THEORIES OF LIGHT Is light a wave or a stream of particles?

1. THEORIES OF LIGHT Is light a wave or a stream of particles? Let’s first analyze characteristics behaviors of light as a wave: All waves are known to undergo reflection or the bouncing off of an obstacle.

2. All waves are known to undergo refraction when they pass from one medium to another medium. Diffraction involves a change in direction of waves as they pass through an opening or around an obstacle in their path.

3. Wave interference is a phenomenon that occurs when two waves meet while traveling along the same medium. Polarized light waves are light waves in which the vibrations occur in a single plane. The process of transforming un-polarized light into polarized light is known as polarization.

4. Now what about the particle-like behavior?

5. The photoelectric effect is observed when light of a certain frequency strikes a metal and ejects electrons.

6. Phenomenon Can be explained in terms of waves Can be explained in terms of particles Reflection Refraction Interference Diffraction Polarization Photo-electric effect

7. THEORIES OF LIGHT Newton's theory - light consists of particles called corpuscles; this theory only explained reflection and refraction. Wave theory of light (Maxwell's theory) - light behaves like a wave; this explained all the properties of light such as reflection, refraction, diffraction, interference and polarization; it did not explain the photoelectric effect or radiation produced by an incandescent light. Quantum theory - light has a dual nature: when light is transmitted through space or matter, it behaves like a wave; when light is emitted or absorbed, it behaves like a particle called a photon.

8. ELECTROMAGNETIC WAVES Electromagnetic waves are waves that are capable of traveling through a vacuum. They consist of oscillating electric and magnetic fields with different wavelengths. The wave speed equation is: c = f λ wherecis the speed of light.

9. The Electromagnetic Spectrum 

10. Wavelengths

11. Coherent Light A beam of light composed of wavefronts that are vibrating in the same phase. To maintain a common phase over long distances, coherent wavefronts must be monochromatic (have the same wavelength). As an example, most laser sources produce monochromatic, linearly polarized, highly coherent wavefronts.

12. YOUNG’S DOUBLE SLIT EXPERIMENT Two coherentsources producing waves of the same frequency and amplitude produce an interferencepattern.

13. (a) The coherent waves from two slits are shown in blue (top slit) and red (bottom slit). The waves spread out as a result of diffraction from narrow slits. The waves interfere, producing alternating maxima and minima, or bright and dark fringes, on the screen. (b) An interference pattern. Note the symmetry of the pattern about the central maximum (n = 0).

14. Young’s double slit experimentshows that monochromatic light passing through two openings produces an interferencepattern.

15. The position of lines of constructive interference can be determined fromthe following equation: m λ = d sin θ where d is the distance between the slits, and θ is the grating angle. This angle is equal to the angle formed by a line drawn from the center between the slits to the region of constructive interference and the normal to the center of the line which connects the slits. x

16. m λ = d sin θ λ is the wavelength of the monochromatic light incident on the double slit, x is the separation between fringes and L is the distance from the light source to the screen. x If the angle θ is small, we can approximate the wavelength by: So:

17. m λ = d sin θ m λ is the path difference between the sources and the region of constructive interference. The path difference is a whole number of wavelengths for constructive interference.

18. The interference that produces bright or dark fringes depends on the difference in the path lengths of the light from the two slits. (a) The path-length difference at the position of the central maximum is zero, so the waves arrive in phase and interfere constructively. (b) At the position of the first dark fringe, the path-length difference is 1/2 and the waves interfere destructively. (c) At the position of the first bright fringe, the path-length difference is 1 and the interference is constructive.

19. m λ = d sin θ m is the order of the interference fringe. mis a dimensionless number which takes on integer values starting with zero. Bright fringesm = 0, 1, 2,… The zeroth-order fringe (m = 0) corresponds to the central maximum, the first-order fringe (m = 1) is the first bright fringe on either side of the central maximum, and so on.

