Homework lab

profileFoot
diffraction_presentationA.pdf

Wave Optics:� Interference and

Diffraction

H-1

H-2

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

H-3

Double-Slit

H-4

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) _______.

H-5

slit separation

distance from slits to screen

wavelength of light

0, ½, 1, 1.5, 2, 2.5, …

increases increases decreases

Diffraction

•  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.

H-6

• •

•  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).

• •

slit

all of these interfere destructively

a

Slit width = a Comparable in size to λ

Single-Slit Diffraction Pattern

H-7

Quantitatively

•  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

H-8

Slit Width Compared to Wavelength

•  Narrow slit: a << λ à circular wavefronts, medium bright screen

•  Medium slit: a ~ λ à single-slit pattern

H-9

Slit Width Compared to Wavelength

•  Wide 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

H-10

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?

H-11

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

H-15

Complementarity

•  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?