Chapter 33: Problem 71
What is the magnification of a telescope with \(f_{0}=1.00 \cdot 10^{2} \mathrm{~cm}\) and \(f_{e}=5.00 \mathrm{~cm} ?\)
Short Answer
Expert verified
Answer: The magnification of the telescope is 20.
Step by step solution
01
Given values
We are given the focal length of the objective lens \(f_{0} = 1.00 \cdot 10^{2} \mathrm{cm}\) and the focal length of the eyepiece lens \(f_{e} = 5.00 \mathrm{cm}\).
02
Formula for magnification
The formula for calculating the magnification \(M\) is: \(M = \frac{f_0}{f_e}\)
03
Calculate magnification
Now, plug in the given values into the formula:
\(M = \frac{1.00 \cdot 10^{2} \mathrm{cm}}{5.00 \mathrm{cm}}\)
\(M = \frac{100 \mathrm{cm}}{5 \mathrm{cm}}\)
04
Solve for M
Divide 100 by 5:
\(M = 20\)
The magnification of the telescope is 20.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Understanding Focal Length in Telescopes
The concept of focal length is fundamental in the world of optical physics and is crucial for understanding how telescopes work. Focal length is the distance between a lens or mirror and the point where it converges a beam of light to a focus. For telescopes, there are typically two important lenses: the objective lens (or mirror), which collects light from distant objects, and the eyepiece lens, through which the observer views the image.
In a simple refracting telescope, the objective lens creates an image of a distant object at its focal point, and this image is what the eyepiece magnifies for the observer's eye. The longer the focal length of the objective lens, the larger the image that is formed, which translates into a potential for greater magnification. However, a longer focal length also results in a longer, bulkier telescope.
On the other hand, the eyepiece's focal length is key to determining the magnification power of the telescope. A shorter focal length of the eyepiece will increase the magnification. When you use the telescope to gaze at the stars, what you're actually seeing is the magnified version of the real image that the objective lens has projected at its focal point. Hence, the focal length is an indispensable aspect of a telescope's design.
In a simple refracting telescope, the objective lens creates an image of a distant object at its focal point, and this image is what the eyepiece magnifies for the observer's eye. The longer the focal length of the objective lens, the larger the image that is formed, which translates into a potential for greater magnification. However, a longer focal length also results in a longer, bulkier telescope.
On the other hand, the eyepiece's focal length is key to determining the magnification power of the telescope. A shorter focal length of the eyepiece will increase the magnification. When you use the telescope to gaze at the stars, what you're actually seeing is the magnified version of the real image that the objective lens has projected at its focal point. Hence, the focal length is an indispensable aspect of a telescope's design.
The Basics of Optical Physics
The field of optical physics involves the study of light and its interactions with matter. It encompasses a range of phenomena including reflection, refraction, diffraction, and interference. These principles are at the heart of how telescopes, including both refracting and reflecting types, manipulate light to bring distant objects into view.
When accessing the wonders of the night sky, the quality of your telescope's optics determines everything. Refraction is the bending of light as it passes from one medium to another, which is governed by Snell's Law. It's through refraction that a lens can converge or diverge beams of light, forming an image. Conversely, reflection involves bouncing light off a surface, and in telescopes like the Newtonian reflector, mirrors are utilized instead of lenses to form the image.
In any telescope, aberrations can be an issue—these are distortions in the image due to imperfections in the optical components. To minimize these, high-quality telescopes strive for precise shapes and configurations of lenses and mirrors. Unraveling the complexities of optical physics allows us to design telescopes that not only magnify distant objects but do so with remarkable clarity.
When accessing the wonders of the night sky, the quality of your telescope's optics determines everything. Refraction is the bending of light as it passes from one medium to another, which is governed by Snell's Law. It's through refraction that a lens can converge or diverge beams of light, forming an image. Conversely, reflection involves bouncing light off a surface, and in telescopes like the Newtonian reflector, mirrors are utilized instead of lenses to form the image.
In any telescope, aberrations can be an issue—these are distortions in the image due to imperfections in the optical components. To minimize these, high-quality telescopes strive for precise shapes and configurations of lenses and mirrors. Unraveling the complexities of optical physics allows us to design telescopes that not only magnify distant objects but do so with remarkable clarity.
How to Calculate Lens Magnification
The magnification of a telescope is a measure of how much larger the telescope makes objects appear. To calculate the magnification, you can use the straightforward formula involving the focal lengths of the telescope's objective lens and eyepiece lens, which is \(M = \frac{f_{o}}{f_{e}}\), where \(f_{o}\) is the focal length of the objective lens and \(f_{e}\) is the focal length of the eyepiece lens.
From our exercise, we know that the objective lens has a focal length of \(f_{o} = 1.00 \cdot 10^{2} \mathrm{cm}\), and the eyepiece has a focal length of \(f_{e} = 5.00 \mathrm{cm}\). According to the lens magnification calculation, you divide the focal length of the objective lens by that of the eyepiece lens, leading to \(M = \frac{1.00 \cdot 10^{2} \mathrm{cm}}{5.00 \mathrm{cm}}\), resulting in a magnification of 20.
To visualize its significance, imagine viewing an object through a telescope without magnification—it appears at its actual size. With a magnification of 20, the same object appears twenty times larger, details once invisible to the naked eye come into sharp relief. It's this principle that enables telescopes to function as time machines, bringing us visually closer to the stars and planets that have fascinated mankind since antiquity.
From our exercise, we know that the objective lens has a focal length of \(f_{o} = 1.00 \cdot 10^{2} \mathrm{cm}\), and the eyepiece has a focal length of \(f_{e} = 5.00 \mathrm{cm}\). According to the lens magnification calculation, you divide the focal length of the objective lens by that of the eyepiece lens, leading to \(M = \frac{1.00 \cdot 10^{2} \mathrm{cm}}{5.00 \mathrm{cm}}\), resulting in a magnification of 20.
To visualize its significance, imagine viewing an object through a telescope without magnification—it appears at its actual size. With a magnification of 20, the same object appears twenty times larger, details once invisible to the naked eye come into sharp relief. It's this principle that enables telescopes to function as time machines, bringing us visually closer to the stars and planets that have fascinated mankind since antiquity.
