REFUGES– Summer 2014

Interference of Light

Gernot LaicherUniversity of Utah - Department of Physics & Astronomy

Light = travelling electromagnetic wave (em wave)

Different colors = different frequencies of em waves.

Mechanical waves need medium to travel (e.g., air molecules for sound waves).

Light can travel through vacuum (needs no medium)

Speed of light in vacuum approx. 3x108m/s (different in other media, e.g. 2x108m/s in glass).

Wave propagation:

Wave crests move with the speed of light.

Period T (of electric field vector oscillation) :

Time required for one crest to move forward by a distance equal to its wavelength.

Frequency f: f=1/T

In short:

Huygen’s Principle:

Every point on a wave-front may be considered a source of secondary spherical wavelets which spread out in the forward

direction at the speed of light. The new wave-front is the tangential surface to all of these secondary wavelets.

Diffraction:

Example +Demo: Plane wave encounters a single slit.

Intensity distribution of diffraction pattern is mathematically quite involved. Location of the so-called minima fairly easy to understand.

a<<

a

L

y

Single SlitWidth=a

Screen

L

ymin

2ymin

Lya min

Diffraction pattern of a circular aperture

Without derivation: For circular aperture (a hole) of diameter q the diffraction pattern is an “airy disk”.

ymin = RADIUS of first dark ringq = diameter of holed = distance from hole to screen

Babinet’s Principle

The diffraction patterns from an opaque body is identical to that from a hole of the same size and shape except for the overall forward beam intensity.

Example:

Diffraction pattern produced by circular disc = same from circular hole of the same size.

We will use this principle to determine the thickness of a hair and the size of small particles from their respective diffraction patterns.

Double Slit Diffraction

Wave fronts of light

Double slit

Screen

Wave going through this slit travels a bit further to get to this particular place on the screen.Waves from the two slits are out of

phase by half a wavelength in that directionWaves annihilate each other in that direction

(“destructive interference”).Darkness on that place on the screen.

Dark

The waves going through both slits travel the same distance to the screen.Waves from the two slits in phase.Waves add together to twice the amplitude (“constructive interference”). Bright spot in center.

Dark

Bright

Double SlitWidth = aSeparation = d

Screen

L

ymax

4ymax

Lyd max

Double SlitWidth = aSeparation = d

Screen

L

ymax

4ymax

Lyd max

…if you had multiple colors

Diffractiongrating

difference in path length

n

d

Diffraction GratingSeparation = d

Screen

L

ymax

4ymax

Lyd max

Diffraction GratingSeparation = d

Screen

L

ymax

4ymax

Lyd max