More Light and Optics

Light – Wave or particle?• For many years scientists argued over the

nature of light, "Is light a wave or a stream of particles?"

• In some experiments light exhibits wave like properties, the Doppler effect, interference, refraction, diffraction

• and in other experiments, like the photo electric effect, it exhibits particle like properties

• The fact is that light exhibits behaviors which are characteristic of both waves and particles.

Models of Light - Waves• Electromagnetic waves (light) originate from vibrating or

accelerating electric charges• Electromagnetic waves are made up of an electric field and a

magnetic field oscillating at right angles relative to one another

Unlike other waves, light waves can travel through a vacuum

• An electromagnetic wave (light) is a transverse wave

Models of Light - Particles• Particle of light are called photons

• Photons have zero rest mass and travel at the speed of light through a vacuum.

Speed of Light - c• In the early 17th century, many scientists believed that

there was no such thing as the "speed of light"; they thought light could travel any distance in no time at all.

• In the 1670's Roemer was able to calculate a value for the speed of light by carefully studying the orbit of one of Jupiter’s moons, Io. He noticed that the time between the eclipses of the moons of Jupiter was less as the distance away from Earth is decreasing than when it is increasing.

• In 1926 scientist Albert Michelson used the reflection from a rotating mirror on a distant mountain and measured the speed of light at 299,796 km/second

• The current accepted value is 300,000,000 meters per second (3 x 108 m/s) or 186,000 miles per second. Light waves

obey the wave equation, c = f

Things the produce electromagnetic waves

• Radio waves – electrons moving up and down an antenna

• Visible Light – electrons changing energy states in an atom

Wave/ParticlePhenomenon Can be explained in terms

of waves.Can be explained in terms of particles

Reflection yes yes

Refraction yes yes

Interference yes no

Diffraction yes no

Polarization yes no

Photoelectric effect no yes

Light and Energy• For waves, the amplitude or intensity is usually

related to the energy of the wave• For light, this is not true. The energy of light waves

was found to be directly related it is frequency.• An experiment demonstrating the photoelectric

effect demonstrated the particle nature of light and that E = hf, where E is energy, h is Planks constant, and f is frequency.

http://phet.colorado.edu/new/simulations/sims.php?sim=Photoelectric_Effect

The Photoelectric Effect• Laws of photoelectric emission• For a given metal and frequency of incident radiation, the rate at which

photoelectrons are ejected is directly proportional to the intensity of the incident light.

• For a given metal, there exists a certain minimum frequency of incident radiation below which no photoelectrons can be emitted. This frequency is called the threshold frequency.

• Above the threshold frequency, the maximum kinetic energy of the emitted photoelectron is independent of the intensity of the incident light but depends on the frequency of the incident light.

• The time lag between the incidence of radiation and the emission of a photoelectron is very small, less than 10-9 second

The equation is , where h is Planck's constant, f is the frequency of the incident photon,Φ is the work function (sometimes denoted W instead), the minimum energy required to remove a delocalised electron from the surface of any given metal.

R O Y G B I V

The Electromagnetic SpectrumThe electromagnetic spectrum is the range of electromagnetic waves extending from radio waves to gamma rays

Increasing frequency

The Visible Spectrum• We can only see a small part of the

electromagnetic spectrum• The visible spectrum is a range of light waves

extending in wavelength from about 400 to 700 nanometers.

Increasing frequencyIncreasing energy

Increasing wavelength

Things that can separate white light

• Prism• Raindrops• CD’s• Diffraction Grating

Young’s Double-Slit Experiment• The wave theory of light came to prominence with Thomas Young’s

double-slit experiment, performed in 1801.• The double-slit experiment proves that light has wave properties because

it relies on the principles of constructive interference and destructive interference, which are unique to waves.

Constructive and Destructive Interference• At any point P on the back screen, there is light from

two different sources: the two slits. The line joining P to the point exactly between the two slits intersects the perpendicular to the front screen at an angle .

• The light from the right slit—the bottom slit in our diagram—travels a distance of l = d sin more than the light from the other slit before it reaches the screen at the point P.

• As a result, the two beams of light arrive at P out of phase by d sin. If d sin = (n + 1/2), where n is an integer, then the two waves are half a wavelength out of phase and will destructively interfere.

• On the other hand, if d sin = n, then the two waves are in phase and constructively interfere, so the most light hits the screen at these points. Accordingly, these points are called the maxima of the pattern.

Double-Slit Diffraction/Interference Pattern

Double-Slit Diffraction/Interference Pattern

If x = , then = d sin For L>>d, in large and small triangles are equal. L is distance to screen.

Double-Slit Diffraction/Interference Pattern

= d sin tan = y/L, where y is the distance between the bright spots and L is the distance to screen. For small angles tan = sin so = d y/L

y =L/d

L

y

Single-Slit Diffraction Pattern

= W sin

OR

= a sin

This time the solution is for the destructive points (the dark spots) By the same argument as in double slits y =L/a y is measured from the center to the first dark spot.

a and W are slit width

Diffraction Grating• A diffraction grating is a screen with a bunch of

parallel slits, each spaced a distance d apart• The condition for maximum intensity is the same as

that for a double slit. However, angular separation of the maxima is generally much greater because the slit spacing is so small for a diffraction grating.

Polarization• As an electromagnetic wave

traveled towards you, then you would observe the vibrations of the slinky occurring in more than one plane of vibration

• A light wave which is vibrating in more than one plane is referred to as unpolarized light.

• Light emitted by the sun, by a lamp in the classroom, or by a candle flame is unpolarized light

The Structure of the Atom and Emission• An atom is composed of electrons,

protons and neutrons.• When an electron is raised to a

higher energy level, the atom is said to be excited.

• When the electron returns to a lower energy level, energy is released in the form of light.

• Different transitions from high levels to low levels result in different colors of light.

The Kirchhoff-Bunsen Experiment

• These two scientists found that burning chemicals over an open flame resulted in a spectrum with bright lines.

• They found that each chemical element produced its own characteristic pattern of bright spectral lines.

Emission Spectra of Hydrogen

Photographic Film

Slit

Low DensityGlowing

Hydrogen Gas

Discrete Emission Spectrum

Film

Prism

Hot gas produces a bright line emission spectrum. RH is 1.09678 x 10-2 nm-1

Calculating the energy in a transition

The Rydberg Equation:

RH is 1.09678 x 10-2 nm-1

1 eV = 1.6 x 10-19 J

Every element can be “fingerprinted” by it spectra.

Helium

Hydrogen

Oxygen

Carbon

Incandescence• Hot, dense solids produce a continuous

spectrum.

• The brightness and color of light emitted by a hot object changes with its temperature.

• Glowing object colors:• Reddish coolest glowing object• Orange-ish• Yellowish• White• Bluish hottest glowing object

Continuous Spectrum

Absorption Spectra

• Cool gas in front of a continuous source of light produces an absorption line spectrum.

• Fraunhofer lines in our Sun's spectrum showed that cool helium gas surrounds the Sun

Absorption Spectrum

Absorption Spectra of Hydrogen

Discrete Absorption Spectrum

Prism

Photographic Film

Film

Slit

White Light Source

Discrete Emission Spectrum

Hydrogen Gas

Sources

• Conceptual Physics by Paul Hewitt• www.physicsclassroom.com• http://observe.phy.sfasu.edu/courses/

phy101/lectures101/