Chapter 24

1. Chapter 24 Wave Optics

2. Review – waves • T=1/fperiod, frequency • v =  fvelocity, wavelength • Huygen’s principle • Diffraction • Superposition • Interference • Reflection/Transmission • Phase change • Transverse wave • Polarization wavelength amplitude phase

3. Diffraction • Huygens’ principle requires that the waves spread out after they pass through narrow slits • This spreading out of light from its initial line of travel is called diffraction • In general, diffraction occurs when waves pass through small openings, around obstacles or by sharp edges

4. Diffraction and Interference Sections 6 – 8

5. Diffraction Grating • The diffracting grating consists of many equally spaced parallel slits of width d • A typical grating contains several thousand lines per centimeter • The intensity of the pattern on the screen is the result of the combined effects of interference and diffraction

6. Diffraction Grating, 2 • The condition for maxima is • d sin θbright = m λ m = 0, 1, 2, … • The integer m is the order number of the diffraction pattern • If the incident radiation contains several wavelengths, each wavelength deviates through a specific angle

7. Diffraction Grating, 3 • All the wavelengths are focused at m = 0 • This is called the zeroth order maximum • The first order maximum corresponds to m = 1 • Note the sharpness of the principle maxima and the broad range of the dark area • This is in contrast to the broad, bright fringes characteristic of the two-slit interference pattern Active Figure: The Diffraction Grating

8. Which color will diffract largest angle (m=1)in a diffraction grating? 10 • Red (700 nm) • Green (550 nm) • Blue (460 nm) • d sin θbright = m λ

9. Diffraction Grating Spectrometer • The emission spectrum for hydrogen contains four visible wavelengths • All wavelengths are focused at m = 0 • For higher orders, each wavelength deviates through a specific angle • Each order contains the four wavelengths Active Figure: The Diffraction Grating Spectrometer

10. Single-Slit Diffraction • A single slit placed between a distant light source and a screen produces a diffraction pattern • It will have a broad, intense central band – central maximum • The central band will be flanked by a series of narrower, less intense secondary bands – secondary maxima • The central band will also be flanked by a series of dark bands – minima • The results of the single slit cannot be explained by geometric optics • Geometric optics would say that light rays traveling in straight lines should cast a sharp image of the slit on the screen

11. Single-Slit Diffraction • Fraunhofer Diffraction occurs when the rays leave the diffracting object in parallel directions • Screen very far from the slit • Converging lens (shown) • A bright fringe is seen along the axis (θ = 0) with alternating bright and dark fringes on each side

12. Single-Slit Diffraction • According to Huygens’ principle, each portion of the slit acts as a source of waves • The light from one portion of the slit can interfere with light from another portion • All the waves that originate at the slit are in phase • Wave 1 travels farther than wave 3 by an amount equal to the path difference δ = (a/2) sin θ • Similarly, wave 3 travels farther than wave 5 by an amount equal to the path difference δ = (a/2) sin θ

13. Single-Slit Diffraction • If the path difference δ is exactly a half wavelength, the two waves cancel each other and destructive interference results δ =½ λ = (a/2) sin θ -» sin θ = λ / a • In general, destructive interference occurs for a single slit of width a when sin θdark = mλ / a m = 1, 2, 3, …

14. Single-Slit Diffraction • A broad central bright fringe is flanked by much weaker bright fringes alternating with dark fringes • The points of constructive interference lie approximately halfway between the dark fringes • ym = L tan θdark , where sin θdark = mλ / a Active Figure: Fraunhofer Diffraction Pattern for a Single Slit

15. Reflection and InterferencePhase Change Sections 2, 6 – 8

16. Phase Change Due To Reflection • An electromagnetic wave undergoes a phase change of 180° upon reflection from a medium of higher index of refraction than the one in which it was traveling • Analogous to a reflected pulse on a string

17. No Phase Changes Due To Reflection • There is no phase change when the wave is reflected from a medium of lower index of refraction than the one in which it was traveling • Analogous to a pulse in a string reflecting from a free support

18. Lloyd’s Mirror • An arrangement for producing an interference pattern with a single light source • Waves reach point P either by a direct path or by reflection • The reflected ray can be treated as a ray from the source S’ behind the mirror

19. Interference Pattern from the Lloyd’s Mirror • An interference pattern is formed • The positions of the dark and bright fringes are reversed relative to pattern of two real sources • This is because there is a 180° phase change produced by the reflection

20. Thin Films

21. incident wave destructive interference constructive interference destructive interference constructive interference refl. trans. refl. refl./trans. trans. refl. refl./trans. 180 180 180 180 180 0 trans. refl. 0 refl./trans. 0 trans. refl. trans. trans. 0 trans. trans. trans.

22. incident wave constructive interference destructive interference constructive interference destructive interference inc. refl. trans. refl. trans. refl. trans./refl. trans. refl. 180 180 180 180 180 180 trans./refl. trans. refl. trans./refl. 180 180 trans. trans. 180 trans. trans. trans.

23. Polarization Section 9

24. Polarization of Light Waves • Each atom produces a wave with its own orientation of • All directions of the electric field vector are equally possible and lie in a plane perpendicular to the direction of propagation • This is an unpolarized wave

25. Polarization of Light, cont • A wave is said to be linearly polarized if the resultant electric field vibrates in the same direction at all times at a particular point • Polarization can be obtained from an unpolarized beam by • Selective absorption • Reflection • Scattering

26. Polarization by Selective Absorption • E. H. Land discovered a material that polarizes light through selective absorption • He called the material Polaroid • The molecules readily absorb light whose electric field vector is parallel to their lengths and transmit light whose electric field vector is perpendicular to their lengths

27. Selective Absorption, cont • The most common technique for polarizing light • Uses a material that transmits waves whose electric field vectors in the plane are parallel to a certain direction and absorbs waves whose electric field vectors are perpendicular to that direction

28. Selective Absorption, final • The intensity of the polarized beam transmitted through the second polarizing sheet (the analyzer) varies as • I = Io cos2 θ • Io is the intensity of the polarized wave incident on the analyzer • This is known as Malus’ Law and applies to any two polarizing materials whose transmission axes are at an angle of θ to each other Active Figure: The Linear Polarizer

29. Polarization by Reflection • When an unpolarized light beam is reflected from a surface, the reflected light is • Completely polarized • Partially polarized • Unpolarized • It depends on the angle of incidence • If the angle is 0° or 90°, the reflected beam is unpolarized • For angles between this, there is some degree of polarization • For one particular angle, the beam is completely polarized

30. Polarization by Reflection, cont • The angle of incidence for which the reflected beam is completely polarized is called the polarizing angle, θp • Brewster’s Law relates the polarizing angle to the index of refraction for the material • θp may also be called Brewster’s Angle

31. Polarization by Scattering • When light is incident on a system of particles, the electrons in the medium can absorb and reradiate part of the light • This process is called scattering • An example of scattering is the sunlight reaching an observer on the earth becoming polarized

32. Polarization of Sunlight by Scattering • Unpolarized sunlight is incident on an air molecule • The horizontal part of the electric field vector in the incident wave causes the charges to vibrate horizontally • The vertical part of the vector simultaneously causes the charges to vibrate vertically • Horizontally polarized waves are emitted downward toward the observer • Vertically polarized waves are emitted parallel to the Earth

33. Review for Exam III