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

(YF 38.3)

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

• 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

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.

0h f e V 0

hV f

e e

work function Φ, Planck constant h, frequency f,

charge of electron e, stopping potential V0

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!

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:

Compton scattering can only be explained if the incoming photon is treated as

a particle

Compton scattering effect (1923)

' (1 cos )h

m c

(YF 38.26)(YF 38.28)

•Need to ascribe momentum to a

photon as follows

– 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)

hp

• 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.