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Ch 34: Geometric Optics
Chapter 34, Problem 34

Resolution of a Microscope. The formed by a microscope objective with a focal length of 5.00 mm is 160 mm from its second focal point. The eyepiece has a focal length of 26.0 mm. (a) What is the angular magnification of the microscope?

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1
Determine the magnification of the objective lens using the formula \( M_{obj} = \frac{-v}{u} \), where \( v \) is the image distance and \( u \) is the object distance. Since the image is 160 mm from the second focal point and the focal length of the objective is 5.00 mm, calculate \( u \) using \( u = v - f \).
Calculate the magnification of the eyepiece using the formula \( M_{eye} = \frac{25}{f_{eye}} \), where \( f_{eye} \) is the focal length of the eyepiece and 25 cm (250 mm) is the near point of the average human eye, which is the distance at which the eye can comfortably see objects in focus.
Find the total angular magnification of the microscope by multiplying the magnifications of the objective and the eyepiece together: \( M_{total} = M_{obj} \times M_{eye} \).
Substitute the values obtained from steps 1 and 2 into the formula in step 3 to calculate the total angular magnification.
Interpret the result: A higher magnification value indicates a greater ability of the microscope to enlarge small details, making them visible to the human eye.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Focal Length

Focal length is the distance from the lens to the point where parallel rays of light converge or appear to diverge. In microscopes, the focal lengths of the objective and eyepiece lenses are crucial for determining how the lenses will magnify the image. A shorter focal length typically results in greater magnification, which is essential for resolving fine details in microscopic images.
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Angular Magnification

Angular magnification is a measure of how much larger an object appears when viewed through a microscope compared to the naked eye. It is calculated as the ratio of the angle subtended by the image at the eye to the angle subtended by the object at the same position. This concept is vital for understanding how effectively a microscope can enhance the visibility of small objects.
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Compound Microscope

A compound microscope uses two or more lenses to achieve higher magnification and resolution. The objective lens creates a magnified image of the specimen, which is then further magnified by the eyepiece. Understanding the arrangement and function of these lenses is essential for calculating the overall magnification and resolving power of the microscope.
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Related Practice
Textbook Question
BIO Contact Lenses. Contact lenses are placed right on the eyeball, so the distance from the eye to an object (or ) is the same as the distance from the lens to that object (or ). A certain person can see distant objects well, but his near point is 45.0 cm from his eyes instead of the usual 25.0 cm. (a) Is this person nearsighted or farsighted?
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Textbook Question
The focal length of a simple magnifier is 8.00 cm. Assume the magnifier is a thin lens placed very close to the eye. (b) If the object is 1.00 mm high, what is the height of its formed by the magnifier?
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Textbook Question
The focal length of the eyepiece of a certain microscope is 18.0 mm. The focal length of the objective is 8.00 mm. The distance between objective and eyepiece is 19.7 cm. The final formed by the eyepiece is at infinity. Treat all lenses as thin. (b) What is the magnitude of the linear magnification produced by the objective?
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Textbook Question
A telescope is constructed from two lenses with focal lengths of 95.0 cm and 15.0 cm, the 95.0-cm lens being used as the objective. Both the object being viewed and the final are at infinity. (b) Find the height of the formed by the objective of a building 60.0 m tall, 3.00 km away.
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Textbook Question
A concave mirror has a radius of curvature of 34.0 cm. (b) If the mirror is immersed in water (refractive index 1.33), what is its focal length?
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Textbook Question
BIO (a) Where is the near point of an eye for which a contact lens with a power of +2.75 diopters is prescribed?
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