Concept explainers
The magnification of the binoculars when focussed on a object placed at a finite distance from the objective.
Answer to Problem 39P
Solution:
The magnification of the binoculars when focussed on an object placed at a distance of 4.0 m away from the objective is found to be
Explanation of Solution
Binoculars function in a similar manner as a telescope, but they return an upright image as they use prisms to invert the image formed by the lenses. The expression for angular magnification remains the same as it is for a telescope, since the prisms do not produce magnification; they merely turn the refracted rays from the objective.
Angular magnification is given by the expression,
Here, is the angle subtended by the object at the eye when using the device (eyepiece lens)and is the angle it subtends in the absence of the lens.
If the object is at infinity, the image of the object is formed at the focus of the objective but for objects not at infinity, the image is formed at a distance from the object.
Therefore, if h is the height of the image formed by the objective (Fig 25-20 of the text book), then for the object at a finite distance from the objective, the magnification is given by,
Here, the focal length of the eyepiece is .
When the eye is relaxed, then the magnification m of the binoculars is given by the expression,
The focal length of the eyepiece can be calculated using the above expression.
The image distance can be calculated by using the mirror equation.
Given:
The magnification of the binoculars
Focal length of the objective
Distance of the object from the objective
Formula used:
Calculation:
Calculate the focal length of the eyepiece lens using the given values of magnification and the focal length of the objective.
Use the given values of object distance and focal length of the objective to calculate the distance at which the image is formed from the objective, using the mirror equation .
According to sign conventions the focal length of a convex lens is positive, for real objects, the object distance is positive and when a real image is formed, the image distance is also positive.
The image is formed at a distance from the objective.
Use the calculated values of and to calculate the magnification of the binoculars.
Chapter 25 Solutions
Physics: Principles with Applications
Additional Science Textbook Solutions
University Physics Volume 2
College Physics: A Strategic Approach (3rd Edition)
Life in the Universe (4th Edition)
Tutorials in Introductory Physics
The Cosmic Perspective (8th Edition)
Sears And Zemansky's University Physics With Modern Physics
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON