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Wave Optics:� Interference and
Young’s Double-Slit Experiment
•  1801, first to demonstrate the interference of light waves
•  Illustrates the wave nature of light •  See pattern of light and dark bands on screen
(fringes) •  Similar to water waves and sound waves •  Constructive interference à bright •  Destructive interference à dark
Pattern Spacing for Douple-Slit
•  Rearranging, we get the pattern (fringe) spacing:
y = λLm/d o  y = distance from center of pattern to fringe of interest
o  d = ______________________
o  L = ______________________
o  λ = ______________________
o  m = _____________________
•  If d increases, the pattern spacing (y) _______. •  If L increases, the pattern spacing (y) _______. •  If λ increases, the pattern spacing (y) _______.
slit separation
distance from slits to screen
wavelength of light
0, ½, 1, 1.5, 2, 2.5, …
increases increases decreases
•  Diffraction: waves spread out •  Light enters regions that would otherwise be
shadowed •  Occurs when waves pass through small
openings, go around obstacles, or pass by sharp edges
•  Light going through a narrow slit similar to water waves.
• •
•  Each portion of the slit acts like a source of waves
•  Light from one portion of the slit can interfere with light from another portion of the slit.
•  There’s a path difference between light from each part of the slit to screen
•  Central bright fringe wider than others.
•  Get minima where the points sum to zero (dark spots).
• •
all of these interfere destructively
Slit width = a Comparable in size to λ
Single-Slit Diffraction Pattern
•  Intensity on screen depends on direction θ •  Get destructive interference when:
sin θ = mλ/a (m = 1, 2, 3, …)
•  This formula locates minima •  Interference only occurs when a ~ λ
Slit Width Compared to Wavelength
•  Narrow slit: a <> λ à dot, because light goes in straight lines
•  Application: importance of wavelength à can pick up radio waves when visible light is blocked since radio wavelengths are longer
Back up a sec…
•  What is light anyway? A photon? A wave? •  Both! •  Wave-Particle Duality
o  Light behaves like a particle when emitted by an atom or absorbed by photographic film or other detectors
o  Light behaves like a wave while traveling from a source to the place where it is detected.
•  What does this have to do with electrons?
De Broglie Wavelengths
•  Matter can behave like a wave??!? •  Yup! Wavelength = h/momentum
λ = h/mv
This wavelength is called the de Broglie wavelength, after a French physicist
De Broglie Wavelengths
Example: What is the de Broglie wavelength of a ping-pong ball of mass 2 grams after it has been slammed across the table at a speed of 5 m/s? λ = h/mv
Electron Diffraction
•  The de Broglie hypothesis was unexpectedly experimentally confirmed in 1927 by two scientists firing electrons at a nickel crystal
•  The regular spacing between atoms in the crystal acts like
a diffraction grating
Electrons over time and probability
•  Both matter and light have both wave and particle properties
•  The type of question that we ask (or the type of measurement that we seek to make) determines the properties that we will see!
•  The wave and particle natures of matter and light are two complementary properties, like two sides to the same coin
•  In what ways do photons act like waves? In what ways do they act like particles?
•  In what ways do electrons act like waves? In what ways do they act like particles?
•  What’s the experimental evidence?

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