Recap Waves propagate spherically outward from source: Far from the source, they become plane waves -Wave fronts, Wavelength, Speed: c=λf -Rays are just the direction of the wavefronts Here a lens has refracted spherical waves into plane waves

Recap Waves carry Energy ~ E 2 -How much energy?Watts: Energy/sec “Brightness” -How intense is the energy?Watts/Area Intensity (S or I) Example: 100 watt light-bulb: 100 joules/second How Intense? At surface:r = 4 cm A =.02 m 2 Intensity = 5000 W/m 2 10 meters away:r = 10 m A = 1260 m 2 Intensity: =.08 W/m 2 “Intensity falls off with square of distance”

Now we look at the behavior of Light 1. Reflection & Refraction – Reflection: Angle of incidence = Angle of reflection –Refraction: n i sinθ i = n r sinθ r 2.Interference & Diffraction 3. Wave/Particle Nature of Light “Quantum” nature of light

Behavior of Light All these subjects involve the questions:: -How is light generated? -How does light propagate? -How does light interact with materials (i.e., not vacuum)?

The Historical Debate Newton and others:Light is a stream of particles: They can bounce off a surface (reflection) They can pass through a surface (transmission) ?But why does light refract? Huygens and others:Light is a wave It can diffract (spread out) It obeys wave mechanics: Interference ?But how does light exert a force? The UndecidedEither way: ?what happens to light after it heats water?

The Young Double-Slit Experiment Thomas Young, early 19 th century, shined light through two slits. The resulting intensity pattern was indicative of wave behavior: (Image is actually water going through two openings)

Comparison of Particle vs Wave Intensity on a Screen BB’s might give this pattern. Waves give this pattern.

Wave Mechanics (briefly) 1. Superposition At any point:A net = A 1 +A Interference: Constructive and Destructive Note Intensity on Screen: Two equal magnitude EM waves in phase: (E 1 = E 2 ) E sum = E 1 + E 2 = 2E 1 S = ε 0 c(2E 1 ) 2 = ε 0 c4E 1 2 Not:S = S 1 + S 2 = ε 0 c2E 1 2

Superposition & Interference of Waves

Wave Mechanics 3. Diffraction: - Waves spread out from narrow opening. (Why? See below.)

Diffraction Opening ~ λOpening >> λ

Double Slit Revisited

Huygen’s Principle  Each point on a wave front acts as a point source of light.  We can use this to “explain” geometric optics.

Huygen’s Principle Plane Wave : Interference among all the point sources along the wave front results in – another plane wave. Diffraction: When a plane wave passes through an narrow opening, however, the point sources on either side are blocked off. Rays at an angle to the wave front are no longer suppressed. The wave front becomes a spherical wave again. Single Slit Interference: An interference pattern results from a single slit because different points in the opening are interfering with each other. Refraction: See below

Refraction (at last) At an interface between two mediums, light changes direction. Depends on the indices of refraction of incident and refracting media Illustration shows the angles involved

Refraction & Huygens As it propagates through any non-vacuum medium, light is continually being absorbed and re-emitted. NOTE: This is not explained yet! It takes time for this process to occur. The “slower” the medium, the longer it takes. So light slows down. But the frequency of the waves remains the same. (EM theory) Using Huygens Principle: The wavelets from the points inside the material are moving slower. So the wave front bends..

Why does light refract? 1. As it goes through a material, EM radiation is being absorbed and re-emitted by the atoms/molecules of the material. (We’ll talk later about the Interaction of Light & Matter.) 2. It is re-emitted with the same frequency it had previously. 3. However, the absorption & re-emission process takes time. 4. This means light slows down in a material. (Speed v < c.) 5. This also means that the wavelength of light changes in the material. (λ = v/f) The result: Look at a prism >> The prism doubly refracts the light. >> Each wavelength refracts at a different angle: Dispersion (That is, the bending depends on the wavelength.) >> So we see “fringes” of color around an object when we look through a prism. Dispersion has separated the wavelengths in white light.

Still ahead: -How is light absorbed & emitted? -Why does some light reflect and some light refract at an interface? -What about the “photoelectric effect”? How can light create a current?