The Interaction of Light and Matter Commonly drawn symbol for photon A more physically meaningful symbol for the photon as an energy wavepacket confined

The Interaction of Light and Matter

Commonly drawn symbol for photon A more physically meaningful symbol

for the photon as an energy wavepacket confined in space

Learning Objectives Wave-like properties of light:

Reflection, Refraction, Diffraction, and Interference

Particle-like properties of light:Photoelectric effect

Compton effect

Wave-particle duality of light:Light – in the form of electromagnetic waves – shows its wave-like

properties as it propagates through space. Light – in the form of photons – shows its particle-like properties as it

interacts with matter.




Compton effect




Wave-Like Properties of Light Light has wave-like properties. Like sound or water waves, light undergoes reflection

Wave-Like Properties of Light Light has wave-like properties. Like sound or water waves, light undergoes reflection, refraction

Wave-Like Properties of Light Recall that light travels at a speed

as predicted by Maxwell’s equation.

Recall also that light waves do not require a medium (a postulated luminiferous ether) in which to propagate.

The speed of light as given by Maxwell’s equation is for light propagating through a vacuum.

In a medium (air, water, glass, etc.), the speed of light can be smaller than c. As light propagates through a medium, it is absorbed and then reemitted by atoms. The time delay between the light being absorbed and then reemitted causes a slower-than-c speeds in a medium.



Swimming Pool Moon


Star

Earth

Image of Star

Wave-Like Properties of Light Light has wave-like properties. Like sound or water waves, light undergoes reflection, refraction, diffraction

Light diffracted by a straight edge

Wave-Like Properties of Light Light has wave-like properties. Like sound or water waves, light undergoes reflection, refraction, diffraction, and most convincingly interference as demonstrated by the English scientist Thomas Young in 1803 in his famous double-slit experiment.

Wave-Like Properties of Light Superposition principle for two (or more) waves travelling through the same medium at the same time: waves pass through each other without being disturbed, such that the net displacement of the medium at any point in space or time is equal to the sum of the individual wave displacements.

Superposition Principle

+

=







Compton effect




The Photoelectric Effect In 1887, the German physicist Heinrich Rudolf Hertz observed

what is now known as the photoelectric effect.

When light shines on a metal surface, electrons are ejected from the surface:

- if the incident light exceeds a certain threshold frequency - above this threshold frequency, increasing the light

intensity increases the number of ejected electrons (i.e., current)

Heinrich Rudolf Hertz, 1857-1894

A current flows when one of the metal plates is exposed to light.

metal plate

metal plate

evacuated tube

The Photoelectric Effect Furthermore:

- increasing the light intensity does not increase the maximum kinetic energy of the electrons (no need to change stopping voltage to prevent a current from

flowing)- increasing the light frequency increases the maximum kinetic energy of the

electrons (need to increase stopping voltage to prevent a current from flowing)

The Photoelectric Effect The photoelectric effect therefore shows that the energy of light depends on its

frequency:- the incident light must exceed a threshold frequency before electrons are

ejected- the maximum kinetic energy of the electrons depends on the frequency

rather than the intensity of the incident light

In Maxwell’s equations, which describe light as electromagnetic waves, the energy of light depends only on the amplitude of its electric and magnetic fields, not frequency.

The energy per unit time per unit area carried by a light wave is (see §3.3):

and if averaged over one cycle:

Blackbody Radiation To derive theoretically the spectrum of blackbody radiation in

1900, the German physicist Max Planck imagined a perfectly conducting box filled with electromagnetic waves. These waves caused electrical charges in the walls of the box to oscillate. In turn, the oscillating charges radiated electromagnetic waves.

Planck found that he could not reproduce the blackbody radiation curve if the oscillators radiated energy continuously as the classical theory would demand. Instead, he required the oscillators to only lose or gain energy in chunks, called quanta, of size hυ, for an oscillator of frequency ν.

Planck considered quantization as a purely formal assumption, with no physical implications for the nature of light.

(See Chap. 3 of textbook for a description of blackbody radiation, and notes posted on course website for theoretical work on reproducing the blackbody radiation curve.)

