# Chapter 33: Interference and Diffraction Homework: 17, 31,

Chapter 33: Interference and Diffraction Homework: 17, 31, 37, 55 Cover Sections: 1, 2, 3, 4, 6, 7 Omit Sectons: 5, 8

1 Outline: Phase Difference and Coherence Interference in Thin Films Single Slit Diffraction Pattern Two Slit Interference

Fraunhofer and Fresnel Diffraction Diffraction and Resolution 2 3 33-1

Phase Difference and Coherence Phase Difference: The fractional part of a period which represents the offset in peak positions of waves. Coherence: The existence of a correlation between the phases of two or more waves such that interference effects can be observed.

Interference: The variation with distance or time of the amplitude of a wave which results from the superposition of two or more waves. 4 5

33-2 Interference in Thin Films 6 7

Change in Wavelength c f v f n n

n n = index of refraction 8

9 10 11

Condition: Ray 1 and 2 will be out of phase by radians for 589nm light. Path difference = 2t. 2t

2 9 589 10 m / 1.33 5.32t 589 10 9 m t 110 nm 0.110 m

12 33-3 Two-Slit Interference Pattern 13

14 y-axis bright/dark are symmetric m = 2 bright fringe

L m = 1 bright fringe central max m = 1 dark fringe m = 2 dark fringe m = 3 dark fringe

15 16 17

18 Example: slit-separation d = 1.5mm. Light = 589nm. Bright fringes occur at: 1 sin 1 (1)(589 10 9 m) / 1.5 10 3 m 0.0224

2 sin 1 (2)(589 10 9 m) / 1.5 10 3 m 0.0449 3 sin 1 (3)(589 10 9 m) / 1.5 10 3 m 0.0674 etc. 19 Example: L = 3m. slit-separation d = 1.5mm. Light = 589nm.

y2 (2)(589 10 9 m)(3m) / 1.5 10 3 m 2.36mm y3 (3)(589 10 9 m)(3m) / 1.5 10 3 m 3.53mm Bright fringe spacing = y3 y2 = 1.17 mm 20 Example: slit-separation d = 1.5mm. Light = 589nm.

2nd Dark fringe occurs at: 2 sin 1 (2 12 )(589 10 9 m) / 1.5 10 3 m 0.0337 The 2nd Dark fringe should occur between 1st and 2nd Bright fringes: 0.0224 0.0449

2 0.0337 2 21 33-4 Diffraction Pattern of

a Single Slit 22 23 a = Slit-Width

(a d) 24 25 Example: slit-width a = 0.200mm. Light = 589nm.

Dark fringes occur at: 1 sin 1 (1)(589 10 9 m) / 0.200 10 3 m 0.168 2 sin 1 (2)(589 10 9 m) / 0.200 10 3 m 0.337 etc. 26

(Omit) 33-5 Using Phasors to Add Harmonic Waves 27

33-6 Fraunhofer and Fresnel Diffraction 28

Fraunhofer and Fresnel Diffraction Patterns Fresnel Pattern: observed near obstacle causing diffraction. Fraunhofer Pattern: observed far from away from the obstacle. The criterion for determining near and far is

the convergence angle of the light which makes up the pattern. 29 33-7 Diffraction and Resolution

30 First Diffraction Minimum of a Circular Aperture 1.22 D

31 Rayleigh Criterion occurs when two point sources of light are close enough

together that light coming from them passes through a circular aperture so that the 1st minimums of the diffraction patterns fall on the central maximum of the other. A single ellipsoid is seen instead of two separate objects. 32

Rayleigh Criterion Formula is a condition for the angle of convergence of rays emanating from the objects that pass through the aperture. This angle is called alpha, and occurs when: c 1.22

D 33 Summary: Phase Difference and Path Difference Coherence defined

Interference in Thin Films Single Slit and Two Slit Patterns Fraunhofer and Fresnel Diffraction Diffraction limits ultimate resolution 34

Omit 33-8 Diffraction Gratings End of 33 35

36 37 38

39

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