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W14D2:Interference and Diffraction

Experiment 6

Today’s Reading Course Notes: Sections 14.4-14.9

Announcements

PS 11 is only for practice. It will not be graded.

Next Reading Assignment W14D3 Course Notes: Sections 14.9-14.11

Final Exam Mon May 20 9 am-12 noon in Johnson Athletic Center

Review Sessions TBA

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Outline

Review Interference

Diffraction

Interference and Diffraction

Experiment 6

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Interference – Phase ShiftWhat can introduce a phase shift?

1. From different, out of phase sources

2. Sources in phase, but travel different distances because they come from different locations

constructive destructive

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Microwave Interference

http://youtu.be/-O8V2QHkaLI

http://web.mit.edu/viz/EM/movies/light/distant.avi

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ReviewThe Light Equivalent:

Two Slits

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Young’s Double-Slit Experiment

Bright Fringes: Constructive interference

Dark Fringes: Destructive interference

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Two In-Phase Sources: Geometry

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Interference for Two Sources in Phase

Constructive:

Destructive:

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Intensity DistributionWhat is intensity of two waves out of phase?

Average Intensity:

Use

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Average Intensity

Average intensity:

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Diffraction

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Diffraction Diffraction: The bending of waves as they pass by

certain obstacles

No spreading after passing though slits

Spreading after passing though slits

No Diffraction Diffraction

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Single-Slit Diffraction

Destructive interference:

“Derivation” (Motivation) by Division:

Divide slit into two portions:

Don’t get confused – this is DESTRUCTIVE!

Now divide slit into four portions:

Generalization:

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Intensity Distribution

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Concept Question: Lower Limit?Using diffraction seems to be a useful technique for measuring the size of small objects.

Is there a lower limit for the size of objects that can be measured this way?

1. Yes – and if we used blue light instead of red light we can measure even smaller objects than the ones we measure using red light

2. Yes – and if we used blue light instead of red light we couldn’t even measure objects as small as the ones we measure using red light

3. No

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Concept Q. Answer: Lower Limit?

Once the feature size a is as small as the light wavelength you can’t go to an angle large enough to satisfy the above equation for any m > 0.

Blue light has a shorter wavelength than red light, so you can measure smaller sizes using blue light.

Answer: 1. we have the condition that

There is a lower limit imposed by the condition, namely that

sin 1 a

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Interference & DiffractionTogether

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Two Slits With Finite WidthWith more than one slit having finite width a, we must consider

1. Diffraction due to the individual slit

2. Interference of waves from different slits

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Lecture Demonstration:Double Slits with Diffraction

http://tsgphysics.mit.edu/front/?page=demo.php&letnum=P%2010&show=0

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Two Slits With Finite Width

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Interference & Diffraction

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Con. Q.: Interference & Diffraction

The resulting pattern on a screen far away is shown above, with distantly-spaced zeroes of the envelope, as indicated by the length X above, and closely-spaced zeroes of the rapidly varying fringes, as indicated by the length Y above.

Which length in the pattern above is due to the finite width a of the apertures?

1. X2. Y3. X and Y4. Neither X nor Y

Coherent monochromatic plane waves impinge on two long narrow apertures (width a) that are separated by a distance d with d > a.

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Concept Q. Ans.: Inter. & Diffraction

Answer: 1. The ‘envelope’ length X depends on slit width.

You could infer this in two ways.

1)Slit width a < slit separation d. Angles and size scale inversely, so the bigger features come from a.

2)Interference patterns are roughly equal in magnitude while diffraction creates a strong central peak. So the envelope is from diffraction.

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Worked Problem: InterferenceIn an experiment you shine red laser light (600 nm) at a slide and see the following pattern on a screen placed 1 m away:

a) Are you looking at a single slit or at two slits?

b) What are the relevant lengths (width, separation if 2 slits)? What is the orientation of the slits?

You measure the

distance between

successive fringes

to be 20 mm

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Solution: Interference

(a) Must be two slits

a

d

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Solution: Interferencetan

sin /

y L

L Lm d

constructive inteference

At 60 mm…

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You just observed an interference pattern using a red laser. What if instead you had used a blue laser? In that case the interference maxima you just saw would be

Concept Q.: Changing Wavelengths

1. closer together.

2. further apart.

3. came distance apart.

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Concept Q. Ans.: Changing Colors

Blue light is a higher frequency (smaller wavelength) so the angular distance between maxima is smaller for blue light than for red light

Answer: 1. Closer Together

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Experiment 6, Part I:Measure Laser Wavelength

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Experiment 6, Part II:Interference from a CD

Diffraction Gratingd = distance between openings

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From 2 to N Slits

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Experiment 6, Part II:Diffraction Grating: CD

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Experiment 6, Part III:Measure Hair Thickness

Single hair strand acts as a single slit (Babinet’s Principle)