The Nature of Light

Particle (Corpuscular) Theory

• Advocated by Newton
• Said energy is carried by tiny particles from source
• Could explain rectilinear propagation, reflection, refraction; all observed in 17th century
• Predicted light would travel faster in water than in air

Wave Theory

• Advocated by Christian Huygens, Dutch astronomer, physicist
• Explained reflection
• Explained refraction if light traveled slower in water than in air
• Had trouble explaining rectilinear propagation
• Huygen's principle: Each point on a wave front may be regarded as a new source of disturbance
• Interference of light not known until 19th cent.
• Diffraction couldn't be explained without it
• Discover of interference of light in 1801 and explanation of diffraction in 1816 proved wave theory
• Foucault found speed of light slower in water -- further proof of wave theory
• Since all known waves needed a medium, mysterious substance called ether proposed that enabled light to travel through space.

Electromagnetic Theory

• Light and heat radiate through space
• Faraday proposed lines of force to visualize electric field
• Maxwell developed series of equations explaining light & heat were electromagnetic waves all moving at speed of light
• Each e-m wve has electrical and magnetic components perpendicular to each other and to direction of wave travel
• Hertz discovered radio waves also e-m, moving at same speed with different frequency and wavelength
• Electromagnetic spectrum includes waves from 10 Hz to 10²⁵ Hz
• All e-m waves travel at 3 x 10⁸ m/s ( c)
• Wavelengths range from 3 x 10⁷ m to less than 3 x 10^-17 m
• Often expressed in nanometers or Angstroms (Å)
• Visible region is about 4000 - 7600 Å or 400 - 760 nm

The Photoelectric Effect

• Hertz observed spark discharges improved with illumination (1898)
• Illumination of metal by electromagnetic radiation causes emission of electrons
• Could not be explained by wave theory
• Frequency of e-m radiation determines if emission occurs, not intensity
• Each metal has minimum energy that must be supplied by light before emission occurs: called the work function of the metal.
• Each metal found to have cutoff frequency of incident light below which no emission occurs , no matter how intense the light
• Only particle theory of light could explain this

Quantum Theory

• Max Planck, examining heat radiation ( ir light) proposes energy is quantized, or occurring in discrete small packets with a definite minimum value. (1901)
• All energy amounts were multiple of a certain constant, called Planck's constant h with a value of 6.63 x 10^-34 Js
• Energy of radiation, E = hf

Einstein's Explanation

• Light consists of stream of massless particles called photons having energy hf, moving along electromagnetic waves (1905)
• When photon strikes electron, it gives up all its energy to the electron
• If hf > w (work function of metal), emission occurs
• Light intensity makes no difference if frequency is too low.
• Max. electron kinetic energy = hf - w
• Einstein won Nobel Prize for explanation

Laws of Photoelectric Emission

1. Rate of emission is directly proportional to intensity of incident light
2. Kinetic energy of photoelectrons is independent of intensity of incident light.
3. Maximum kinetic energy of photoelectrons varies directly with difference between frequency of incident light and cutoff frequency of metal

The Quantized Atom

• Rutherford's discovery of nucleus (1911) led to "solar system" model of atom
• Orbiting electrons contradicted e-m theory
• Niels Bohr (1913) proposed model of atom with electron orbits based on quantized energy states
• Difference between energy states always some multiple of Planck's constant

Line Spectra

• Electrons absorb energy and "jump" to higher energy level
• When electrons fall to lower level, they emit photon whose energy equals difference in electron energy at the two levels
• Since frequency depends on energy, different energy changes cause different colors (frequencies) of light emitted
• Unique structure of each element results in unique pattern of emission for each element allowing identification by spectroscopy

The Hydrogen Spectrum

• Hydrogen spectrum first to be analyzed
• Visible emission lines predicted and observed by Balmer; called Balmer series.
• 6 uv emission lines (Lyman series) and 4 ir lines (Paschen series) discovered later.

