Homework lab

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?