Announcements 3/25/11 Prayer One lab due Saturday, two new labs start on

Saturday. We are nearing the homestretch for

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

Exam 3 starts a week from tomorrowa. Review session next Thurs or Friday. I

sent survey link. I will schedule the room on Monday morning, so please select your favorite times before then.

Reading Quiz

Which of the following can generate a diffraction or interference pattern?

a. Light passing through a pinhole in a card

b. Light passing through an array of regularly spaced pinholes

c. Light clipped by the edge of a razor blade

d. Both A and Be. All of the above

Review: Interference from slits

Quick writing: Using no equations, and in hopefully no more than two sentences, please explain how to solve slit problems.

A “wide” slit (book: “narrow” slits)

HW 34-3. How do we solve this?

Result:

2

0sin

( ) sinca

I I

approx.2: siny

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 max?

Under what conditions will you get a min?

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

What sincx and sinc2x look like The two formulas above (on notecard,

unless you can quickly derive them) How to do the integral (HW 34-3) Conditions for max/min (on notecard,

unless you can quickly derive them)

20

sin( ) sinc

aI I

20( ) sinc

ayI I

L

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.d. Masspacity Not the answer!!

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