/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 39 The wing of an insect is \(1.0 \... [FREE SOLUTION] | 91影视

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Chapter 24: Problem 39

The wing of an insect is \(1.0 \mathrm{mm}\) long. When viewed through a microscope, the image is \(1.0 \mathrm{m}\) long and is located \(5.0 \mathrm{m}\) away. Determine the angular magnification.

Short Answer

Expert verified
Answer: The angular magnification of the microscope is 50.

Step by step solution

01

Calculate the angle subtended by the insect wing when viewed with the naked eye

To calculate the angle subtended by the wing in the naked eye, we assume standard viewing distance of 25 cm or 0.25 m. Then we use the small angle approximation formula: tan 胃 鈮� 胃 = object size (height) / distance, where 胃 is the angle subtended by the object. 胃_naked_eye = (1.0 mm) / (0.25 m) We need to convert the object size in mm to meters: 1.0 mm = 0.001 m. 胃_naked_eye = (0.001 m) / (0.25 m)
02

Calculate the angle subtended by the insect wing when viewed through the microscope

This time, we're given the size of the image when viewed through the microscope (1.0 m), and the distance of the image from the eye (5.0 m). Using the small angle approximation formula again, we can calculate the angle subtended by the image formed through the microscope. 胃_microscope = object size (height) / distance 胃_microscope = (1.0 m) / (5.0 m)
03

Calculate the angular magnification

The angular magnification is the ratio of the angle subtended by the object when viewed through a microscope to the angle subtended by the object when viewed with the naked eye. M = 胃_microscope / 胃_naked_eye M = (1.0 m / 5.0 m) / (0.001 m / 0.25 m)
04

End: Final Answer

With all the necessary calculations, we can now determine the angular magnification of the microscope. M = (1.0/5.0)/(0.001/0.25) = 0.2/0.004 = 50. So the angular magnification of the microscope is 50.

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Most popular questions from this chapter

Comprehensive Problems Good lenses used in cameras and other optical devices are actually compound lenses, made of five or more lenses put together to minimize distortions, including chromatic aberration. Suppose a converging lens with a focal length of \(4.00 \mathrm{cm}\) is placed right next to a diverging lens with focal length of \(-20.0 \mathrm{cm} .\) An object is placed \(2.50 \mathrm{m}\) to the left of this combination. (a) Where will the image be located? (b) Is the image real or virtual?
Unless the problem states otherwise, assume that the distance from the comea- lens system to the retina is \(2.0 \mathrm{cm}\) and the normal near point is \(25 \mathrm{cm}.\) If the distance from the lens system (cornea + lens) to the retina is $2.00 \mathrm{cm},$ show that the focal length of the lens system must vary between \(1.85 \mathrm{cm}\) and \(2.00 \mathrm{cm}\) to see objects from $25.0 \mathrm{cm}$ to infinity.
Show that if two thin lenses are close together \((s,\) the distance between the lenses, is negligibly small), the two lenses can be replaced by a single equivalent lens with focal length \(f_{\mathrm{eq}} .\) Find the value of \(f_{\mathrm{eq}}\) in terms of \(f_{1}\) and \(f_{2}.\)
Keesha is looking at a beetle with a magnifying glass. She wants to see an upright, enlarged image at a distance of \(25 \mathrm{cm} .\) The focal length of the magnifying glass is \(+5.0 \mathrm{cm} .\) Assume that Keesha's eye is close to the magnifying glass. (a) What should be the distance between the magnifying glass and the beetle? (b) What is the angular magnification? (tutorial: magnifying glass II).
An object is placed \(12.0 \mathrm{cm}\) in front of a lens of focal length $5.0 \mathrm{cm} .\( Another lens of focal length \)4.0 \mathrm{cm}\( is placed \)2.0 \mathrm{cm}$ past the first lens. (a) Where is the final image? Is it real or virtual? (b) What is the overall magnification? (interactive: virtual optics lab).
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