nochromatic light falls on a screen 1.70 m from two slits separated by 2.06 mm. The first- and second-order bright fringes are separated by 0.548 mm. What is the wavelength of the light?
nochromatic light falls on a screen 1.70 m from two slits separated by 2.06 mm. The first- and second-order bright fringes are separated by 0.548 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)...
Related questions
Question
![**Double-Slit Experiment: Calculating Wavelength of Light**
Monochromatic light falls on a screen 1.70 meters from two slits separated by 2.06 millimeters. The first- and second-order bright fringes are separated by 0.548 millimeters. What is the wavelength of the light?
**Explanation of Variables:**
- Distance from the slits to the screen: 1.70 m
- Separation between the slits: 2.06 mm
- Separation between the first- and second-order bright fringes: 0.548 mm
**Conceptual Framework:**
In the double-slit experiment, light passes through two closely spaced slits and forms an interference pattern on a screen. The bright fringes occur at points of constructive interference and can be used to calculate the light's wavelength using the formula for fringe separation in interference patterns:
\[
\Delta y = \frac{\lambda L}{d}
\]
Where:
- \(\Delta y\) is the separation between fringes (0.548 mm).
- \(\lambda\) is the wavelength of light.
- \(L\) is the distance from slits to screen (1.70 m).
- \(d\) is the distance between slits (2.06 mm).
This problem involves determining the wavelength \(\lambda\) using the known values. Solving for \(\lambda\), we get:
\[
\lambda = \frac{\Delta y \cdot d}{L}
\]
Convert all units to meters before calculation for consistency:
- \(\Delta y = 0.548 \, \text{mm} = 0.000548 \, \text{m}\)
- \(d = 2.06 \, \text{mm} = 0.00206 \, \text{m}\)
Substitute in the values:
\[
\lambda = \frac{0.000548 \times 0.00206}{1.70}
\]
Perform the calculation to find the wavelength \(\lambda\). This wavelength indicates the color and type of monochromatic light used in the experiment.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9413ee1b-018f-4e4f-9457-fb88f0adac84%2F01796a68-3ba9-4ebe-9f80-fbf43bee2f91%2Fcfyyd3_processed.png&w=3840&q=75)
Transcribed Image Text:**Double-Slit Experiment: Calculating Wavelength of Light**
Monochromatic light falls on a screen 1.70 meters from two slits separated by 2.06 millimeters. The first- and second-order bright fringes are separated by 0.548 millimeters. What is the wavelength of the light?
**Explanation of Variables:**
- Distance from the slits to the screen: 1.70 m
- Separation between the slits: 2.06 mm
- Separation between the first- and second-order bright fringes: 0.548 mm
**Conceptual Framework:**
In the double-slit experiment, light passes through two closely spaced slits and forms an interference pattern on a screen. The bright fringes occur at points of constructive interference and can be used to calculate the light's wavelength using the formula for fringe separation in interference patterns:
\[
\Delta y = \frac{\lambda L}{d}
\]
Where:
- \(\Delta y\) is the separation between fringes (0.548 mm).
- \(\lambda\) is the wavelength of light.
- \(L\) is the distance from slits to screen (1.70 m).
- \(d\) is the distance between slits (2.06 mm).
This problem involves determining the wavelength \(\lambda\) using the known values. Solving for \(\lambda\), we get:
\[
\lambda = \frac{\Delta y \cdot d}{L}
\]
Convert all units to meters before calculation for consistency:
- \(\Delta y = 0.548 \, \text{mm} = 0.000548 \, \text{m}\)
- \(d = 2.06 \, \text{mm} = 0.00206 \, \text{m}\)
Substitute in the values:
\[
\lambda = \frac{0.000548 \times 0.00206}{1.70}
\]
Perform the calculation to find the wavelength \(\lambda\). This wavelength indicates the color and type of monochromatic light used in the experiment.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON