**Problem Statement:**Christopher uses monochromatic light and shines it on a material with an index of refraction 1.5, surrounded by water on one side and air on the other side. If the light has a wavelength of 534 nm within the film, what is the film thickness in nanometers for which maximum constructive interference between the incident beam and the reflected beam occurs? Please give your answer as a whole number.**Solution Explanation:**To determine the film thickness \( t \) for maximum constructive interference, we must use the formula:\[ 2 t = m \lambda_n \]where:- \( m \) is the order of interference (m = 0, 1, 2,... for constructive interference)- \( \lambda_n \) is the wavelength of light in the film.Given:- \( \lambda_n = 534 \) nm- The index of refraction \( n = 1.5 \)For the first order (constructive interference, m = 1):\[ 2t = 1 \times 534\ \text{nm} \]\[ t = \frac{534}{2}\ \text{nm} \]\[ t = 267\ \text{nm} \]So, the film thickness for maximum constructive interference is **267 nanometers**.

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Christopher uses monochromatic light and shines it on a material with index of refraction 1.5, surrounded by water on one side and air on the other side. If the light has wavelength 534 nm within the film, what is the film thickness in nanometers for which maximum constructive interference between the incident beam and the reflected beam occurs? Please give your answer as a whole number.

Christopher uses monochromatic light and shines it on a material with index of refraction 1.5, surrounded by water on one side and air on the other side. If the light has wavelength 534 nm within the film, what is the film thickness in nanometers for which maximum constructive interference between the incident beam and the reflected beam occurs? Please give your answer as a whole number.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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