IL
(approx. 1 only) (approx. 1 and 2)
screen here
max
min
max
min
inte
nsity
screen here
max
min
max
min
max
min
max
Maxima/minima, revisited
Max: cosx = 1 …
Min: cosx = 0 …
20
2cos sin
2
dI I
20 cos
dyI I
L
sind m
12
sin ( )d m
What you need to know
HW 32-4: Solve the three slit problem Exam problem likely (possibly extra credit) Disclaimer: This only works for very narrow slits
Lecture after next: “wide” slits
20
2cos sin
2
dI I
20 cos
dyI I
L
Given on exam Not given on exam
sind m
12sind m
2 PL
(approx. #2)y L
PL sin (approx. #1)d
1 20 ...i iE E e e 2
~I E Demo: Double slit experiment!