20. m λ = d sin θ The position of lines of destructive interference can be found from: (m + 1/2) λ = d sin θ (m + 1/2) λ is the path difference between the sources to the points of destructive interference. Dark fringesm = 1, 3, 5,…

21. 10.9 In Young’s experiment, the two slits are 0.04 mm apart, and the screen is located 2 m away from the slits. The third brightfringe from the center is displaced 8.3 cm from the central fringe. a. Determine the wavelength of the incident light. d = 4x10-5 m L = 2 m m = 3 x = 8.3x10-2 m = 5.53x10-7 m

22. b. Where will the second dark fringe appear? dark fringe: 1/2 λ m = 3 = 4.15x10-2 m

23. DIFFRACTION Waves will bend and spread out as they pass an obstacle or narrow opening. In the case of a narrow opening, the amount of bending increases as the size of the opening decreases. Because the wavelength of light is much shorter than that of water waves or sound waves, the diffractionof light is only noticeable when the size of the opening is comparable to the wavelength of the light.

24. SINGLE SLIT DIFFRACTION Due to the combined effects of diffraction and interference, monochromatic light passing through a single slit of width Dproduces an interference pattern of alternating bright and dark lines. The positions of lines of destructiveinterference can be determined by the following equations: m λ = d sin θ and mis the order of the dark fringe, m = 1, 2, 3…

25. The diffraction of light by a single slit gives rise to a diffraction pattern consisting of a large and bright central maximum and a symmetric array of side fringes. The order number m corresponds to the minima or dark fringes.

26. 10.10 A 630 nm laser beam is incident on a single slit of width 0.300 mm. The diffraction pattern is formed on a screen 1.00 m from the slit. Calculate the distance from the center of the central maximum to the second-order dark fringe. λ = 6.3x10-7 m d = 0.3 mm L = 1 m m = 2 = 4.2x10-3 m

27. DIFFRACTION GRATING A diffraction grating consists of a large number of closely spaced parallel slits that diffract light incident on the grating.

28. A diffraction grating produces a sharply defined interference/diffraction pattern.

29. The diffracted light will exhibitconstructive interferenceat points given by the equation: m λ = d sin θ where mis the order of the bright fringe, m = 0, 1, 2, etc. The grating equation has the same form as the equation found in the Young double slit experiment. In the double slit experiment the distance d was measured between the centers of the two slits. In the diffraction grating equation d refers to the distance between the centers of adjacent slits. The amount of light passing through the diffraction grating is much greater than in the case of the double slit. As a result, the intensity of the bright lines is much greater.

30. A diffraction grating is particularly useful in separating the component wavelengths of the light incident on the grating. Because of this, it is frequently used in the analysis of spectrum produced by various gases, e.g., mercury, hydrogen, and helium.

31. INTERFERENCE BY THIN FILMS Young was able to explain the colors arising from thin films: the colors of soap bubbles and oil slicks on a wet pavement, the rainbow that appears on oxidized metal surfaces, etc.

32. The dynamic interplay of colors is generated by the simultaneous reflection of light from both the inside and outside surfaces of the bubble. The two surfaces are very close together, but the light reflected from the inner surface of the bubble must still travel further than light reflected from the outer surface. When the waves reflected from the inner and outer surface combine they interfere with each other, removing or reinforcing some parts of white light, resulting in the appearance of color.

33. If the extra distance traveled by the inner light waves is exactly the wavelength of the outer light waves, constructive interference occurs and bright colors of those wavelengths are produced. In places where the waves are out of step, destructive interference transpires, canceling the reflected light and the color.

34. Thin transparent filmsgenerate fringe patterns when the two waves reflected from the front and back surfaces interfere. Where the film is non-uniform, there is a pattern of fringes of equal thickness. CASE 1. When the index of refraction of the film lies between the indices of the surrounding two media: n1> nf>n2 or n1 < nf<n2 reflected maxima occur where the thickness (d) is: m = 1, 2, 3,…

35. An even more commonly occurring situation is for: CASE 2. When the index of refraction of the film is greater or less than the indices of the surrounding two media: n1< nf>n2 or n1> nf<n2 Now maxima occur where: m = 0, 1, 2,…

36. 10.11 A soap film in air has an index of refraction of 1.34. If a region of the film appears bright red (λo=633 nm) in normally reflected light, what is its minimum thickness there? nf = 1.34 λ = 6.33x10-7 m m = 0 This is an example of Case 2. 1< 1.34 >1 = 1.18x10-7 m