Both sides of a uniform film that has index of refraction n and thickness d are in contact with air. For normal incidence of light, an intensity minimum is observed in the reflected light at λ2 and an intensity maximum is observedat λ1, where λ1> λ2. (a) Assuming no intensity minima are observed between λ1 and λ2, find an expression for the integer m in as shown in terms of the wavelengths λ1 and λ2. (b) Assuming n = 1.40, λ1 = 500 nm, and λ2 = 370 nm, determine the best estimate for the thickness of the film. This condition takes into account two factors: (1) the difference in path length forthe two rays (the term md„) and (2) the 180° phase change upon reflection (theterm a,). Because A, = 1/n, we can write Equation 36.11 as2nt = (m+ )A m = 0, 1, 2, ...(36.12)If the extra distance 2t traveled by ray 2 corresponds to a multiple of A,, the twowaves combine out of phase and the result is destructive interference. The generalequation for destructive interference in thin films is2nt 3D ma т %3D 0, 1, 2, ...(36.13)

The minimum and maximum intensity for the normal incidence in reflected light is given as,

Answered: This condition takes into account two…

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter4: Diffraction

Section: Chapter Questions

Problem 70P: If a microscope can accept light from objects at angles as large as =70 , what is the smallest...

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Both sides of a uniform film that has index of refraction n and thickness d are in contact with air. For normal incidence of light, an intensity minimum is observed in the reflected light at λ₂ and an intensity maximum is observed
at λ₁, where λ₁> λ₂. (a) Assuming no intensity minima are observed between λ₁ and λ₂, find an expression for the integer m in as shown in terms of the wavelengths λ₁ and λ₂. (b) Assuming n = 1.40, λ₁ = 500 nm, and λ₂ = 370 nm, determine the best estimate for the thickness of the film.

This condition takes into account two factors: (1) the difference in path length for
the two rays (the term md„) and (2) the 180° phase change upon reflection (the
term a,). Because A, = 1/n, we can write Equation 36.11 as
2nt = (m+ )A m = 0, 1, 2, ...
(36.12)
If the extra distance 2t traveled by ray 2 corresponds to a multiple of A,, the two
waves combine out of phase and the result is destructive interference. The general
equation for destructive interference in thin films is
2nt 3D ma т %3D 0, 1, 2, ...
(36.13)

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