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•  What are the values of ΔD for the lines perpendicular to the sources? 0 à this will always be true

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1

Wave Optics

Chapter 28: Walker

2

Last time

•  What did we learn last time? •  What patterns did you notice?

3

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

4

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)

5

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 = 0

2.5λ

3λ – 2.5λ = 0.5λ

6

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

7

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

8

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)

9

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

10

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.

11

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

12

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.

13

Lab

•  Investigate changing the source (slit) size and separation

•  Measure the wavelength of light in a double- slit simulation
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