26 Interference & Diffraction--Physical/Wave Optics

Thin film interference

Interference & Coherent Sources

Superposition & Interference

Superposition: The net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually (wikipedia)

Key factor: phase.

Double Slits Interference-1

Fringes

,...)2,1,0,...)2,1,0

)2

1(1212

mm

mrrmrr

( (

Double Slits Interference-2

Mirror Equation

,...)2,1,0

)2/1(

tansin

,...)2,1,0

)2

1(sin

sin

sin12

m

eDestructivd

mRy

veConstructid

mRy

R

ydR

m

eDestructiv

md

veConstructi

md

drr

m

m

(

, if

(

Example: Determining

,...)2,1,0

m

veConstructid

mRym

(

Interference in Thin Film

,...)2,1,0

)2

1(2

2

m

eDestructiv

mt

veConstructi

mt

(

Note: when nb > na, reflected wave undergoes an additional half cycle (i.e., /2) phase shift.

Example: Interference Fringes

(note: additional /2 phase shift from the bottom reflection)

,...)2,1,0

2

m

eDestructiv

mt

(

Newton Rings & Applications

Non-reflective & Reflective Coatings

Diffraction & Geometric Optics

Diffraction—Reality

Fresnel diffraction: near-field diffraction Fraunhofer diffraction: far-field diffraction

Single Slit Diffraction

Fresnel & Fraunhofer: Single Slit

Huygens’s Principle: Every point of a wave front may be considered the source of secondary wavelets that spread out in all directions with a speed equal to the speed of propagation of the waves.

Dark Fringes

,...)3,2,1(2

sin

m

ma

,...)3,2,1

tansin

ma

mRy

R

y

m

(

small, very is Normally,

R

Multiple Slits & Diffraction Gratings

,...)3,2,1,0

sin

m

md

(

Constructive interference or bright fringes occur:

Destructive interference or dark fringes occur:

,...)3,2,10

)2/1(sin

m

md

(

X-Ray Diffraction

Circular Apertures & Resolving Power

First Dark Ring occurs

D

22.1sin 1

Resolving Power

Rayleigh’s Criterion (increase D or reduce could improve the resolution)

Dres

22.1sin 1

Holography

Summary: Superposition, interference, & Coherent Sources

Summary: Double Slits Interference

Summary: Thin Film Interference

Summary: Diffraction & Gratings

Summary: X-Ray Diffraction

Summary: Circular Apertures & Resolving Power

D

22.1sin 1

Summary: Holography

Ch 26 HomeworkAnswers to multiple choice problems

Problems: 1, 6, 11, 15, 25, 27, 47