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Chapter 16. Interference and Diffraction. 16.1 - Interference. Objectives: Describe how light waves interfere with each other to produce bright and dark fringes Identify the conditions required for interference to occur
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Chapter 16 Interference and Diffraction
16.1 - Interference Objectives: Describe how light waves interfere with each other to produce bright and dark fringes Identify the conditions required for interference to occur Predict the location of interference fringes using the equation for double-slit interference
Interference • Occurs when waves combine by superposition • Can be constructive (resultant wave has an amplitude greater than that of any of the individual component waves) • Can be destructive (resultant wave has an amplitude less than that of either of the individual component waves)
Interference, cont. In phase: If the crest of one wave overlaps the crest of another wave, with a phase difference of 0o Out of phase: If the crest of one wave overlaps the trough of another wave, with a phase difference of 180o Coherence: when the phase difference between two waves is constant; the waves do not shift relative to each other over time
Interference • Waves must have a constant phase difference (coherence) in order for interference to be observed. • If interference is to be clearly observed, the interfering waves must also have the same wavelength (i.e., they must be the same color, also known as monochromatic) • Coherence can be obtained using a single wave source. It cannot be obtained using two different sources.
Interference, cont. Double slit wave pattern, monochromatic light Double slit wave pattern, white light
Thin Film Interference • Occurs due to differences in thickness of the film at various points
Thin Film Interference Problems: • Determine the type of interference that occurs in the problem: where, what kind • Remember that the wave reflected from the lower surface of the film has to travel 2x the thickness before returning to the upper surface, where it interferes with the portion of the wave that reflects at the upper surface
Demonstrating Interference Light passing through two narrow slits act as two light sources that are coherent. When the coherent waves constructively interfere, you see a bright stripe. When the the coherent waves destructively interfere, you see a dark stripe. The alternating dark and bright parallel bands are called fringes.
Predicting location of interference fringes d The bottom beam has to travel slightly farther than the top beam to meet at point P. This distance is called the path difference and is equal to d(sinθ), where d is the distance between the two slits. This path difference has to equal a whole number multiple of the wavelength to create constructive interference. The path difference would be a (multiple plus ½) of wavelength for destructive interference to occur.
Predicting location of interference fringes Constructive fringes (bright) : d(sinθ) = m m is the order number of the fringe. The center bright fringe is the zeroth order, or m=0 (when θ=0). This is also called the central maximum. The next bright fringe is the first order, m=1, etc.
Fringe calculation example The distance between two slits is 0.030mm. The second-order bright fringe is measured on a viewing screen at an angle of 2.15o from the central maximum. What is the wavelength of the light? What do we know? d(sinθ) = m d = 0.030mm = 3x10-5m Second order means m=2 Bright fringe means constructive interference θ = 2.15o = 5.63 x 10-7m
16.2 - Diffraction • Objectives: • Describe how light waves diffract around obstacles and produce bright and dark fringes • Calculate the position of fringes for a diffraction grating • Describe how diffraction determines an optical instrument’s ability to resolve imagesnterference
Diffraction • Is the spreading of light into a region behind an obstruction • Occurs when waves pass through small openings, around obstacles, or by sharp edges
Interference - Coherence • Coherence produces an interference pattern. • In order to produce the interference pattern, the component waves producing coherence must be of the same wavelength.
Interference - Coherence • Interference patterns are VERY predictable. These patterns are called diffraction patterns if the light comes from a single slit (various portions of a single wave interfere), but interference patterns if the waves added come from two or more openings.
Interference (Diffraction) caused by Thin Slits • Patterns of light and dark parallel bands (fringes) appear on viewing screen • The light fringes are due to constructive interference (light fringes are called maxima) • The dark fringes are due to destructive interference (dark fringes are called minima)
Interference/Diffraction is caused by Three Common Types of Slits • Single Slit • Double Slit • Diffraction Grating
Single slit diffraction pattern Produces one very large, bright central maximum band that is twice as wide as the secondary maximas. The dark bands are called minima.
Young’s Double Slit Equations Bright fringes d(sin θ) = mλ Dark fringes d(sin θ) = (m + ½ )λ also, y/L = λ/d θ < 5o
Diffraction Gratings • Use diffraction and interference to disperse light. • If white light is used, the light will break into its component colors (like a prism)
Diffraction Gratings • The result is separation and repeated color blocks, from m=0 (zero order) to infinity. • In reality, only a few m values are seen.
Diffraction Equations for diffraction gratings d(sin θ) = mλ m = 0, + 1, + 2, . . . for bright fringes y/L = λ/d will NOT work because θ > 5o So, use tan θ = y/L to find θ Then use d(sin θ) = mλ
Diffraction grating example problem Monochromatic light from a helium-neon laser (=632.8nm) Shines at a right angle to the surface of a diffraction grating that contains 150,500 lines/m. Find the angles at which one would observe the first and second order maxima.
Compact Discs are Diffraction Gratings The disc has alternating rows of pits (inscribed data) and smooth surfaces. The data pits don’t reflect nearly as much light as the smooth surfaces in between them, And the reflected light constructively interferes. Depending on the direction of the incoming light, the orientation of the disc and the light’s wavelength, you’ll see a “rainbow” of colors coming off the disc.
