w14d2: interference and diffraction experiment 6
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W14D2: Interference and Diffraction Experiment 6. Today ’ s Reading Course Notes: Sections 14.4-14.9. 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 - PowerPoint PPT PresentationTRANSCRIPT
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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)