White light is incident normally on a thin soap film having an index of refraction of 1.34. It reflects with an interference maximum at 684 nm and an interference minimum at 570 nm with no minima between those two values. The film has air on both sides of it. What is the thickness of the soap film? O 510 nm O 894 nm O 638 nm O 766 nm O 627 nm
White light is incident normally on a thin soap film having an index of refraction of 1.34. It reflects with an interference maximum at 684 nm and an interference minimum at 570 nm with no minima between those two values. The film has air on both sides of it. What is the thickness of the soap film? O 510 nm O 894 nm O 638 nm O 766 nm O 627 nm
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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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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![### Understanding Soap Film Interference
**Problem Statement:**
White light is incident normally on a thin soap film with an index of refraction of 1.34. The light reflects with an interference maximum at 684 nm and an interference minimum at 570 nm, with no minima between these two values. The film has air on both sides. What is the thickness of the soap film?
**Options:**
- 510 nm
- 894 nm
- **638 nm (Selected)**
- 766 nm
- 627 nm
**Explanation:**
When white light strikes a thin film of soap, interference patterns are observed due to the constructive and destructive interference of light waves reflecting from the film's surfaces. These interference patterns depend on the film thickness and the wavelength of light.
For constructive interference (maximum), the condition is:
\[ 2nt = m\lambda \]
where:
- \( n \) is the refractive index (1.34 for soap film),
- \( t \) is the thickness of the film,
- \( \lambda \) is the wavelength of light,
- \( m \) is the order of the maximum (integer).
For destructive interference (minimum), the condition is:
\[ 2nt = (m + \frac{1}{2})\lambda \]
We are given an interference maximum at \( 684 \) nm and a minimum at \( 570 \) nm.
To solve the problem, consider the conditions for these interference patterns and calculate the film thickness \( t \). The indicated correct answer is \( 638 \) nm, which is the best fit based on the provided conditions and interference theory.
**Conclusion:**
Understanding the principles of thin film interference helps explain optical phenomena such as the colorful patterns observed in soap bubbles. These principles are significant in various scientific and industrial applications, including coatings and optical devices.
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This educational example demonstrates the practical application of physics concepts to a real-world problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F212d4b15-52d8-4abc-bca6-3221f0b23928%2Fdc82eebf-8cde-4430-b5bb-f244a6ef68f2%2Fgoa3dn_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Soap Film Interference
**Problem Statement:**
White light is incident normally on a thin soap film with an index of refraction of 1.34. The light reflects with an interference maximum at 684 nm and an interference minimum at 570 nm, with no minima between these two values. The film has air on both sides. What is the thickness of the soap film?
**Options:**
- 510 nm
- 894 nm
- **638 nm (Selected)**
- 766 nm
- 627 nm
**Explanation:**
When white light strikes a thin film of soap, interference patterns are observed due to the constructive and destructive interference of light waves reflecting from the film's surfaces. These interference patterns depend on the film thickness and the wavelength of light.
For constructive interference (maximum), the condition is:
\[ 2nt = m\lambda \]
where:
- \( n \) is the refractive index (1.34 for soap film),
- \( t \) is the thickness of the film,
- \( \lambda \) is the wavelength of light,
- \( m \) is the order of the maximum (integer).
For destructive interference (minimum), the condition is:
\[ 2nt = (m + \frac{1}{2})\lambda \]
We are given an interference maximum at \( 684 \) nm and a minimum at \( 570 \) nm.
To solve the problem, consider the conditions for these interference patterns and calculate the film thickness \( t \). The indicated correct answer is \( 638 \) nm, which is the best fit based on the provided conditions and interference theory.
**Conclusion:**
Understanding the principles of thin film interference helps explain optical phenomena such as the colorful patterns observed in soap bubbles. These principles are significant in various scientific and industrial applications, including coatings and optical devices.
---
This educational example demonstrates the practical application of physics concepts to a real-world problem.
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