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Chapter 2: Problem 103

A large reflecting telescope has an objective mirror with a \(10.0-\mathrm{m}\) radius of curvature. What angular magnification does it produce when a \(3.00 \mathrm{m}\) -focal length eyepiece is used?

Short Answer

Expert verified
The angular magnification of the telescope is -1.67, which means that the image appears 1.67 times larger than the actual size and is inverted.

Step by step solution

01

Calculate the focal length of the objective lens

The radius of curvature of the objective mirror is given as 10.0 m. Since the focal length of a mirror is half the radius of curvature, the focal length of the objective lens (f_o) is: \[f_o = \frac{R}{2} = \frac{10.0}{2} \mathrm{m} = 5.0 \mathrm{m}\]
02

Calculate the angular magnification

Now, we can use the formula for angular magnification of a telescope: M = -(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. Substitute the values of f_o = 5.0 m and f_e = 3.00 m in the formula and solve for M: \[M = -\frac{5.0}{3.00} = -1.67\]
03

Find the angular magnification

The angular magnification of the telescope is -1.67. The negative sign indicates that the image is inverted, which is typical for a telescope. The magnification value of 1.67 means that the image appears 1.67 times larger than the actual size.

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Most popular questions from this chapter

Suppose your \(50.0 \mathrm{mm}\) -focal length camera lens is \(51.0 \mathrm{mm}\) away from the film in the camera. (a) How far away is an object that is in focus? (b) What is the height of the object if its image is \(2.00 \mathrm{cm}\) high?

A camera with a 50.0 -mm focal length lens is being used to photograph a person standing \(3.00 \mathrm{m}\) away. (a) How far from the lens must the film be? (b) If the film is 36.0 mm high, what fraction of a 1.75 -m-tall person will fit on it? (c) Discuss how reasonable this seems, based on your experience in taking or posing for photographs.

A far-sighted person has a near point of \(100 \mathrm{cm}\). How far in front or behind the retina does the image of an object placed \(25 \mathrm{cm}\) from the eye form? Use the cornea to retina distance of \(2.5 \mathrm{cm}\)

Two convex lenses of focal lengths \(20 \mathrm{cm}\) and 10 \(\mathrm{cm}\) are placed \(30 \mathrm{cm}\) apart, with the lens with the longer focal length on the right. An object of height \(2.0 \mathrm{cm}\) is placed midway between them and observed through each lens from the left and from the right. Describe what you will see, such as where the image(s) will appear, whether they will be upright or inverted and their magnifications.

A magnifying glass produces an angular magnification of 4.5 when used by a young person with a near point of 18 cm. What is the maximum angular magnification obtained by an older person with a near point of \(45 \mathrm{cm} ?\)
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