THE NATURE OF LIGHT

THE NATURE OF LIGHT Light is an ELECTROMAGNETIC WAVE Light is also a PARTICLE: the PHOTON This nominal contradiction is an example of COMPLEMENTARITY or DUALITY in QUANTUM MECHANICS. Depending on circumstances it is preferable to use one or the other point of view for light, electrons, protons, atoms: anything which is too small to be described by normal physics and directly experience requires using quantum mechanics

First, the Wave Nature • Light is a TRANSVERSE ELECTROMAGNETIC WAVE. • Electric (E) fields oscillate perpendicular to • Magnetic (B) fields and the ENERGY FLOWS PERPENDICULAR to both fields. • Other transverse waves: WATER waves, SECONDARY (shear) SEISMIC waves. • LONGITUDINAL WAVES have ENERGY FLOWS PARALLEL to oscillations: SOUND, PRIMARY (compressional) SEISMIC waves.

Transverse Electromagnetic (EM) Wave

Electric and Magnetic Fields • Charged particles (protons or ions +, electrons -) attract or repel each other. • Electric fields accelerate charged particles along the lines. • Charged particles orbit around magnetic field lines.

Characteristics of All Waves • Frequency (f or  [nu]): oscillations per sec (Hz) • Speed (v): depends on medium, sometimes  (cm/s or m/s) • Wavelength ( [lambda]): distance between crests (cm) • Amplitude (A): strength of oscillation • Anatomy of a Wave Applet

Key Relations for ALL Waves • Speed = Wavelength x Frequency v = f • Or f = v/  or  = v/f • Power Amplitude2P  A2 • Surface Waves in a Pond

Wavelength and Frequency for Light wavelength x frequency = speed of light = constant

For EM Waves ONLY v = c = 2.9979x108 m s-1 = 3.00x1010 cm s-1 = 3.00x105 km s-1= 186,000 miles/s The speed of light does not depend upon direction or frequency in a vacuum and doesn’t need a medium. It is a CONSTANT of NATURE. • In matter, v < c and the same frequency has a shorter wavelength than in vacuum. The INDEX OF REFRACTION, n = c/v >= 1. In air, n = 1.0003; in normal glass, n  1.5

Special Topic: Polarized Light • EM WAVES CAN ALSO BE POLARIZED: • E field in a particular plane; B field in one perpendicular plane  LINEAR POLARIZATION: this is the only kind of polarization we'll worry about. • Reflection can change the polarization of light • Polarized sunglasses block light that reflects off of horizontal surfaces

The Seven Bands of the EM Spectrum  Microwave or millimeter between Radio and IR

Atmospheric Transmission • Radio  > 1 cm -- The longest waves or lowest frequencies. • Penetrates atmosphere if <15 m • So AM reflects off ionosphere while FM penetrates • Millimeter or microwave: 1 cm >  > 0.003 cm -- partially penetrates atm; molecules absorb. • Infrared (IR) 0.003 cm >  > 7.2x10-5 cm = 720 nm • CO2 , H2O etc absorb most but some s penetrate

Visible Wavelengths • VISIBLE (OPTICAL): 720 nm = 7200 Å >  > 380 nm = 3800 Å, 4.2 x 1014 Hz < f < 7.9 x 1014 Hz. • Penetrates atmosphere (shorter scatter more) • Visible spectrum: RED (longest wavelength), ORANGE, YELLOW, GREEN, BLUE, VIOLET (shortest wavelength -- highest frequency) • Our eyes evolved to see this light, since the Sun produces most of its radiation in this band, and since nearly all of this radiation gets through the atmosphere. • Visible Light Applet

Colors of Light • White light is made up of many different colors

Shortest Wavelengths • ULTRAVIOLET (UV): 380 nm >  > 300Å = 30nm Mostly absorbed in atmosphere: ozone (O3) Good thing, since UV radiation causes skin cancer. • X-RAY: 300 Å >  > 0.1 Å = 0.01nm, Absorbed in atmosphere: by any atom (N, O) A good thing too: X-rays can penetrate the body and cause cancer in many organs. • GAMMA-RAY(-ray):  < 0.1 Å =0.01 nm, The most energetic form of EM radiation. Absorbed high in atmosphere: by any atomic nucleus. A VERY good thing: gamma-rays quicklycause severe burns and cancer.

Blue light is (compared to red light), • Shorter wavelength • Longer wavelength • Higher energy photons • 1 and 3 • None of the above

We can’t see infrared, but we can perceive it as: • Heat • Radar • Sound • AM • FM

How are Electromagnetic Waves Made? • Most come from ATOMIC, MOLECULAR or NUCLEAR TRANSITIONS. I.e., electrons or protons changing quantum states. • BUT FUNDAMENTALLY, EM RADIATION IS PRODUCED BY AN ACCELERATED CHARGED PARTICLE. • Since ELECTRONS have the LOWEST MASSES they are MOST EASILY ACCELERATED, therefore, electrons produce most EM waves.

Examples of EM Wave Generation • Radio - TV - Cell Phone transmission towers. Electrons oscillate up & down • Synchrotron Radiationproduced by electrons spiraling around magnetic field lines, when moving at nearly speed of light. • The circular part of the motion is ACCELERATED and produces the radiation. Synchrotron radiation is strongly POLARIZED; most EM radiation is basically UNPOLARIZED

How do Waves Interact with Matter? • EMIT (light is sent out when a bulb is turned on) • REFLECT (angle of incidence = angle of reflection) or Scatter (spread out reflection) • TRANSMIT (low opacity) • ABSORB (high opacity) • REFRACT (bend towards normal when entering a medium with a slower propagation speed) • INTERFERE (only a WAVE can do this) Either: CONSTRUCTIVE (waves add when in phase) DESTRUCTIVE (waves cancel when out of phase) • DIFFRACT (only a WAVE can do this) Waves spread out when passing through a hole or slit. This is important only if the size of the hole or slit is comparable to the wavelength.