Max Planck, 1858-1947

The Photoelectric Effect Einstein, however, took Planck’s idea seriously. In 1905, Einstein proposed that

light consists of a stream of massless particles called photons, each of which carries a quantum of energy:

Can you now explain why, in the photoelectric effect, - electrons are ejected only if the incident light exceeds a certain threshold

frequency?- above this threshold frequency, increasing the light

intensity increases the number of ejected electrons? -above this threshold frequency, increasing the light intensity does not increase

the maximum kinetic energy of the ejected electrons?- increasing the light frequency increases the maximum

kinetic energy of the ejected electrons?

The Photoelectric Effect Einstein, however, took Planck’s idea seriously. In 1905, Einstein proposed that

light consists of a stream of massless particles called photons, each of which carries a quantum of energy:

and explained the photoelectric effect in the following manner:- the incident photons must have sufficient energy (and therefore

exceed a threshold frequency) to overcome the binding energy of the electron to the metal before electrons are ejected -the photon energy above the binding energy is transferred to the kinetic energy

of the ejected electron. Increasing the light intensity (the number of incident photons per unit time per unit area) does not increase the kinetic energy, but only the rate, of the ejected electrons. Increasing the light frequency (the

energy of each photon) increases the kinetic energy of the ejected electrons




Compton effect




The Compton Effect While the interpretation of the photoelectric effect was still being debated, an

even more convincing experiment was made showing that light behaves like particles when interacting with matter.

Arthur H. Compton, 1892-1962

In 1922, the American physicist Arthur Holly Compton measured the effect of shining X-rays on a block of carbon. He found a fraction of the incident X-ray radiation was scattered at different angles θ, and furthermore that the wavelength of the scattered radiation shifted to longer wavelengths at larger angles θ. This effect is now known as the Compton effect.

The Compton Effect Let us see if there is an explanation for the Compton effect if we describe light as

electromagnetic waves.

Like sound or water waves, electromagnetic waves carry momentum: the momentum per unit time per unit area carried by an electromagnetic wave is 〈 S 〉 / c = E0 B0/2μoc (see §3.3), and therefore depends only on the amplitude of its electric and magnetic fields. If the electromagnetic wave transfers a part of its momentum to an electron, we would expect the amplitude of it electric and magnetic field to decrease, but for its wavelength to remain the same.

The Compton Effect If as Einstein proposed light comprises massless photons, then from the Theory of

Special Relativity the (linear) momentum carried by each photon is related to its energy by (c.f., Eq. 4.48, with m = 0).

The momentum of a photon is therefore E/c. The energy per unit time per unit area 〈 S 〉≡ E / (A Δt), and so the momentum per unit time per unit area of an electromagnetic wave is 〈 S 〉 / c as described earlier.

Compton proposed that the incident photons transferred a part of their (linear) momentum to electrons, resulting in a loss of (linear) momentum and therefore energy, and consequently shifted to longer wavelengths.

The Compton Effect By applying the principles of conservation of both (relativistic) momentum and

energy, Compton showed that the wavelength of the scattered X-rays is shifted by an amount

as was observed.

The Compton Effect

The Compton Effect




Compton effect




Wave-Particle Duality of Light Thus, light exhibits both wave-like and particle-like properties.

Light – in the form of electromagnetic waves – shows its wave-like properties as it propagates through space.

Light – in the form of photons – shows its particle-like properties as it interacts with matter.

If our eyes detect individual photons, why do we not see the world as “grainy?”

Wave-Particle Duality of Light

Wave-Particle Duality of Light By contrast, in observational astronomy, we are often photon starved: every photon is precious! The X-ray spectrum on the right is of the supernova Cassiopeia A from a 14-hr integration with the Chandra X-ray Observatory.

Cassiopeia A Supernova Remnant in X-rays

Wave-Particle Duality of Light By contrast, in observational astronomy, we are often photon starved: every photon is precious!

At optical wavelengths, the human eye only detects ~3% (daytime) to ~10% (nightime) of incident photons. The best photographic plates detect ~10% of incident photons. By contrast, Charge Coupled Devices (CCDs) typically detect >90% of incident photons.

Documents

The Interaction of Light and Matter Commonly drawn symbol for photon A more physically meaningful symbol for the photon as an energy wavepacket confined