8. A single slit, which is 0.0500 mm wide, is illuminated by light of 550 nm wavelength. What is the angular separation between the first two minima on either side of the central maximum?
8. A single slit, which is 0.0500 mm wide, is illuminated by light of 550 nm wavelength. What is the angular separation between the first two minima on either side of the central maximum?
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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![**Question 8:**
A single slit, which is 0.0500 mm wide, is illuminated by light of 550 nm wavelength. What is the angular separation between the first two minima on either side of the central maximum?
**Explanation for Educational Website:**
This question involves understanding a fundamental concept in wave optics, specifically the diffraction of light through a single slit. The angular position of the minima in a single-slit diffraction pattern is determined using the formula for minima:
\[ a \cdot \sin(\theta) = m \cdot \lambda \]
where:
- \( a \) is the slit width (0.0500 mm),
- \( \lambda \) is the wavelength of light (550 nm = 550 x 10^-9 m),
- \( m \) is the order of the minimum (m = ±1, ±2, ...),
- \( \theta \) is the angle relative to the original direction of the wave.
For the first minima (\( m = ±1 \)):
\[ \sin(\theta) = \frac{m \cdot \lambda}{a} \]
Calculate the angle \( \theta \) for the first minima on either side of the central maximum. The angular separation is the difference in angle between these two positions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d0fca7b-87e2-42be-9458-260269753889%2Ffe6af4b7-b8d9-4147-a53b-9236849d9a5c%2Fjxjq8ra_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 8:**
A single slit, which is 0.0500 mm wide, is illuminated by light of 550 nm wavelength. What is the angular separation between the first two minima on either side of the central maximum?
**Explanation for Educational Website:**
This question involves understanding a fundamental concept in wave optics, specifically the diffraction of light through a single slit. The angular position of the minima in a single-slit diffraction pattern is determined using the formula for minima:
\[ a \cdot \sin(\theta) = m \cdot \lambda \]
where:
- \( a \) is the slit width (0.0500 mm),
- \( \lambda \) is the wavelength of light (550 nm = 550 x 10^-9 m),
- \( m \) is the order of the minimum (m = ±1, ±2, ...),
- \( \theta \) is the angle relative to the original direction of the wave.
For the first minima (\( m = ±1 \)):
\[ \sin(\theta) = \frac{m \cdot \lambda}{a} \]
Calculate the angle \( \theta \) for the first minima on either side of the central maximum. The angular separation is the difference in angle between these two positions.
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