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)
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)
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter38: Refraction And Images Formed By Refraction
Section: Chapter Questions
Problem 97PQ
Related questions
Question
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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd8a227fb-4576-45c5-adae-07e9e7fecd56%2F65e54683-3739-475e-8be1-6d1cb6dc6024%2Fgg1mfu.png&w=3840&q=75)
Transcribed Image Text: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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