### Physics Problem: Interference in Thin Films**Problem Statement:**3. As shown in the picture below, two flat glass plates touch at one edge and are separated at the other edge by a spacer. Five dark fringes are observed on top of the plates when light of wavelength \(\lambda = 589 \: \text{nm}\) is shone vertically on the plates. What is the thickness of the spacer?**Diagram Explanation:**- The diagram provided shows two flat glass plates. One side of the plates is in contact, while the other side is separated by a spacer.- The separation between the plates gradually increases from the edge where they touch.- The spacer is depicted as a small cylindrical object of diameter \( d \), placed between the plates.- The variable \( t \) represents the thickness of the spacer.### Analytical Approach:In this setup, an interference pattern is formed due to the variation in the thickness of the air film between the glass plates. The dark fringes occur at points of destructive interference.**Given Data:**- Wavelength of light, \( \lambda = 589 \: \text{nm} \)- Number of dark fringes, \( m = 5 \)**Understanding the Relationship:**The thickness at the \( m \)-th dark fringe (considering constructive interference conditions for maxima and destructive for minima) can be expressed using the equation for destructive interference in thin films:\[ 2t = (m - \frac{1}{2})\lambda \]Here, \( t \) is the separation of the plates at the location of the \( m \)-th dark fringe.### Calculation:Using the given data, we substitute the values to find the thickness of the spacer:\[ 2t = (5 - \frac{1}{2}) \times 589 \: \text{nm} \]\[ 2t = 4.5 \times 589 \: \text{nm} \]\[ 2t = 2650.5 \: \text{nm} \]\[ t = \frac{2650.5}{2} \: \text{nm} \]\[ t = 1325.25 \: \text{nm} \]Thus, the thickness of the spacer is approximately \( 1325.25 \: \text{nm} \).

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As shown in the picture below, two flat glass plates touch at one edge and are separated at the other edge by a spacer. Five dark fringes are observed on top of the plates when light of wavelength 2=589 nm is shone vertically on the plates. What is the thickness of the spacer?

As shown in the picture below, two flat glass plates touch at one edge and are separated at the other edge by a spacer. Five dark fringes are observed on top of the plates when light of wavelength 2=589 nm is shone vertically on the plates. What is the thickness of the spacer?

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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