Reflection and Scattering Mirror reflects light in a particular direction Movie screen scatters light in all directions

Interactions of Light with Matter Interactions between light and matter determine the appearance of everything around us: objects reflect some wavelengths, absorb others and emit others.

When light approaches matter, it can • Be absorbed by the atoms in the matter • Go through the matter, and be transmitted • Bounce off the matter, and be reflected • Any of the above • Only 2 or 3

Thought QuestionWhy is a rose red? • The rose absorbs red light. • The rose transmits red light. • The rose emits red light. • The rose reflects red light.

Interference and Diffraction

Light as Particles • ELECTROMAGNETIC ENERGY IS CARRIED BY PHOTONS: • A PHOTON is a SINGLE QUANTUM OF LIGHT. The energy of one photon of a particular frequency is: • E = hf = h c /  h = 6.63 x 10-34 Joule sec = 6.63 x 10-27 erg sec is PLANCK's CONSTANT. • Along with c, the speed of light; e, the charge on an electron (or proton) and G (Newton's constant of gravity), h is one of the • FUNDAMENTAL CONSTANTS of NATURE.

Thought QuestionThe higher the photon energy… • the longer its wavelength. • the shorter its wavelength. • energy is independent of wavelength.

Photons vs. Waves • These PHOTONS can equally well explain • REFLECTION, • REFRACTION, • TRANSMISSION and • ABSORPTION • as can the Wave picture, • BUT they can't explain • INTERFERENCE and • DIFFRACTION.

Photons vs. Waves, Round 2 • On the other hand the WAVE picture can't explain: • The PHOTOELECTRIC EFFECT (where metals emit electrons when light shines on them) • and SPECTRAL LINES (where only specific wavelengths of light emerge from particular elements) • while the PARTICLE part of the duality in Quantum Mechanics CAN! • We’ll soon discuss each of these key aspects of light: the latter is at the core of modern astronomy.

How can light behave as both a wave and a particle? • It doesn’t really • It really is simultaneously both a wave and a particle • Light and small objects such as atoms behave in ways we never see in everyday objects, so we can’t describe them in everyday terms • This is what quantum mechanics describes • 3 and 4

Radiation, Temperature and Power • Crudely, hotter matter produces more highly accelerated charged particles, which therefore produces more powerful EM radiation. • Heat energy is proportional to temperature: • E = k T (where T is in Kelvins, 0 at ABSOLUTE ZERO). • So the thermal (heat) energy in atoms should be proportional to the photon energy: using math • h f  kT OR •   1/T

Temperature Scales • Only the US has stuck with Fahrenheit temperatures; • The rest of the world normally uses Celcius, but • ENERGIES VANISH AT ABSOLUTE ZERO: THE NATURAL TEMPERATURE SCALE IS KELVINS. • The size of 1 degree C = 1 K and = 1.8 degrees F. • 0 C = 273.16 K (round it off) • The conversion formula is: F = (9/5)*C + 32 • or C = (5/9)*(F - 32)

Wien’s Law Or, max=2,900,000/T (nm) This is the PEAK WAVELENGTH for BLACKBODY (or Thermal, or Planckian) emission from a SOLID, a LIQUID or a DENSE GAS. • Ex: T = 5800K = 5.8x103K =0.5x10-4cm=5x10-5cm =500 nm = 5000Å Wien's Law Applet

Thermal Spectra

Properties of Thermal Radiation Hotter objects emit more light at all frequencies per unit area. Hotter objects emit photons with a higher average energy.

Thought QuestionWhich is hotter? • A blue star. • A red star. • A planet that emits only infrared light.

Thought QuestionWhy don’t we glow in the dark? • People do not emit any kind of light. • People essentially only emit light that is invisible to our eyes. • People are too small to emit enough light for us to see. • People do not contain enough radioactive material.

The Photoelectric Effect • Electrons can be expelled from many materials if light shines upon them. • If the wavelength is TOO LONG (low frequency) nothing happens, • EVEN IF the INTENSITY of the light is HIGH. • Above a CRITICAL FREQUENCY the emitted electrons have a maximum energy (or velocity) that RISES with the FREQUENCY. • Ee = h f - h fcrit • Increasing the INTENSITY of light above the critical frequency increases only the number of ejected electrons, but NOT their energies.

Photoelectric Effect, Illustrated

Importance of Photoelectric Effect • Einstein pointed out that the wave theory could not explain this, while quanta of energy, with E = h f could. • The wave theory predicted that even red light, if intense enough, would eject electrons -- but this never happened. • The wave theory also said that as the blue light was made brighter, faster electrons would emerge: • instead only more of them came out, • but their maximum kinetic (motion) energy was a function ONLY of the light's FREQUENCY.

The Stefan-Boltzmann Law • Integrate (add up) a blackbody spectrum and find that the FLUX, or ENERGY/TIME/AREA is given by • F =  T4 where  = 5.67x10-8W m-2 K-4 =5.67x10-5erg s-1cm-2K-4 • POWER = FLUX x AREA, or, for a sphere (of AREA = 4  R2) L = 4   R2 T4 • For example, double T and raise L 16 times! Or raise T by 1% and L goes up about 4%.

Peer Instruction Question:What happens to thermal radiation (a continuous spectrum) if you make the source hotter? • More energy comes out at all wavelengths • The peak of the spectrum-energy curve (the wavelength at which mostenergy is emitted) shifts redward • The peak of the spectrum-energy curve shifts blueward • 1 and 2 • 1 and 3

THE NATURE OF LIGHT