Light of wavelength 580 nm falls on a double slit, and the first bright fringe of the interference pattern is seen at an angle of 16.8° from the central maximum. Find the separation between the slits. um
Light of wavelength 580 nm falls on a double slit, and the first bright fringe of the interference pattern is seen at an angle of 16.8° from the central maximum. Find the separation between the slits. um
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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![**Problem Statement:**
Light of wavelength 580 nm falls on a double slit, and the first bright fringe of the interference pattern is seen at an angle of 16.8° from the central maximum. Find the separation between the slits.
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**Answer Box:**
- [ ] μm
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**Additional Materials:**
- [eBook]
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**Explanation:**
This problem involves understanding the double-slit interference pattern. When light passes through two narrow slits, it creates an interference pattern on a screen. The formula for the position of the bright fringes (constructive interference) is given by:
\[ d \sin \theta = m \lambda \]
Where:
- \( d \) is the distance between the slits.
- \( \theta \) is the angle at which the bright fringe is observed.
- \( m \) is the order of the fringe (m = 1 for the first bright fringe).
- \( \lambda \) is the wavelength of the light.
You are required to solve for \( d \) using the given values:
- \( \lambda = 580 \) nm (convert this to meters: \( 580 \times 10^{-9} \) m)
- \( \theta = 16.8^\circ \)
- \( m = 1 \)
Use the formula to find the separation \( d \):
\[ d = \frac{m \lambda}{\sin \theta} \]
Substitute the values and solve for the separation between the slits.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6688bf34-803d-422e-8b53-54ed6c9e4dc2%2F35507c43-34d7-451e-a904-82f3161e4a87%2Fbwt4fn_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Light of wavelength 580 nm falls on a double slit, and the first bright fringe of the interference pattern is seen at an angle of 16.8° from the central maximum. Find the separation between the slits.
---
**Answer Box:**
- [ ] μm
---
**Additional Materials:**
- [eBook]
---
**Explanation:**
This problem involves understanding the double-slit interference pattern. When light passes through two narrow slits, it creates an interference pattern on a screen. The formula for the position of the bright fringes (constructive interference) is given by:
\[ d \sin \theta = m \lambda \]
Where:
- \( d \) is the distance between the slits.
- \( \theta \) is the angle at which the bright fringe is observed.
- \( m \) is the order of the fringe (m = 1 for the first bright fringe).
- \( \lambda \) is the wavelength of the light.
You are required to solve for \( d \) using the given values:
- \( \lambda = 580 \) nm (convert this to meters: \( 580 \times 10^{-9} \) m)
- \( \theta = 16.8^\circ \)
- \( m = 1 \)
Use the formula to find the separation \( d \):
\[ d = \frac{m \lambda}{\sin \theta} \]
Substitute the values and solve for the separation between the slits.
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