Interference and DiffractionPhysics

Mrs. Coyle

Light’s Nature

• Wave nature (electromagnetic wave)

• Particle nature (bundles of energy called photons)

Past- Separate Theories of Either Wave or Particle Nature

• Corpuscular theory of Newton (1670) • Light corpuscles have mass and travel at

extremely high speeds in straight lines

• Huygens (1680) • Wavelets-each point on a wavefront acts

as a source for the next wavefront   

Why was it difficult to prove the wave part of the nature of light?

Proofs of Wave Nature• Thomas Young's Double Slit Experiment (1807) bright (constructive) and dark (destructive)

fringes seen on screen • Thin Film Interference Patterns

• Poisson/Arago Spot (1820) • Diffraction fringes seen within and around a

small obstacle or through a narrow opening

Proof of Particle Nature:The Photoelectric Effect

• Albert Einstein 1905• Light energy is quantized• Photon is a quantum or packet of energy

The Photoelectric Effect

• Heinrich Hertz first observed the photoelectric effect in 1887

• Einstein explained it in 1905 and won the Nobel prize for this.

Thomas Young’s Double Slit Interference Experiment

• Showed an interference pattern

• Measured the wavelength of the light

Two Waves Interfering

Young’s Double SlitInterference Pattern

http://galileo.phys.virginia.edu/classes/USEM/SciImg/home_files/introduction_files/doubleslit.jpg

Interference of Waves FromTwo Sources

• Simulation “Ripple Tank” http://www3.interscience.wiley.com:8100/legacy/college/halliday/0471320005/simulations6e/index.htm?newwindow=true

Interference

• Young’s Double Slit Interference• http://galileo.phys.virginia.edu/

classes/109N/more_stuff/flashlets/youngexpt4.htm

For Constructive Interference:

The waves must arrive to the point of study in phase.

So their path difference must be integral multiples of the wavelength:

L= n n=0,1,2,3,………

For destructive interference:

, the waves must arrive to the point of study out of phase.

So the path difference must be an odd multiple of /2:

L= n m=1/2,3/2,5/2,….

Typical Question

• Where is the first location of constructive or destructive interference?

Fo Constructive Interference of Waves from Two Sources

x=Ltan

sinL/dL=n

For small angles:Lsin~Ltan

dsinn

ndx L

d

L

x

n=0,1,2,3,…

Double Slit Interference

dsinn

ndx L

Constructive (brights) n=0,1,2,3,…..Destructive (darks) n=1/2, 3/2, 5/2,…..

Note:To find maximum # of fringes set to 90o for n.

Question

• How does x change with wavelength?

• How does x change with slit distance?

ProblemTwo slits are 0.05 m apart. A laser ofwavelength 633nm is incident to the slits. A screen is placed 2m from the slits.

a) Calculate the position of the first and second bright fringe.

b) What is the maximum number of destructive interference spots there can be on either side of the central maximum?

Diffraction Grating

http://des.memphis.edu/lurbano/vpython/matter_interactions/spectrum/spectrum_02.jpg

Diffraction Grating• Large number of equally spaced parallel slits.• Equations are same as for double slit interference

but first calculate the d (slit separation) from the grating density, N.

d=1/N , N slits per unit lengthdsinnndx

LConstructive (brights) n=0,1,2,3,…..Destructive (darks) n=1/2, 3/2, 5/2,…..

Problem

A neon laser of wavelength 633nm is pointedat a diffraction grating of 3000lines/cm. Find

the angle where the first bright occurs.(Hint: slit separation d is inverse of grating

density)

Diffraction

Wave bends as it passes an obstacle.

Diffraction through a Narrow Slit Each part of the slit acts as a point source

that interferes with the others. (Based on Huygens Principle)

Pattern of Diffraction of Light through a Narrow Slit

L

wx

Intensity of the Diffraction Interference Patterns

• Simulation “Interference of Light”

• http://www3.interscience.wiley.com:8100/legacy/college/halliday/0471320005/simulations6e/index.htm?newwindow=true

Diffraction from Narrow Slit

wsinn nw y

L w: is the width of the slit

Destructive (dark fringes): m=0,1,2,3,….

Questions

• How does x change with the width?

• How does x change with the wavelength

Diffraction around a Penny and Poison Spot

Example of Diffraction