Lectures 19-20 Wave Optics-1 Chapter 22 PHYSICS 270 Dennis Papadopoulos March 26-29, 2010

Chapter 22. Wave Optics Light is an electromagnetic wave(!!!).The interference of light waves produces the colors reflected from a CD, the iridescence of bird feathers, and the technology underlying supermarket checkout scanners and optical computers. Chapter Goal: To understand and apply the wave model of light.

Wave Optics Topics: Light and Optics The Interference of Light The Diffraction Grating Single-Slit Diffraction Circular-Aperture Diffraction Interferometers

What is the nature of Light ?

Models of Light The wave model: under many circumstances, light exhibits the same behavior as sound or water waves. The study of light as a wave is called wave optics. The ray model: The properties of prisms, mirrors, and lenses are best understood in terms of light rays. The ray model is the basis of ray optics. The photon model: In the quantum world, light behaves like neither a wave nor a particle. Instead, light consists of photons that have both wave-like and particle-like properties. This is the quantum theory of light.

The invention of radio? Hertz proves that light is really an electromagnetic wave. Waves could be generated in one circuit, and electric pulses with the same frequency could be induced in an antenna some distance away. These electromagnetic waves could be reflected, and refracted, focused, polarized, and made to interfere—just like light!

Everything is a wave “Okay…what you have to realize is…to first order…everything is a simple harmonic oscillator. Once you’ve got that, it’s all downhill from there.”

Waves 101 Part 1: Oscillations An oscillation is a time-varying disturbance. Phasor Representation oscillation y A f=wt x

Travelling Waves wave A wave is a time-varying disturbance that also propagates in space.

Waves vs.Particles Interference waves can interfere (add or cancel). Consequences are that: 1+1 not always 2 , refraction (bend corners), diffraction (spread out of hole), reflection.. waves are not localized and can be polarized particles 1+1 makes 2, localized

The Mathematics of Interference y x

Interference Standing Waves waves can interfere (add or cancel) Vector addition of phasors

Interference in Waves

The Physics of Two Slit Interference ml/2 I=0 I=4A2 ml l ml/4 I=2A2

Positions of bright fringes L>>d Positions of bright fringes Positions of dark fringes Dark fringes exactly halfway between bright fringes

Double Slit experiment for light Minima Maxima

Analyzing Double-Slit Interference The mth bright fringe emerging from the double slit is at an angle where θm is in radians, and we have used the small-angle approximation. The y-position on the screen of the mth fringe is while dark fringes are located at positions

Question 1 Question 2 Light of wavelength l1 illuminates a double slit, and interference fringes are observed on a screen behind the slits. When the wavelength is changed to l2, the fringes get closer together. How large is l2 relative to l1? X l2 is smaller than l1. l2 is larger than l1. Cannot be determined from this information Suppose the viewing screen in the figure is moved closer to the double slit. What happens to the interference fringes? On a plain sheet of paper write Your name Date Your answers to the questions They fade out and disappear. They get out of focus. They get brighter and closer together. They get brighter and farther apart. They get brighter but otherwise do not change. X ym=m(lL/d)

Double slit intensity pattern If there was no interference intensity for two slits  2I1 I1 light intensity of single slit

The Diffraction Grating Suppose we were to replace the double slit with an opaque screen that has N closely spaced slits. When illuminated from one side, each of these slits becomes the source of a light wave that diffracts, or spreads out, behind the slit. Such a multi-slit device is called a diffraction grating. Bright fringes will occur at angles θm, such that The y-positions of these fringes will occur at

m is the order of diffraction

Atotal= NA=10A Itot=(NA)2=N2I1=100I1 Key dependence N2

Dispersive effect – Light with longer wavelength diffracts more Interference pattern is mostly dark but with a small number of very bright and very narrow lines. Why ? L NI1 Dispersive effect – Light with longer wavelength diffracts more

Spectral analysis or Spectroscopy Transmission Grating -> Many parallel slits

Single Slit Diffraction Like water wave passing through a barrier Point sources vs. extended sources Huygen’s Principle

Each point of a wavefront is the source of a spherical wavelet that spreads out at the wave speed At a later time the shape of the waveform is the tangent to all the wavelets

Single Slit Diffraction a<l

Pair wavelets with extra distance traveled l/2 etc

White light passes through a diffraction grating and forms rainbow patterns on a screen behind the grating. For each rainbow, the red side is farthest from the center of the screen, the violet side is closest to the center. the red side is closest to the center of the screen, the violet side is farthest from the center. the red side is on the left, the violet side on the right. the red side is on the right, the violet side on the left. STT22.3 Answer: A

White light passes through a diffraction grating and forms rainbow patterns on a screen behind the grating. For each rainbow, the red side is farthest from the center of the  screen, the violet side is closest to the center. the red side is closest to the center of the screen,  the violet side is farthest from the center. the red side is on the left, the violet side on  the right. the red side is on the right, the violet side on  the left. STT22.3