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Ch 17: Superposition
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 17: SuperpositionProblema 24
Capitolo 17, Problema 24

What is the thinnest film of MgF2 (n=1.39) on glass that produces a strong reflection for orange light with a wavelength of 600 nm?

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Identify the condition for constructive interference in thin films. For a film with a lower refractive index (n=1.39) on a higher refractive index substrate (glass), the reflected light undergoes a phase shift of half a wavelength (λ/2) at the top surface. The condition for constructive interference is: 2 * n * t = m * λ, where t is the thickness of the film, n is the refractive index of the film, λ is the wavelength of light in vacuum, and m is an integer (order of interference).
Since the problem asks for the thinnest film, we use the first order of interference (m=1). Substitute m=1 into the equation: 2 * n * t = λ.
Rearrange the equation to solve for the thickness t: t = λ / (2 * n).
Substitute the given values into the equation. The wavelength of light in vacuum is λ = 600 nm, and the refractive index of the film is n = 1.39. Ensure the units are consistent (convert nanometers to meters if necessary).
Perform the calculation to find the thickness t. This will give the thinnest film of MgF₂ that produces a strong reflection for orange light with a wavelength of 600 nm.

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Thin Film Interference

Thin film interference occurs when light waves reflect off the boundaries of a thin film, such as a soap bubble or a layer of MgF₂. The reflected waves can interfere constructively or destructively depending on the film's thickness and the wavelength of light. For strong reflection, constructive interference must occur, which is influenced by the film's refractive index and the wavelength of the incident light.
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Wave Interference & Superposition

Refractive Index

The refractive index (n) of a material indicates how much light slows down when entering that material compared to its speed in a vacuum. In this case, MgF₂ has a refractive index of 1.39, which affects how light reflects and refracts at the film's surface. The refractive index is crucial for determining the phase change that occurs upon reflection, which influences the conditions for constructive interference.
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Wavelength and Film Thickness Relationship

The relationship between the wavelength of light and the thickness of the film is essential for achieving constructive interference. For a film of thickness t, the condition for strong reflection (constructive interference) is given by the equation 2nt = mλ, where m is an integer (order of interference) and λ is the wavelength of light in a vacuum. This relationship helps calculate the minimum thickness of the MgF₂ film needed to produce a strong reflection for the specified wavelength of 600 nm.
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