The physics of interference, diffraction,
thin films and more...
Wave Superposition and
• What happens when waves meet?
• Path Difference - Phase Difference:
illustrate this with the following applet
Double and Multi-Slit
• Simple Case: Assume each slit acts as
a single source
• The Grating Equation for Antinodes:
n d sin
where d = separation between slits
• Use the following applet to help explore
the different interference patterns
produced by single, double and multiple
Single Slit Diffraction...
• A single slit can interfere with itself!
• Equation for Nodes: n W sin
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
The Physics of Thin Films
• A Phase difference can occur because
– path differences for different combining
– phase shifts introduced under certain
– go to applet thin film
Path Differences to Phase Shifts...
How to calculate
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
– 0,1,2,3,… n then constructive interference will result
Structural Colour in Plants and
• 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
• Light reflects from
places along the
surface. An optical
path difference is
Some colours work - some
• 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:
2l / cos n
Application… Lens Coating
• Why do some lens
have a purple
• Use the applet thin
film to help
power of the
So - if it’s a wave - What Kind
• 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 glancing
collisions can exhibit a “new property” polarization
• Light is a transverse wave