Diffraction, Interference, and Thin Films

1. Diffraction is the bending of waves around obstacles or the edges of an opening. Huygen’s Principle - Every point on a wave front acts as a source of tiny wavelets that move forward with the same speed as the wave; the wave front at a later instant is the surface that is tangent to the wavelets.

2. Interference alters the intensity (brightness) of light, just as it effects the loudness of sound. The waves combine following the principle of linear superposition.

3. When identical waves cross in phase the waves reinforce each other: constructive interference. When the waves are out of phase they cancel each other: destructive interference.

4. If the wave sources are coherent sources, the interference will continue without change.

5. In 1801 Thomas Young (English) performed a historic experiment showing that two overlapping light waves interfere with each other.

6. Monochromatic light passes through a single narrow slit and falls on two closely spaced narrow slits S1 and S2. These two slits act as coherent sources of light that interfere with each other.

7. If illuminated with monochromatic light, successive pairs of slit images will appear on either side of the principle image. The first pair are called the first-order images, the second pair are the second-order images.

9. d is the distance between the slits, and is called the grating constantl is the wavelengthθ is the diffraction angle

10. Diffraction gratings have as many as 12,000 equally spaced parallel grooves. When illuminated with white light, each slit produces a new wave front. These wave fronts interfere and produce pairs of continuous spectra equally spaced on opposite sides of the principle image.

11. If illuminated with monochromatic light, successive pairs of slit images will appear on either side of the principle image. The first pair are called the first-order images, the second pair are the second-order images.

13. d is the distance between the slits, and is called the grating constantl is the wavelengthθ is the diffraction angle

14. If white light is used rather than monochromatic light, a central white band results. Outside the central point, fringes of all colors result. At the central point all colors are incident producing white light. Outside the central white fringe there is a bright fringe for each value of l.

15. In these light colored bands, red is farther out than the other colors. Violet is closest to the white central spot. Red light’s l is larger than violet’s; therefore by sin q = ml/d (l = d sin q/m) , the red band is farther from the center. There is one group of colored fringes for each value of m.

16. Thin transparent soap films, oil slicks, and wedge-shaped films of air show varying patterns of colors when viewed by reflected white light. Monochromatic light produces light and dark bands.

17. Some light is reflected at the top surface, some is refracted and then partially reflected at the bottom surface, eventually refracted again at the top surface and exiting parallel to the original reflected ray.

18. If the film is 1/4 wavelength in thickness, the second ray exits 1/2 wavelength behind the originally reflected ray. This should destructively interfere and the film should appear dark.

19. If the film is 1/2 wavelength in thickness, the second ray should be one whole wavelength behind and constructive interference should occur.

20. Observation shows the opposite effect of that expected. This occurs when air is on both sides of the film. Very thin layers of soap film are very dark, although we would expect them to be bright.

21. Thomas Young explained this by suggesting that one of the reflected waves undergoes a 180° phase change during reflection.

22. The reflection where the medium beyond has a greater index of refraction (top) undergoes the phase shift. When the medium beyond has a lower index of refraction there is no phase shift.

23. Thus the rule for constructive and destructive interference for thin films bounded on both sides by a medium of lower index of refraction is this:

24. Maximum constructive interference occurs if the optical path difference is an odd number of half wavelengths (film thickness is an odd number of quarter wavelengths)and:

25. Maximum destructive interference occurs when the optical path difference is a whole number of wavelengths (film thickness is an even number of quarter wavelengths).

26. A vertical cross section of soap film meets the odd and even quarter wavelength thicknesses at successive intervals down the film for different colors.

27. Optically flat glass plates separated by a thin film of air produce regular patterns of interference fringes. irregular surfaces produce irregular patterns.

28. An interferometer can be used to measure the smoothness of glass surfaces.

29. Ex. 4 - (a) A thin film of gasoline floats on a puddle of water. Sunlight falls almost perpendicularly on the film a reflects into your eyes. Destructive interference eliminates the blue color (l = 469 nm) , so the film has a yellow hue. If the refractive indices of blue light in gasoline and water are 1.40 and 1.33 respectively, determine the minimum nonzero thickness t of the film. (b) Repeat part (a) assuming that the gasoline is on glass (nglass = 1.52) instead of water.

30. Ex. 5 - Under natural conditions, thin films have a multicolored appearance that often changes while you are watching them. Why are such films multicolored, and what can be inferred from the fact that the colors change in time?

31. Ex. 6 - (a) Assume that green light (l = 552 nm) strikes two glass plates (n = 1.52) nearly perpendicularly. Determine the number of bright fringes that occur between the place where the plates touch and the edge of the sheet of paper (thickness = 4.10 x 10-5 m). (b) Explain why there is a dark fringe where the plates touch.

32. Single-slit diffraction- A slit that is only a few wavelengths wide will produce alternating light and dark bands. The very center of the image is almost equidistant from all parts of the slit, so it is very bright because all interference is constructive.

33. At points below and above this bright band, where the distance to each edge of the slit differs by whole wavelength, the difference in the edge and the center differs by 1/2 a wavelength.

34. For every point from the bottom of the slit to the center, there is a point from the center to the top that is 1/2 wavelength different in distance from the screen. Therefore, all light is canceled and the band is dark.

35. At two points further from the center, the distance to each edge of the slit differs by 1.5 wavelengths. In this case three wavelets arrive, all offset by 1/2 a wavelength. Two of these interfere constructively, the third provides the light band (dimmer than the center light band).

36. If the difference in distance to the two edges is two wavelengths, a dark band results. If the difference is 2.5 wavelengths, a light band again results, etc. The intensity of the light bands decreases with distance.

37. The angle to the normal at which the bright fringes (constructive interference) are located can be found using this equation:sin q = ml/d. d is the distance between the slits; m is the order of the image.

38. The formula for the dark fringes is: sin q = (m + ½)l/d. The dark fringes must be halfway between the bright fringes.

39. Ex. 2 - Red light (l = 664 nm in vacuum) is used in Young’s experiment with the slits separated by a distance d = 1.20 x 10-4 m. The screen is located at a distance from the slits of L = 2.75 m. Find the distance y on the screen between the central bright fringe and the third-order bright fringe.

40. A Michelson interferometer splits light rays into two parts then reunites them after making one part travel a longer distance. At integer + 1/2 l differentials, the reunited rays destructively interfere. At integer l differentials, the reunited rays interfere constructively. These distances can be measured to find the l of light.