**Double-Slit Interference Pattern: Calculating the Position of the Second Dark Fringe****Problem Statement:**How far is the second dark fringe to the right of the central bright fringe in the double-slit interference pattern seen on a screen 2 m from the slits? The slits are separated by 0.4 mm and are illuminated by monochromatic light of wavelength 625 nm.**Given Data:**- Distance from the slits to the screen ($L$): 2 m- Slit separation ($d$): 0.4 mm (or 0.4 × 10^(-3) m)- Wavelength of the light ($\lambda$): 625 nm (or 625 × 10^(-9) m)- Order of the dark fringe ($m$): 2 (for the second dark fringe)**Explanation:**In a double-slit experiment, the position of the dark fringes (destructive interference) on the screen can be calculated using the following formula:\[ y_m = \left( \frac{(m + \frac{1}{2}) \lambda L}{d} \right) \]Where:- $y_m$ is the distance of the m-th dark fringe from the central bright fringe.- $m$ is the order of the dark fringe (for the second dark fringe, $m$ = 2).- $\lambda$ is the wavelength of the light.- $L$ is the distance from the slits to the screen.- $d$ is the distance between the slits.By substituting the given values:\[ y_2 = \left( \frac{(2 + \frac{1}{2}) \times 625 \times 10^{-9} \times 2}{0.4 \times 10^{-3}} \right) \]\[ y_2 = \left( \frac{2.5 \times 625 \times 10^{-9} \times 2}{0.4 \times 10^{-3}} \right) \]\[ y_2 = \left( \frac{3.125 \times 10^{-6} \times 2}{0.4 \times 10^{-3}} \right) \]\[ y_2 = \left( \frac{6.25 \times 10

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How far is the second dark fringe to the right of the central bright fringe in the double-slit interference pattern seen on a screen 2 m from the slits? The slits are separated by 0.4 mm and are illuminated by monochromatic light of wavelength 625 nm.

How far is the second dark fringe to the right of the central bright fringe in the double-slit interference pattern seen on a screen 2 m from the slits? The slits are separated by 0.4 mm and are illuminated by monochromatic light of wavelength 625 nm.

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

**Double-Slit Interference Pattern: Calculating the Position of the Second Dark Fringe**

**Problem Statement:**

How far is the second dark fringe to the right of the central bright fringe in the double-slit interference pattern seen on a screen 2 m from the slits? The slits are separated by 0.4 mm and are illuminated by monochromatic light of wavelength 625 nm.

**Given Data:**
- Distance from the slits to the screen ($L$): 2 m
- Slit separation ($d$): 0.4 mm (or 0.4 × 10^(-3) m)
- Wavelength of the light ($\lambda$): 625 nm (or 625 × 10^(-9) m)
- Order of the dark fringe ($m$): 2 (for the second dark fringe)

**Explanation:**

In a double-slit experiment, the position of the dark fringes (destructive interference) on the screen can be calculated using the following formula:

\[ y_m = \left( \frac{(m + \frac{1}{2}) \lambda L}{d} \right) \]

Where:
- $y_m$ is the distance of the m-th dark fringe from the central bright fringe.
- $m$ is the order of the dark fringe (for the second dark fringe, $m$ = 2).
- $\lambda$ is the wavelength of the light.
- $L$ is the distance from the slits to the screen.
- $d$ is the distance between the slits.

By substituting the given values:

\[ y_2 = \left( \frac{(2 + \frac{1}{2}) \times 625 \times 10^{-9} \times 2}{0.4 \times 10^{-3}} \right) \]

\[ y_2 = \left( \frac{2.5 \times 625 \times 10^{-9} \times 2}{0.4 \times 10^{-3}} \right) \]

\[ y_2 = \left( \frac{3.125 \times 10^{-6} \times 2}{0.4 \times 10^{-3}} \right) \]

\[ y_2 = \left( \frac{6.25 \times 10

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