Download 3. The nature of light 3.1 Light as a wave

3. The nature of light
3.1 Light as a wave
•Some Greek philosophers: light emitted from the eye detects
surrounding
•Newton: particles (corpuscles) emitted from bodies, collected in
eyes
•Huygens (1678): light propagates as a wave, motion of a wave
front / light ray, ray optics or geometrical optics
particular wave properties of light: physical optics.
•1873, Maxwell: light as electromagnetic waves.
• laws of reflection and refraction (Snell’s law)
may be derived using Huygens principle
“Every point of a wave front may be considered
the source of secondary wavelets that spread
out in all directions with a speed equal to the
speed of propagation of the wave.”
http://www.walter-fendt.de/ph14e/huygenspr.htm
wave character of light: interference phenomena
(e.g. colours of oil on water, or soap films) +
diffraction “travelling around corners”
• Theoretical Problem: medium for light waves?
• Ether? properties? suppress longitudinal waves
• detect (through interference) motion of earth
through ether? NO (Michelson and Morley,1887)
• Einstein’s theory of special relativity: no medium
required BUT accept velocity of light as maximum
velocity and relativity of time and simultaneity
• Maxwell’s wave equations still hold, but new
challenging experimental fact, addressed by
Einstein (1905, annus mirabilis).
3.2 Light as a particle: the photo-electric
effect
1886-1900: photoelectric effect experiments by Hertz, Halwachs, Lennard
1897 – e- discovered by J. J. Thompson (see section 4)
Photo-effect: unexplainable by classical wave nature / description of light
(YF 38.3)
• minimum threshold frequency of light below which no
electrons are emitted (dependent on material of cathode)
• Speed of emitted electrons determined by stopping voltage
V0: e V0 = 1/2 m v2max, (e, charge of electron)
(YF, 38.4, 38.5)
VAC: potential of anode relative to cathode
problems for classical physics:
• stopping potential V0 independent of light
intensity, although intensity is energy per
unit area per unit time
• why threshold frequency fmin? (intensity of
a wave is independent on frequency)
• V0 is a linear function of frequency
Einstein, 1905 (Nobel Prize 1921)
• Energy quantised (Planck)
• Postulate: light consists of small energy packages (photons)
E = h f = h c/λ
• Photon arriving at cathode absorbed by an electron. If energy of
photon higher than material dependent work function Φ, then
electron escapes from surface
• Higher light intensity of light: more photons → more electrons
• Φ, minimum energy needed, corresponding to minimum
frequency fmin
Visit the photoelectric effect applet at
http://media.pearsoncmg.com/aw/aw_activphysics/aw_young_physics/part6.htm
and also visit http://www.lon-capa.org/~mmp/kap28/PhotoEffect/photo.htm
h  f    e V0
h

V0   f 
e
e
work function Φ, Planck constant h, frequency f,
charge of electron e, stopping potential V0
Graph of V0 as a function of f gives straight line of slope h/e and
intersect Φ/e. Must know e to determine h or vice versa.
charge of electron determined by Millikan (1909)
(see section 4.3)
1e = 1.602×10-19 C → h = 6.626×10-34 J·s
today: h = 6.62606876(52) ×10-34 J·s
relative error = |h2006-h1909|/h2006 = 1.04×10-5
3.3 Matter waves and “duality”
• Light: particle (but rest mass zero and moving at the
speed of light) and wave properties.
• de Broglie,1924: matter may behave wave-like,
wave length λ of a particle of momentum p= mv:
λ = h/p = h/(mv) (m: mass, v: speed)
• experiments1927 (Davisson and Germer): beam of
electrons through nickel crystal (lattice = diffraction
grating)
wave length very small for macroscopic objects
(about 10-34m). Not of relevance in normal day life!
Compton scattering effect (1923)
further evidence of quantum nature of light.
X-rays when interacting with matter are sometimes observed to scatter. When
they scatter they appear to have longer wavelengths, observed to be
dependent upon the angle of scattering as follows:
h
 '  
(1  cos  )
mc
(YF 38.28)
(YF 38.26)
Compton scattering can only be explained if the incoming photon is treated as
a particle
– this
photon quantum of light as
“particle” is then involved in a collision
with an electron
– scatters off the electron at an angle 
– losing energy and thus shifting to lower
frequency (longer wavelength)
- but photon must carry momentum!
(YF 38.27)
•Need to ascribe momentum to a
photon as follows
p
h

• Duality, i.e. having both wave and particle
properties, is at the heart of physics at the
atomic and sub-atomic level, described by
quantum-mechanics.
• Light and matter are neither particle nor
wave. Depending on experimental situation
one aspect might dominate over the other.
• Hard to grasp intellectually, due to lack of
everyday life experience.