Announcements 11/14/12 Prayer Labs 8, 9 due Saturday.

Lab 10 due Tuesday. We are nearing the

homestretch for Optics… just two lectures after today. (After that, relativity!)

We do have class Tuesday of next week: Intro to Relativity

Exam 3 starts Monday after Thanksgiving break

Vote for review session, Mon/Tues/Wed next week

SpeedBump

From warmup

Extra time on?

Other comments?

From warmup: As shown below, the

diffraction pattern of a single slit has a broad maximum in the middle, then narrower maxima to the sides. How does the intensity of the broad middle peak compare to the intensity of the closest side peaks?

a. Broad peak is a lot more intense (~21x)

b. Broad peak is a little more intense

c. Same intensityd. Side peaks are a lot more

intensee. Side peaks are a little more

intense

From warmup: This is the diffraction

pattern for a single wide slit. What will happen to the pattern if the slit is made narrower? (The bottom physical pattern not the top mathematical plot.)

a. If the slit is made narrower ("a" decreases), then the spacing between minima and maxima will increase. That is, the pattern will spread out.

Review: Interference from slits

Quick writing: Using no equations, and in hopefully no more than two sentences, please explain the basic idea(s) behind solving slit problems.

A “wide” slit (book: “narrow” slit)

HW 34-3. How do we solve this?

Result:

2

0sin

( ) sinca

I I

approx.2: sin screeny

L

sinsinc( )

xx

xNew function:

What is

0

sinlimx

x

x

“a” = width of slit

The sinc function

sinc(x) [sinc(x)]2

15 10 5 5 10 15 0.2

0.2

0.4

0.6

0.8

1.0

15 10 5 0 5 10 15

0.2

0.4

0.6

0.8

1.0

Image credit: http://scripts.mit.edu/~tsg/www/list.php?letter=Q

Single slit max/min

Under what conditions will you get a min?

Under what conditions will you get a max?

2

0sin

( ) sinca

I I

1

5

10

5

05

10

15

0.2

0.4

0.6

0.8

1.0

What you need to know

20

2cos sin

2

dI I

Given on exam Not given on exam

max : sind m

12min : sind m

2 PL :y L y L PL sind

1 20 ...i iE E e e 2

~I E

20

sinsinc

aI I

two narrow slits:

one wide slit:

min : sina m

Clicker question:

I shine light through two tiny slits spaced by d. Then I shine the same light through a single slit with width d. Which diffraction pattern has the broadest middle peak?

a. The two slit patternb. The single slit patternc. Both middle peaks are the same size.

λλ = 5 = 5 aaImage credit: Single slit diffraction pictures from Dr. Durfee

λλ = = aa

λλ = = aa/2/2

λλ = = aa/3/3

λλ = = aa/5/5

λλ = = aa/10/10

Demo

Diffraction from a slit Diffraction from a hair (Babinet’s

principle, HW 34-2)

Clicker question:

When you have two slits close to each other, each slit being “wide” (at least, not infinitely narrow), the intensity you get on the screen is:

a. A double-slit patternb. A “wide” single-slit patternc. A double-slit pattern PLUS a single-slit

patternd. A double-slit pattern TIMES a single-slit

pattern

From warmup This is the diffraction pattern for

two wide slits. (a) What will happen here if the distance between slits is made narrower? (b) What is the distance is held constant but the width of each slit is made narrower.

a. (a) If the distance between slits is made narrower, the "fringes" (high frequency oscillation) will spread out, but the "diffraction minima" (low frequency oscillation) will stay in the same places.

b. (b) If the width of each slit is made narrower, the diffraction minima will spread out but the interference fringes will stay in the same places.

1.5 1.0 0.5 0.0 0.5 1.0 1.5

0.20.40.60.81.0

Combination of patterns HW 34-4 maxmins max?

2-D patterns Pattern from x-direction Pattern from y-direction

Thought question: Which dimension of the rectangle was the narrowest?

a. Xb. Y

Example: rectangular aperture zoomed in

xy

Circular Aperture (more on this next time)

Rectangle & Circle, side-by-side

Array of Circles

Clicker question:I shine light through a piece of foil I shine light through a piece of foil which has two identical holes shapedwhich has two identical holes shapedlike tiny llamas spaced apart by a like tiny llamas spaced apart by a distance distance dd. What will the diffraction . What will the diffraction pattern look like?pattern look like?

A : The same as two narrow slits separated by A : The same as two narrow slits separated by dd..B : The same produced by a single slit of width B : The same produced by a single slit of width dd..C : The diffraction pattern of a single llama.C : The diffraction pattern of a single llama.D : The diffraction pattern of a single llama multiplied D : The diffraction pattern of a single llama multiplied

by the two-slit pattern.by the two-slit pattern.E : none of the aboveE : none of the above

Credit: All llama slides are from Dr. Durfee

Important: No llamas were harmed in the making of these images