assignment B
Foot
waveoptics-introA.pdf
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Wave Optics
Chapter 28: Walker
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Last time
• What did we learn last time? • What patterns did you notice?
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Poll
Let’s measure distances on the diagram in terms of wavelength • What is the length of the red line below?
A. 1.5 λ B. 3.0 λ C. 4.5 λ D. 6.0 λ
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Poll
• How far apart are the sources?
A. 1.5 λ B. 3.0 λ C. 4.5 λ D. 6.0 λ
This is called the source separation (d)
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Path Difference
• The difference in distance between a point on the line of nodes or point on a line of constructive interference is called ΔD, the path length difference.
Example 1: Distance from source 1 = Distance from source 2 = Difference ΔD =
Example 2: Distance from source 1 = Distance from source 2 = Difference ΔD =
X X
2λ
2λ
2λ - 2λ = 0
3λ
2.5λ
3λ – 2.5λ = 0.5λ
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POLL • What is the path difference between the purple
and green lines?
A. 2.5 λ B. 2.0 λ C. 1.0 λ D. 0.5 λ
Note: ΔD is the same for all of the orange dots
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Finding ΔD on the Diagram Label ΔD for every line on your diagram
ΔD = 0 λ
ΔD = 0 λ
ΔD = ½ λΔD = ½ λ
ΔD = ½ λΔD = ½ λ
ΔD = 1 λ
ΔD = 1 λΔD = 1 λ
ΔD = 1 λ
ΔD = 1.5 λΔD = 1.5 λ
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Patterns of ΔD on the Diagram
• What patterns do you notice? Alternate constructive / destructive
• What are the values of ΔD for the lines perpendicular to the sources? 0 à this will always be true
• What are the values of ΔD for the lines of nodes?
Half-integer: 0.5 λ, 1.5 λ • What are the values of ΔD for lines of
constructive interference? Integer: 0 λ, 1 λ
• What is the largest value of ΔD? How does this compare to the source separation (d)? They’re equal! (1.5 λ in this case)
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Pattern on the Screen
1.5 λ destructive 1 λ constructive 0.5 λ destructive 0 λ constructive 0.5 λ destructive 1 λ constructive 1.5 λ destructive
alternating light (constructive) and dark (destructive, aka nodal) Spots on the screen are called fringes
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Screen a distance L from slits
Single source of monochromatic light λ
d
2 slits separated by d
L
Constructive and Destructive
Constructive: At points where the difference in path length ΔD = 0, λ, 2λ, 3λ … the screen is bright.
Destructive: At points where the difference in path length ΔD = λ/2, 3 λ /2, 5 λ /2 … the screen is dark.
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Pattern Spacing for Douple-Slit
• Rearranging, we get the pattern (fringe) spacing:
y = mλL/d o y = distance from center of pattern to fringe of interest
o d = ______________________
o L = ______________________
o λ = ______________________
o m = _____________________
• If d increases, the pattern spacing (y) _______. • If L increases, the pattern spacing (y) _______. • If λ increases, the pattern spacing (y) _______.
slit separation
distance from slits to screen
wavelength of light
0, ½, 1, 1.5, 2, 2.5, …
increases increases decreases
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Slits in a Barrier
Waves spread out • Waves enter regions that would otherwise be
shadowed • Occurs when waves pass through small
openings, go around obstacles, or pass by sharp edges
• Light going through a narrow slit similar to water waves.
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Lab
• Investigate changing the source (slit) size and separation
• Measure the wavelength of light in a double- slit simulation
