The Wave Nature of Light

1. The Wave Nature of Light Chapter 24

2. Overview • Light sometimes acts as a wave • Diffraction • Interference • Considered an EM wave by the end of the 19th century • Light sometimes acts as a particle • Compton Effect • Photoelectric Effect • Early 20th century

3. Huygens’ Principle and Diffraction • Christian Huygens (1629–1695) • Every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at the speed of the wave itself. • The new wave front is the envelope of all the wavelets – that is, tangent to all of them.

4. Huygens’ Principle Cont. • Huygens’ Principle explains diffraction • Diffraction • Bending of light around an object • At some point there is only one point where the wave is either blocked or free to continue • The ray model cannot explain diffraction

5. Huygens’ Principle and the Law of Refraction Ray • At point A, the wave front emitting from A travels a shorter distance than the wave front from B • The angle of incidence is perpendicular to the old wave front • The angle of refraction is perpendicular to the new wave front wave front θ1 v1t B Medium 1 A D Medium 2 v2t C θ2 Ray

6. Huygens’ Principle and the Law of Refraction Ray • Angle ADC = θ2 • Angle BAD = θ1 • Both triangles have common sides AD • sinθ1 = v1t/AD • sin θ2 = v2t/AD • sinθ1/sinθ2 = v1/v2 • v = c/n • n1sinθ1 = n2sinθ2 • Wavelength changes as the light moves to a different medium • λn = λ/n wave front θ1 v1t B Medium 1 A D Medium 2 v2t C θ2 Ray

7. Interference – Young’s Double-Slit • Thomas Young (1773-1829) • Experiment (1801) • Provided evidence of wave nature of light • Method of measuring wavelength of light • Light strikes two very close slits • Series of bright lines and dark spots

8. Constructive vs. Destructive Interference • Constructive Interference • Waves combine together • Creates a bright spot • Destructive Interference • Waves cancel out • Creates a dark spot

9. Young’s Double-Slit Experiment • Center • Travel same distance • Two waves are in phase • Constructive interference • Bright spot S1 d S2 L

10. Young’s Double-Slit Experiment • Bright Spot • Bottom slit wave travels an extra wavelength in distance • Two waves are in phase • Constructive interference θ S1 θ d λ S2 L

11. Young’s Double-Slit Experiment • Dark Spot • Bottom slit wave travels an extra ½ wavelength in distance • Two waves are out of phase • Destructive interference θ S1 θ d λ/2 S2 L

12. Young’s Double-Slit Experiment • Determining bright and dark spots • Bright Spot • dsinθ = mλ for m = 0, 1, 2, … for constructive • Dark Spot • dsinθ = mλ for m = 0, 1, 2, … for destructive • Intensity decreases as the value “m” increases

13. Example • A screen containing two slits 0.1 mm apart is 1.2 m from the viewing screen. Light of wavelength 500 nm falls on the slits from a distant source. Approximately how far apart will adjacent bright interference fringes be on the screen?

14. Young’s Double-Slit Experiment • White Light • Only the central maximum is white • Different wavelengths in the equation change the angle • The spectrum is visible at each of the other maxima • Young was able to determine the wavelengths of different colors of light

15. Example • White light passes through two slits 0.5 mm apart, and an interference pattern is observed on a screen 2.5 m away. The first-order fringe resembles a rainbow and the red 2.5 mm from the center of the central white fringe. Estimate the wavelenghts for the violet and red light.

16. The Visible Spectrum and Dispersion • Brightness and color are two distinct characteristics of visible light • Brightness – energy of the wave per unit time • Color – wavelength • 400 nm – 750 nm (violet – red) • Ultraviolet is smaller • Infrared is larger

17. The Visible Spectrum and Dispersion • Prisms • Separates white light into a spectrum • Index of refraction depends on wavelength • Greater for shorter wavelengths • Dispersion - spreading light into a spectrum • Rainbows • Diamonds

18. Diffraction by a Single Slit • Diffraction patterns • Exist around any sharp object illuminated by a point source • Due to interference of waves diffracted around an object

19. Diffraction by a Single Slit • Parallel rays pass through a single slit • Central is a maximum • All are in phase • Minimum • Dsinθ = mλ, m = 1, 2, … • D = length of slit (m) • θ = angle from a line perpendicular to slit • λ = wavelength (m) • m = 1 is the first minimum θ D

20. Example • Light of wavelength 750 nm passes through a slit 1E-3 mm wide. How wide is the central maximum in degrees if the screen is 20 cm away? How wide is the central maximum in centimeters?

