Phys 233
Day 2, Q2: Wave Optics
Thurs 9/6
Q2 wave optics
RE-Q2
Mon. 9/10
Tues. 9/11
Q3 particles
HW1: Q1: S6, S7, R2; Q2: S2, S9, R1; Lab Notebook
RE-Q3
1
Equipment
o Close blinds
o http://www.falstad.com/ripple/
o Laser Diffraction & Interference demo
 HeNe Red laser
 Green laser
 Slits and holders
 Lab jacks for slit holders and green laser
 White light projector, mostly blocked out
 Diffraction grating slide
o Ppt.
o Audio Diffraction & Interference
 2 speakers, one with the tweeter disconnected
 Function generator
 Necessary cables
o Whiteboards with pens and erasers?
o My schedule for office hours
Q2: Wave Nature of Light
Q 2.1 Two-Slit Interference
Q 2.2 Two-Slit Interference of Light
Q 2.3 Diffraction
Q 2.4 Optical Resolution
Questions?
Q 2.1 Two-Slit Interference
Ppt. - Q2T.1 – Waves from two slits S and Q will destructively interfere and cancel at a
point P if the distance between P and S is larger than the distance between P and Q (note
the correction!) by
A. λ
B. nλ (where n is an integer)
C. nλ/2 (where n is an integer)
D. (n + ½)λ (where n is an integer)
E. λ/4
F. Other (specify)
If they don’t agree, we can come back to after working through ppt discussion of making
interference pattern.
Let’s look at 2-slit interference. If you accept that waves passing through a small hole or
slit are circular (which the book makes plausible in the case of water waves), then it’s
essentially a geometric argument to determine the directions in which waves through two
slits will constructively and destructively interfere.
Phys 233
Day 2, Q2: Wave Optics
Demo: http://www.falstad.com/ripple/
o Set two sources and then move to be 3-D to show side view and observe how far
up the water would splash along wall
Demo: Audio interference – 2 speakers playing about 700 Hz – students should hear
strong and weak if they move a little left and right.
Ppt. – build up interference to bee pict.
End up with
o d sin nc n d sin nd n 12
for this question: no one call out: think and then convince table partner that you’re right.
ppt. Consider the demo I did a little earlier in the class: two speakers about 0.1 m apart
playing a pitch around 700 Hz. Consider a line parallel to that connecting the two
speakers but axis but 3 m from it, that is, where the folks are sitting at the back of the
class. At what points along this second line would the sound be the loudest? At what
points would it be weakest?
Q 2.2 Two-Slit Interference of Light
ppt. Q2T.10 - If we shine white light through two slits onto a distant screen, we will see
a clear interference pattern on the screen, true or false?
Demo: Try shining white light through two slits (probably get too faint; could try diffraction
grating)
Demo: Shine red laser through slit
o Close blinds and use can of smoke to bring out troughs and crests
o Return to http://www.falstad.com/ripple/ and its 3-D side view to relate dim and
bright spots to strong and weak wave spots.
Question: If I switch to a narrower set of slits, what will happen to the pattern?
o A: get wider – the sine of the angle to a peak is inversely proportional to d.
o Demo: do it.
Question: If I switch to a green laser, what will happen to the pattern?
o A: get narrower – the sine of the angle is proportional to the wavelength
o Demo: do it.
Question: If I had more slits than just two, what would happen to the pattern?
o Demo: do it.
Question: If I had horizontal as well as vertical slits…
o Demo: do it.
o While the physical structure may be awfully small, the interference pattern of slight
passing through it can give us important information about it – the spacing and
symmetry. Transmission and reflection techniques help people to determine what
crystalline structure something has
2
Phys 233
Day 2, Q2: Wave Optics
3
Q 2.3 Single-Slit Diffraction
Ppt. - Q2T.4 - Imagine that sound waves with a certain definite wavelength pass through a
partially opened sliding door. If the door is closed somewhat further (but not shut entirely), the
angle through which the sound waves are diffracted
A. Decreases
B. Increases
C. Remains the same
D. Depends on quantities not specified (explain)
Demo: Single speaker with tweeter disconnected and grill removed. Play low note and
pan around room, then play high note and pan around room (note: reflection may make
the beaming effect less pronounced.)
o Calculate wavelength (given frequency and v = 344m/s) and compare with
diameter.
Huygen’s Principle
o Q: what is it?
o Looking at a continuous water wave crest, zoom in on just one point along the
crest; if that were taken in isolation and the only bit of water displaced up, then it
would soon fall down and generate a circular ripple, radiating out in all directions.
Huygen’s idea was to consider that even not in isolation, that’s what each spot of
water along a crest would try to do, and it was just for the interplay of each point
trying to create circular ripples out that all but the forward moving crest is
canceled, as in figure Q2.8.
o Now if we consider a wave front that encounters a partial barrier, say, a slit, then
that small bit of the front that make sit through the slit doesn’t have the neighbors
helping to cancel out all but the forward ripple.
o To understand how the wave propagates on through the slit, we then think of the
slit as populated by umpteen individual sources, all radiating circularly – just as
with the two slits, but many more.
Ppt – Diffraction
o Similarly, the next black spot occurs where the top quarter cancels with the
second quarter and the third with the fourth,…
a
sin 1d
a sin 1d
2
2

a
sin
4
a
sin
2n
2d
nd
2
2
a sin
a sin
2d
nd
2
n
n
a
 Demo: http://www.falstad.com/ripple/ single-slit set up
o Demo: laser through single slit. Switch to narrower slit and see wider pattern.
Can of smoke.
nd
sin
1
Phys 233
Day 2, Q2: Wave Optics
4
Q 2.4 Optical Resolution
Diffraction through circular opening
o Ppt. Actually, the speaker, while a good qualitative example isn’t exactly the kind
of system we’ve been modeling – it has a circular opening. Going through the
same kind of reasoning as for the simple slit, but over a circle leads to a Bessel
function rather than a sine function, but the location of the first minima differs
only by a factor of about 1.22 (the locations of the others differ by similar factors)

sin
1d
1.22
a
o Demo: laser through pin hole?
Optical Resolution
o Ppt.