Light and other electromagnetic radiation

Goals--we want to understand:1. the bizarre, dual nature of light2. the structure of atoms3. how we use light to gain information on objects that

we cannot touch4. what determines how bright an object actually is and

how bright it appears to us

Just what IS light, anyway?

Does it consist of waves of electromagnetic energy? (Huygens)-or-

Does it consist of particles (photons)? (Newton)

-YES-

You can devise an experiment that will prove conclusively that eitherof the above cases is true.

• When light propagates, it is best described as a wave.• When light interacts with matter, it is best described as photons.

This is the clearest example of a concept in quantum mechanics calledwave-particle duality.

• On small scales, all things show some behaviour that is “wave-like,” and some that is “particle-like.”

Light as a waveA light wave consists of an electric field, and a magnetic field, both of

which are oscillating.• As the electric field changes, it causes the magnetic field to change,

and vice-versa.• This way, electromagnetic waves are able to propagate through

space all by themselves.– Other waves need some medium through which they can

propagate (sounds waves through air, for example).

If we draw only the electric field, then the light wave looks morefamiliar:

Wavelength, λ

We describe waves by their:•Wavelength (λ): The distance between identical points on the wave.•Frequency (f): The number of wavelengths that pass by each second.

Wavelength and frequency are related by:

λf = c

C = speed of light. The same for all electromagnetic waves.

Question:

A difference between electromagnetic waves and either sound orwater waves is:

a) Electromagnetic waves all have shorter wavelengths.

b) Electromagnetic waves can travel in a vacuum.

c) Electromagnetic waves all have the same amplitude.

d) Electromagnetic waves can travel from place to placeinstantaneously.

Units:Wavelength:• Angstrom (Å): 10-10 meters• Nanometers (nm): 10-9 meters• Microns (µm): 10-6 meters• Millimeters (mm): 10-3 meters• Meters (m): about three feet

Frequency:• Hertz: 1 cycle per second• Megahertz (MHz): 106 cycles per second• Kilohertz (kHz): 103 cycles per second

Our eyes are sensitive to a very small part of the electromagneticspectrum.

Name: Typical wavelengths Frequencies

X-rays < 10 Å > 3x1017 Hz

Ultraviolet 30-3000 Å 9x1014-1017 Hz(sunburn)

Visible light 4000-8000 Å 4-8x1014 Hz

Infrared 1-100 µm 3x1012-3x1014 Hz(heat)

Microwaves 100 µm - few mm about 3x1011 Hz

FM Radio 2.8 - 3.4 m 88 - 108 MHz

AM Radio 188 - 556 m 540 - 1600 kHz

Diffraction and interference are explained if light is a wave: the two-slit experiment shows both of these at work.

Incoming parallelwave crests Screen with

two slits Viewing screen

Bright lines are seen on the screenwhere the difference in the pathlengths from the two slits to thescreen is an integer number ofwavelengths.

Dark lines are seen where thedifference is an odd half number ofwavelengths.

When the paths from the two slits to the screen differ by λ, 2λ…, the twowaves add. This is called constructive interference.

When the path are l/2, 3l/2… different, the waves cancel. This iscalled destructive interference.

+=

+ =

Doppler ShiftThe change in the observed color of light because the source and the

observer are either approaching or moving away from each other.Static light source: color looks the same to all observers.

Circles are crests ofwaves moving awayfrom light source

Moving light source: light waves expand around where the sourcewas when they were emitted.

1 21

3

2

1

Sees a blueshiftSees aredshift

Sees no shift

Question:

In which of the following situations would the light that we see from a starshow a blueshift?

a) The star is moving away from us.b) The star is moving across our field of view.c) The star is moving towards us.

Light as particles

We also think of light as coming in discrete particles, called photons.• Each photon has a wavelength associated with it, the same as the

wavelength of the color light it represents.• Each photon has an energy given by its wavelength (or,

equivalently, its frequency) as:

This view of light was introduced by Einstein to explain thephotoelectric effect.

E = hf

photonselectrons

metal

Types of Spectra

• Continuous spectrum– All colors present to some degree.– From a hot solid, liquid, or very

dense gas.• Emission-line spectrum

– Only light at certain, veryspecific wavelengths is present.

– From a hot gas.• Absorption-line spectrum

– All colors are present, except atcertain wavelengths.

– From a cool gas in front of acontinuous source.

Continuous Spectra

Most sources of continuous spectra emit Planck (or “blackbody”)spectra.

The wavelength where the spectrum peaks depends upon thetemperature of the source, according to Wien’s Law.

λ peak ∝1T

wavelength

energy

The total amount of electromagnetic energy emitted by a continuoussource increases very rapidly with its temperature, as described byStefan’s Law.

• F is the flux. It is the amount of energy emitted by every unit areaof the surface of the light source.

• For example, a star that is twice as hot as the Sun (but the samesize) would be 16 times brighter.

• Because of this, it is the rare hot stars that dominate the light thatwe see from most galaxies.

F ∝ Τ4

By looking at continuous spectra from multiple sources, we see bothStefan’s and Wien’s Laws in action

The total amount of light emitted by an object (the luminosity) alsoincreases with the total amount of emitting area. For a star, thismeans that:

• R is the radius of the emitting object (NOT the distance to it).• A star with twice the radius of the Sun (but the same temperature)

would emit four times more light.

€

L∝Rsource2

Questions:

Two stars have the same radii. One is blue and the other is red. The redstar appears to be twice as bright as the blue star when you see themin the sky.

Which star is emitting more light?

a) The red star.

b) The blue star

Which star is hotter?

a) The red star.

b) The blue star.

Which star is further away?

a) The red star.

b) The blue star.

Emission and Absorption Spectra“Fingerprints of the atoms”

We can think of atoms as looking like miniature Solar Systems.One or more negatively-charged electrons orbit around a nucleus that

consists of positively-charged protons and neutral neutrons.

deuteriumordinaryhydrogen

helium

0

0 0

+

+

+

+

- -

--

Unlike the Solar System, the electrons can only exist in certain orbits,called energy levels.

The lowest possible energy level, where the electron likes to be, iscalled the ground state.

Higher energy

-

+

When a photon of the right energy hits an atom, the electron can usethe energy of the photon to move to a higher energy level.

The photon is absorbed in the process, resulting in an absorption-linespectrum.

before after

Wrong energy

Right energy

In reverse, an electron that is in a high energy level will spontaneously“jump” to a lower level. The energy that it loses is emitted as aphoton. The result is an emission-line spectrum.

before after

The atoms of each element have unique arrangements of energy levels,and so each elements has a unique absorption and emission-linespectrum. By examining an absorption or emission-line spectrum, wecan therefore determine the chemical makeup of the emitting object.

Another inverse-square lawThe apparent brightness of an object (a star, a candle, a flashlight…)

decreases with the square of distance, like gravity.Imagine two spheres centered on a light source.

A = 4πR2 R1R2

The same photons pass through both spheres. The area of a sphere:

The apparent brightness is

total lightarea

∝1R2

This means, for example, that sunlight is 900 times fainter at Neptunethan at Earth.

Question:

Which of the following characteristics of light are associated with the wavenature of light?

a) Constructive interference and diffraction.

b) The Doppler effect and the formation of spectral lines.

c) Formation of spectral lines and the photoelectric effect.

d) Diffraction and the photoelectric effect.