21. Diffraction Grating • Large number of slits in a grating • Useful for determining wavelengths of light • Transmission • Light passes through slits • Will be used in lab • Reflection • Light is reflected off small flat surfaces between raised areas • CD

22. Diffraction Grating • Similar to Young’s double-slit experiment only now we have more slits • Same resulting equation • dsinθ = mλ, m = 0, 1, 2, … • d = distance between gratings (m) • θ = angle from line normal to grating • λ = wavelength (m) • Maxima are much sharper and more intense in brightness

23. Example • Determine the angular positions of the first and second order maxima for light of wavelength 400 nm and 700 nm incident on a grating containing 10000 lines/cm.

24. Example • White light containing wavelengths from 400 nm to 750 nm strikes a grating containing 4000 lines/cm. Show that the blue at 450 nm of the third order spectrum overlaps the red at 700 nm of the second order.

25. Interference by Thin Films • Only occurs if film thickness is on the order of the wavelength of the light • Soap bubbles on water • Spectrum is result of interference between light reflected from two different surfaces close together • Some of the light is reflected, while some is refracted and reflected off of the second surface

26. Interference of Thin Films • Bright vs. Dark Spots • Constructive - total path in film is a multiple of λ • Destructive - total path in film is a multiple of λ/2 • λ n = λ/n • Different colors • Due to viewing angle and thickness of film at that spot • A particular wavelength of color will have constructive interference

27. Interference of Thin Films • Newton’s rings • Dark spot occurs at center • If n2>n1, the reflected wave will have its phase changed by ½ a wavelength B D A C

28. Example • A very fine wire 7.35E-3 mm in diameter is placed between two flat glass plates. Light whose wavelength in air is 600 nm falls (and is viewed) perpendicular to the plates, and a series of bright and dark bands are seen. How many light and dark bands will there be in this case? Will the area next to the wire be bright or dark?

29. Interference by Thin Films • Thin film interference is used to make nonreflecting lenses • Glasses, telescopes, and cameras • Coat the lens • Front surface interferes destructively from light from the rear surface • Choose a material designed for middle of the spectrum (550 nm)

30. Example • What is the thickness of an optical coating of MgF2 whose index of refraction is 1.38 and is designed to eliminate reflected light at wavelengths (in air) around 550 nm when incident normally on glass for which n = 1.5?

31. Polarization • Linearly polarized, or plane-polarized • Oscillates in a plane • Only works for transverse waves • Polarization of a plane-polarized EM wave is taken as the direction of the electric field

32. Polarization • Light is normally not polarized • Can be polarized by using a polaroid sheet or by reflection • I = Iocos2θ • I = Intensity • Io = Original Intensity • θ = angle between polarizer transmission axis and plane of polarization of incoming wave • Polaroid Sheet • Electric field does work on surrounding molecules in the sheet • Only electric field oriented in a certain direction is not affected

33. Example • Unpolarized light passes through two Polaroids: the axis of one is vertical and that of the other is at 60o to the vertical. Describe the orientation and intensity of the transmitted light.

34. Polarization • Reflection • Non metallic surfaces reflect light preferentially in the direction parallel to the surface • Brewster’s Law • tanθp = n2/n1 • θp = Brewster’s Angle (measured with respect to normal) • A wave arriving at brewter’s angle will always have a 90o angle between the reflected and refracted wave

35. Example • At what incident angle is sunlight reflected from a lake with an index of refraction of 1.33 plane-polarized? What is the refracted angle?