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Chapter 24: Problem 71

A refracting telescope has an objective lens with a focal length of $2.20 \mathrm{m}\( and an eyepiece with a focal length of \)1.5 \mathrm{cm} .$ If you look through this telescope the wrong way, that is, with your eye placed at the objective lens, by what factor is the angular size of an observed object reduced?

Short Answer

Expert verified
Answer: The angular size of an observed object is reduced by a factor of approximately 0.0068.

Step by step solution

01

Write the formula for the magnification of a refracting telescope

The magnification M of a refracting telescope can be calculated using the formula: 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.
02

Substitute given values into the formula

The objective lens has a focal length of \(2.20 \mathrm{m}\), and the eyepiece has a focal length of \(1.5 \mathrm{cm}\). To be consistent with units, we will convert the focal length of the eyepiece to meters: \(f_e = 1.5 \mathrm{cm} * \frac{1 \mathrm{m}}{100 \mathrm{cm}} = 0.015 \mathrm{m}\). Now, we can substitute these values into the magnification formula: M = \frac{2.20 \mathrm{m}}{0.015 \mathrm{m}}
03

Calculate the magnification

Now, we can calculate the magnification of the refracting telescope when used in the incorrect manner: M = \frac{2.20}{0.015} = 146.67
04

Determine the angular size reduction factor

The magnification of the telescope when used correctly is 146.67. However, since the telescope is being used incorrectly, the magnification is inverted (i.e., 1/M). Therefore, the angular size reduction factor is: Angular size reduction factor = \frac{1}{M} = \frac{1}{146.67} \approx 0.0068 So, when looking through this telescope the wrong way, the angular size of an observed object is reduced by a factor of approximately 0.0068.

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Most popular questions from this chapter

A camera with a 50.0 -mm lens can focus on objects located from $1.5 \mathrm{m}$ to an infinite distance away by adjusting the distance between the lens and the film. When the focus is changed from that for a distant mountain range to that for a flower bed at \(1.5 \mathrm{m},\) how far does the lens move with respect to the film?
An object is located at \(x=0 .\) At \(x=2.50 \mathrm{cm}\) is a converging lens with a focal length of \(2.00 \mathrm{cm},\) at \(x=16.5 \mathrm{cm}\) is an unknown lens, and at \(x=19.8 \mathrm{cm}\) is another converging lens with focal length \(4.00 \mathrm{cm} .\) An upright image is formed at $x=39.8 \mathrm{cm} .$ For each lens, the object distance exceeds the focal length. The magnification of the system is \(6.84 .\) (a) Is the unknown lens diverging or converging? (b) What is the focal length of the unknown lens? (c) Draw a ray diagram to confirm your answer.
You plan to project an inverted image \(30.0 \mathrm{cm}\) to the right of an object. You have a diverging lens with focal length \(-4.00 \mathrm{cm}\) located \(6.00 \mathrm{cm}\) to the right of the object. Once you put a second lens at \(18.0 \mathrm{cm}\) to the right of the object, you obtain an image in the proper location. (a) What is the focal length of the second lens? (b) Is this lens converging or diverging? (c) What is the total magnification? (d) If the object is \(12.0 \mathrm{cm}\) high. what is the image height?
You have a set of converging lenses with focal lengths $1.00 \mathrm{cm}, 10.0 \mathrm{cm}, 50.0 \mathrm{cm},\( and \)80.0 \mathrm{cm} .$ (a) Which two lenses would you select to make a telescope with the largest magnifying power? What is the angular magnification of the telescope when viewing a distant object? (b) Which lens is used as objective and which as eyepiece? (c) What should be the distance between the objective and eyepiece?
Use the thin-lens equation to show that the transverse magnification due to the objective of a microscope is \(m_{o}=-U f_{o} .\) [Hints: The object is near the focal point of the objective: do not assume it is at the focal point. Eliminate \(p_{0}\) to find the magnification in terms of \(q_{0}\) and $\left.f_{0} . \text { How is } L \text { related to } q_{0} \text { and } f_{0} ?\right].$
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