Wave Optics

The physics of interference, diffraction, thin films and more...

Reading in Text:

• Chapter 24

• Main concept: light exhibits key properties that can only be explained by the wave model:– diffraction– interference– polarization

Wave Superposition and Interference• What happens when waves meet?

• Path Difference - Phase Difference: illustrate this with the following applet

2r

r

Double and Multi-Slit Interfence• Simple Case: Assume each slit acts as

a single source

• The Grating Equation for Antinodes:

where d = separation between slits

sinn d

Interfence Patterns

• Use the following applet to help explore the different interference patterns produced by single, double and multiple slits...

Single Slit Diffraction...

• A single slit can interfere with itself! simulate this

• Equation for Nodes: sinn W

General Equation for Single Slit Diffraction…Nodes• Nodes will always

form whenever

sinn W

Poisson’s Spot - a curious tale!

• By the early 19th century the wave model was becoming accepted and the French Physicist Fresnel had worked out an elaborate mathematical theory of light. However, the famous physicist Poisson claimed to have found a fatal flaw in the theory...

The Physics of Thin Films

• A Phase difference can occur because of…– path differences for different combining

wavetrains– phase shifts introduced under certain

reflections– go to applet thin film

Path Differences to Phase Shifts...

How to calculatephase shift:

• Find path difference• Divide by wavelength of light IN THE FILM• Add any additional phase shifts produced by reflections.• If the phase shift is:

– 0.5, 1.5, 2.5, …. “n.5” then destructive interference will result

– 0,1,2,3,… n then constructive interference will result

Structural Colour in Plants and Animals

• The iridescent sheen of a bluebird wing or the extravagant colours of many butterflies and moths arise - not from chemistry (pigments) but from physics (interference effects)!!

The Physics of Structural Colour

• Light reflects from slightly different places along the surface. An optical path difference is introduced

Some colours work - some don’t...• The optical path

difference is just the extra distance that one ray travels wrt to an adjacent one. It’s easy to see that this leads to:

for constructive interference

2 / cosl n

Application… Lens Coating

• Why do some lens have a purple colour?

• Use the applet thin film to help understand the power of the “quarter wave”!

Keeping Score (early 19th Century)

Particle Model• straight line propagation (1)• reflection (1)• refraction (1)• dispersion (?) = 0.5• interference/diffraction (0)• polarization (0)

score = 3.5

Wave Model• straight line propagation (1)• reflection (1)• refraction (1)• dispersion (1)• interference/diffraction (1)• polarization (1)

score = 6

So - if it’s a wave - What Kind of Wave?• Known since antiquity - some crystals

(calcite) can cause light to refract into two distinct paths when passing through the crystal (1669 - Bartholinus)

• Early 19th century, light under glacninc collisions can exhibit a “new property” - polarization

• Light is a transverse wave

Polarization, Scattering and The Electromagnetic Theory

• Why does glancing reflection from dielectric materials produce horizontally polarized light?

• Why is the sky blue?

• Why is skylight polarized?

• How are scattering and polarization linked?• What is light? go to simulation