Explanation 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, M = θ ' θ Here, θ ' is the angle subtended by the object at the eye when using the device (eyepiece lens)and θ 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 v 0 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, M = θ ' θ = h / f e h / v 0 = v 0 f e Here, the focal length of the eyepiece is f e . When the eye is relaxed, then the magnification m of the binoculars is given by the expression, m = f o f e The focal length of the eyepiece can be calculated using the above expression. The image distance v 0 can be calculated by using the mirror equation. 1 f o = 1 u o + 1 v o Given: The magnification of the binoculars m = 6.5 Focal length of the objective f o = 26 cm = 0.26 m Distance of the object from the objective u o = 4...

7th Edition

ISBN: 9780321625915

Author: Douglas C. Giancoli

Publisher: PEARSON

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Chapter 25, Problem 42P

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The magnification of the binoculars when focussed on a object placed at a finite distance from the objective.

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Chapter 25, Problem 41P

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