**Diffraction Through a Single Slit**When light passes through a single slit, a diffraction pattern is produced on a screen. This phenomenon occurs due to the wave nature of light.### Problem Description- **Slit Width**: $ 5.8 \times 10^{-4} \, \text{m} $- **Screen Distance**: 4.0 m away from the slit- **Fringe Distance**: The distance between the middle of the central bright fringe and the first dark fringe is 3.9 mm**Question**: What is the wavelength of the light?### FormulaTo find the wavelength ($\lambda$), we use the formula for the position of the first dark fringe in single slit diffraction:\[ \lambda = \frac{a \cdot y_1}{L}\]Where:- $ a $ = slit width- $ y_1 $ = distance from the center to the first dark fringe- $ L $ = distance from the slit to the screen### Solution Steps1. Convert $ y_1 $ from mm to meters: \[ y_1 = 3.9 \, \text{mm} = 3.9 \times 10^{-3} \, \text{m} \]2. Substitute the given values into the formula: \[ \lambda = \frac{(5.8 \times 10^{-4} \, \text{m}) \cdot (3.9 \times 10^{-3} \, \text{m})}{4.0 \, \text{m}} \]3. Calculate $\lambda$.This setup demonstrates the principle of single slit diffraction and allows calculation of the wavelength, an important characteristic of light.

Width of slit is Distance between screen and slit is Distance between central fringe and the first…

Light shines through a single slit whose width is 5.8 × 104 m. A diffraction pattern is formed on a flat screen located 4.0 m away. The distance between the middle of the central bright fringe and the first dark fringe is 3.9 mm. What is the wavelength of the light?

Light shines through a single slit whose width is 5.8 × 104 m. A diffraction pattern is formed on a flat screen located 4.0 m away. The distance between the middle of the central bright fringe and the first dark fringe is 3.9 mm. What is the wavelength of the light?

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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Concept explainers

Diffraction of light

In physics, the term diffraction is defined as the bending of light around the corners of the obstacle. As a light ray passes by an aperture, it bends around the edges or through slits, it spreads out through a narrow opening. The diffracted light will produce fringes of bright and dark or colored bands which are labeled as a diffraction pattern.

Question

**Diffraction Through a Single Slit**

When light passes through a single slit, a diffraction pattern is produced on a screen. This phenomenon occurs due to the wave nature of light.

### Problem Description

- **Slit Width**: $ 5.8 \times 10^{-4} \, \text{m} $
- **Screen Distance**: 4.0 m away from the slit
- **Fringe Distance**: The distance between the middle of the central bright fringe and the first dark fringe is 3.9 mm

**Question**: What is the wavelength of the light?

### Formula

To find the wavelength ($\lambda$), we use the formula for the position of the first dark fringe in single slit diffraction:

\[
\lambda = \frac{a \cdot y_1}{L}
\]

Where:
- $ a $ = slit width
- $ y_1 $ = distance from the center to the first dark fringe
- $ L $ = distance from the slit to the screen

### Solution Steps

1. Convert $ y_1 $ from mm to meters:

\[
y_1 = 3.9 \, \text{mm} = 3.9 \times 10^{-3} \, \text{m}
\]

2. Substitute the given values into the formula:

\[
\lambda = \frac{(5.8 \times 10^{-4} \, \text{m}) \cdot (3.9 \times 10^{-3} \, \text{m})}{4.0 \, \text{m}}
\]

3. Calculate $\lambda$.

This setup demonstrates the principle of single slit diffraction and allows calculation of the wavelength, an important characteristic of light.

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