Review Vocabulary interference: results from the superposition of two or more waves; can be constructive or destructive
Review Vocabulary diffraction: the bending of light around a barrier
Learning Objectives Define Coherent and incoherent light and how to convert between them. Solve problems that contain thin film interference.
Two types of light:
Coherent Light light made up of waves of the same wavelength that are in phase with each other.
Incoherent Light Incoherent light is light whose waves are not in phase, such as white light from a light bulb.
What is the source of incoherent light? Monochromatic light is light of only one wavelength. Light from a monochromatic source produces incoherent light.
How to convert monochromatic light (incoherent) to coherent light)? Monochromatic light can be made coherent by passing it through a narrow, single slit. Diffraction by the slit produces nearly cylindrical wavefronts.
Double slit interference
Interference of Coherent Light Because a cylinder is symmetrical, the two portions of the wavefront arriving at the second barrier are in phase. The two small slits at the second barrier produce nearly cylindrical wavefronts, which can then interfere.
Interference of Coherent Light Depending on their phase relationship, the two waves undergo constructive or destructive interference. When the light from the slits is projected on a screen, the constructive and destructive interference results in a pattern of light and dark bands called interference fringes.
Interference of Coherent Light The position of the bands depends on the wavelength of the light. Wavelength from Double-Slit Investigation
Interference of Coherent Light Use with Example Problem 1. Problem When a different light source is used, the separation between the bands in Example Problem 1 is reduced to 19.5 mm. What is the wavelength of the new source? Response SKETCH AND ANALYZE THE PROBLEM Sketch the situation. List the knowns and unknowns. The values for d and L come from Example Problem 1 .
Thin-Film Interference Have you ever seen a spectrum of colors produced by a soap bubble or by the oily film in a water puddle?
Thin-Film Interference Thin-film interference is the phenomenon of a spectrum of colors resulting from constructive and destructive interference of light waves due to reflection from separate surfaces in a thin film. When a light wave strikes the film, it is partially reflected (Ray 1) and partially transmitted. The transmitted wave is partially reflected off the back surface (Ray 2).
Thin-Film Interference When solving thin-film interference problems, use the following strategies: Make a sketch of the thin film and the two coherent waves. Determine whether the interference is constructive or destructive .
Thin-Film Interference Determine if either or both waves inverted on reflection. If the index of refraction changes from a lower to a higher value, then the wave is inverted. Find the thickness of the film needed to create the interference using the appropriate equation from the table.
Thin-Film Interference Equations for Thin-Film Interference Problems Number of Inverted Waves Constructive Interference Destructive Interference 2 d = mλ film 2 d = ( m + ½) λ film 1 2 d = ( m + ½) λ film 2 d = mλ film 2 2 d = mλ film 2 d = ( m + ½) λ film Note: m = 1, 2, 3, etc. In the case of ( m + ½) λ film , m can also be 0.
Thin-Film Interference EVALUATE THE ANSWER This is twice the minimum thickness when the bottom medium is water. Use with Example Problem 2. Problem If the oil film were on glass (n = 1.55) rather than water, what would be the minimum film thickness? Response SKETCH AND ANALYZE THE PROBLEM Sketch the situation. List the knowns and unknowns. KNOWN UNKNOWN λ = 55 5 nm d = ? n oil = 1.45 n glass = 1.55 SOLVE FOR THE UNKNOWN In this case, there are two phase changes. Therefore, for constructive interference, the minimum thickness is given by 2d = λ / n oil .
Quiz visible light D monochromatic light C incoherent light B coherent light A Which is light made up of waves of the same wavelength that are in phase with each other? 1. CORRECT
Quiz Monochromatic light cannot be made coherent. D Pass it through a single narrow slit. C Pass it through two narrow slits. B Pass it through a color filter. A How can monochromatic light be made coherent? 2. CORRECT
constructive interference D destructive interference C Quiz interference fringes B cylindrical wavefronts A Which is the term for the pattern of darkness and brightness on the screen? 3. CORRECT
Quiz 6.10 × 10 −5 nm D 610 nm C 1.52 × 10 −7 nm B 152 nm A Orange light falls on two slits separated by 2.50 × 10 −5 m. A screen is placed 0.500 m away, and the first-order bright band is 0.0122 m from the central bright band. What is the wavelength of the orange light? 4. CORRECT
constructive interference with one inverted wave C constructive interference with two inverted waves D destructive interference with two inverted waves B destructive interference with zero inverted waves A In which case would you use the equation 2 d = mλ film to determine the thickness of a film used to create the interference in a thin-film interference problem? 5. CORRECT Quiz