Matter and Waves

• de Broglie proposed wave-particle duality applied to matter particles, photons must have momentum
• E = hf = mc² ; so mc = h/λ , photon momentum
• λ = h/mv , wavelength of particle with mass m and velocity v

Lasers

• Stands for light amplified by stimulated emission of radiation
• Emit coherent light: same direction, frequency, phase
• Ordinary light sources incoherent

Stimulated Emission

• Normal emission of light is spontaneous, occurs almost instantly when electrons reach higher energy levels
• Many materials can be brought to slightly stable ( metastable) energized state
• Energy input causes population inversion where more atoms are in metastable state than in ground state.
• Spontaneous emission of one photon causes avalanche of identical photons through chain reaction
• All photons have same energy and frequency so light is monochromatic

Laser Construction

• Lasing cavity is shaped for resonance at desired frequency; emissions at other frequencies quickly die out
• Energy input by electricity or light flashes excites lasing medium
• Mirrors at each end reflect laser light back through medium amplifying beam
• Mirror at one end weakly silvered so beam can escape when strong enough
• Some lasers pulse, some continuous
• Many lasing materials discovered, gases, liquids, dyes, solids, semiconductors, crystals, etc.

X-Ray Production

• Reverse of photoelectric effect
• High energy electron beam strike metal causing emission of photons
• E_K = hf_max - w Frequency of photon depends on speed of electron

Light Sources

• Most light comes from the sun
• Incandescent lights use hot filament
• Fluorescent bulbs contain ionized gas that gives off ultraviolet ( uv) radiation absorbed by coating on inside of tube; phosphorus coating then gives off vis. light.
• Hot bodies emit infrared ( ir) radiation--thermal radiation
• Range of frequencies of thermal radiation depends on temp
• "Red hot" is ir plus low frequency vis. (red to orange) about 800° C;
• "White hot" includes higher visible frequencies appearing white, about 3000° C

Terminology

luminous

giving off light because of energy of accelerated particles (sun)

illuminated

seen because of light reflected and scattered from it (moon)

transparent

transmits light readily--clear image can be seen

translucent

light transmitted but scattered--no clear image

opaque

no light transmitted

ray

single line of light

beam

several rays

pencil

narrow beam

diverging

spreading

converging

coming together

focus

converging to a point

umbra

dark central region of a shadow

penumbra

lighter region around the edges of a shadow

Speed of Light

• Originally thought to be instantaneous
• Galileo first to realize it had a finite speed
• Roemer first accurate measurement in 1675 by timing orbital period of Jupiter's moon
• Period varied with Jupiter's distance from earth, must be due to time for light to travel to earth
• First accurate measurement by Michelson using 2 observatories located some distance apart
• Used rotating octagonal mirror to time reflected light and got 299729 km/s in air
• Later did experiments in vacuum, won Nobel prize for this work
• Today c = 2.99792458 x 10⁸ m/s; we will use 3.00 x 10⁸ m/s in air or in vacuum.
• Light travels slower in other transparent substances (water, plastic,etc.)

Light Measurements

Photometry

the quantitative study of light.

Luminous Intensity (I)

measured in candelas, a fundamental unit.

Luminous flux (F)

measured in lumens; energy per unit time delivered through a unit area: a rate of flow.

Illuminance (E)

Density of flux on a surface, measured in lux. 1 lux = 1 lumen/m² and E = F/A

• Since light travels in 3 dim. space, surface for measuring light quantities is a sphere.
• Solid angles are measured in steradians: the ratio of intercepted surface area of a sphere to square of radius
• Angle in steradians = A/r²; 4π steradians in a sphere of one meter radius.
• So: F = 4πI X
• Since area of sphere also 4πr², E = I /r², an inverse square law. Illuminance varies inversely with square of distance from source.
• Luminous Intensity measured with photometer, by comparing light sources in a darkened room.

Photometer types

• Bunsen - grease spot on paper; set known light source on one side, unknown on the other; adjust position of photometer until both sides look equally bright. Calculate intensity with proportion.
• Joly - Like a sandwich of two translucent plastic blocks with metal sheet in middle. Viewed from edge, adjusted until each side equally bright
• Photoelectric - measures current from photoelectric cell. Compare known and unknown light sources.
• Spherical - large hollow sphere painted white with calibrated photocell to measure intensity directly.