Announcements 11/16/11 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 Exam 3 starts Monday after Thanksgiving break Vote for review session, Mon/Tues/Wed next week

Pearls Before Swine

Reading Quiz

A single slit diffraction pattern is characterized by:

a. A narrow central maximum, with other maxima and minima on each side

b. A narrow central minimum, with other maxima and minima on each side

c. A wide central maximum, with other maxima and minima on each side

d. A wide central minimum, with other maxima and minima on each side

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

Thought 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)

Reading Quiz

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

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

Thought QuestionThought QuestionI 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