Consider a thin, transparent film with thickness t and index of refraction n coated onto a piece of a given material. When a light wave of wavelength λ approaches the film, although most of the light is transmitted into the film, a small portion is reflected off the first (air–film) boundary and another portion of the light that continues into the film is reflected off the second (film–material) boundary. The two reflected waves, which have exactly the same frequency, travel back out into the air, where they overlap and interfere. The way they interfere depends on their effective path-length difference, as summarized in this Tactics Box. Follow the light wave as it passes through the film. The wave reflecting from the second boundary travels an extra distance 2t. Note the indices of refraction of the three media: the medium before the film, the film itself, and the medium beyond the film. The first and third may be the same. There’s a reflective phase change at any boundary where the index of refraction increases. 2t=mλn(m=0,1,2,...)If neither or both reflected waves undergo a phase change, the phase changes cancel and the effective path-length difference is Δd=2tΔ. Use the equations for constructive interference and 2t=(m+12)λn(m=0,1,2,...) for destructive interference. 2t=(m+12)λn(m=0,1,2,...) for constructive interference and 2t=mλn(m=0,1,2,...) If only one wave undergoes a phase change, the effective path-length difference is d=2t+12λ. Use the equations for destructive interference. Follow these steps to solve this problem: A very thin oil film (noil=1.25) floats on water (nwater=1.33). What is the thinnest film that produces a strong reflection for green light with a wavelength of 500 nmnm? Part A As light travels from air into the water through the oil film, both of the reflected waves undergo a phase change. neither of the reflected waves undergoes a phase change. only one of the reflected waves undergoes a phase change. Part B Which of the following equations should be used to find the minimum thickness t of the oil film that satisfies the conditions of the problem? Let λ be the wavelength of light in air and n the index of refraction of the thin film. Which of the following equations should be used to find the minimum thickness of the oil film that satisfies the conditions of the problem? Let be the wavelength of light in air and the index of refraction of the thin film. 2t=mλn(m=0,1,2,...) for constructive interference. 2t=(m+12)λn(m=0,1,2,...) for destructive interference. 2t=(m+12)λn(m=0,1,2,...)for constructive interference. 2t=mλn(m=0,1,2,...) for destructive interference. What is the minimum (non-zero) thickness t of the film that produces a strong reflection for green light with a wavelength of 500 nm?

Consider a thin, transparent film with thickness t and index of refraction n coated onto a piece of a given material. When a light wave of wavelength λ approaches the film, although most of the light is transmitted into the film, a small portion is reflected off the first (air–film) boundary and another portion of the light that continues into the film is reflected off the second (film–material) boundary. The two reflected waves, which have exactly the same frequency, travel back out into the air, where they overlap and interfere. The way they interfere depends on their effective path-length difference, as summarized in this Tactics Box. Follow the light wave as it passes through the film. The wave reflecting from the second boundary travels an extra distance 2t. Note the indices of refraction of the three media: the medium before the film, the film itself, and the medium beyond the film. The first and third may be the same. There’s a reflective phase change at any boundary where the index of refraction increases. 2t=mλn(m=0,1,2,...)If neither or both reflected waves undergo a phase change, the phase changes cancel and the effective path-length difference is Δd=2tΔ. Use the equations for constructive interference and 2t=(m+12)λn(m=0,1,2,...) for destructive interference. 2t=(m+12)λn(m=0,1,2,...) for constructive interference and 2t=mλn(m=0,1,2,...) If only one wave undergoes a phase change, the effective path-length difference is d=2t+12λ. Use the equations for destructive interference. Follow these steps to solve this problem: A very thin oil film (noil=1.25) floats on water (nwater=1.33). What is the thinnest film that produces a strong reflection for green light with a wavelength of 500 nmnm? Part A As light travels from air into the water through the oil film, both of the reflected waves undergo a phase change. neither of the reflected waves undergoes a phase change. only one of the reflected waves undergoes a phase change. Part B Which of the following equations should be used to find the minimum thickness t of the oil film that satisfies the conditions of the problem? Let λ be the wavelength of light in air and n the index of refraction of the thin film. Which of the following equations should be used to find the minimum thickness of the oil film that satisfies the conditions of the problem? Let be the wavelength of light in air and the index of refraction of the thin film. 2t=mλn(m=0,1,2,...) for constructive interference. 2t=(m+12)λn(m=0,1,2,...) for destructive interference. 2t=(m+12)λn(m=0,1,2,...)for constructive interference. 2t=mλn(m=0,1,2,...) for destructive interference. What is the minimum (non-zero) thickness t of the film that produces a strong reflection for green light with a wavelength of 500 nm?

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Question

Follow the light wave as it passes through the film. The wave reflecting from the second boundary travels an extra distance 2t.

Note the indices of refraction of the three media: the medium before the film, the film itself, and the medium beyond the film. The first and third may be the same. There’s a reflective phase change at any boundary where the index of refraction increases.
2t=mλn(m=0,1,2,...)If neither or both reflected waves undergo a phase change, the phase changes cancel and the effective path-length difference is Δd=2tΔ. Use the equations
for constructive interference and
2t=(m+12)λn(m=0,1,2,...)
for destructive interference.
2t=(m+12)λn(m=0,1,2,...)
for constructive interference and
2t=mλn(m=0,1,2,...) If only one wave undergoes a phase change, the effective path-length difference is d=2t+12λ. Use the equations
for destructive interference.

Follow these steps to solve this problem: A very thin oil film (noil=1.25) floats on water (nwater=1.33). What is the thinnest film that produces a strong reflection for green light with a wavelength of 500 nmnm?

Part A

As light travels from air into the water through the oil film,

both of the reflected waves undergo a phase change.

neither of the reflected waves undergoes a phase change.

only one of the reflected waves undergoes a phase change.

Part B

Which of the following equations should be used to find the minimum thickness t of the oil film that satisfies the conditions of the problem? Let λ be the wavelength of light in air and n the index of refraction of the thin film.

Which of the following equations should be used to find the minimum thickness of the oil film that satisfies the conditions of the problem? Let be the wavelength of light in air and the index of refraction of the thin film.

2t=mλn(m=0,1,2,...) for constructive interference.

2t=(m+12)λn(m=0,1,2,...) for destructive interference.

2t=(m+12)λn(m=0,1,2,...)for constructive interference.

2t=mλn(m=0,1,2,...) for destructive interference.

What is the minimum (non-zero) thickness t of the film that produces a strong reflection for green light with a wavelength of 500 nm?

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