Ch 34: Geometric Optics

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 34: Geometric Optics

Problem 59b

Chapter 34, Problem 59b

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 image formed by the eyepiece is at infinity. Treat all lenses as thin. What is the magnitude of the linear magnification produced by the objective?

Verified step by step guidance

The linear magnification produced by the objective lens is given by the formula:

m = \frac{v}{u}

, where

v

is the image distance (distance from the objective lens to the intermediate image) and

u

is the object distance (distance from the object to the objective lens).

Since the final image is at infinity, the intermediate image formed by the objective lens must be at the focal point of the eyepiece. Therefore, the distance between the objective and eyepiece (19.7 cm) is equal to the sum of the image distance

v

and the focal length of the eyepiece

f

_e.

Rearrange the equation to find

v

v = d - f

_e, where

d

is the distance between the objective and eyepiece (19.7 cm) and

f

_e is the focal length of the eyepiece (18.0 mm or 1.8 cm).

Use the lens equation for the objective lens to find the object distance

u

\frac{1}{f}

_o=1u+1v, where

f

_o is the focal length of the objective (8.00 mm or 0.8 cm). Rearrange to solve for

u

u = \frac{1}{(}

_o-1v).

Finally, substitute the values of

v

and

u

into the magnification formula

m = \frac{v}{u}

to calculate the linear magnification produced by the objective.

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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 indicates a stronger lens that can produce a larger magnification.

Magnification

Magnification is the ratio of the size of the image produced by a lens to the size of the object being viewed. For microscopes, the total magnification is the product of the magnifications produced by the objective and eyepiece lenses. The linear magnification produced by the objective can be calculated using the formula: M = -d_o / f_o, where d_o is the object distance and f_o is the focal length of the objective.

Thin Lens Formula

The thin lens formula relates the object distance (d_o), image distance (d_i), and focal length (f) of a lens, expressed as 1/f = 1/d_o + 1/d_i. This formula is essential for analyzing lens systems, such as microscopes, as it allows for the calculation of distances and magnifications based on the properties of the lenses involved.

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Thin Lens Equation

Related Practice

Textbook Question

A thin lens with a focal length of 6.00 cm is used as a simple magnifier. What angular magnification is obtainable with the lens if the object is at the focal point?

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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. If the object is 1.00 mm high, what is the height of its image formed by the magnifier?

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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 image are at infinity. Find the height of the image formed by the objective of a building 60.0 m tall, 3.00 km away.

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Textbook Question

BIO A person can see clearly up close but cannot focus on objects beyond 75.0 cm. She opts for contact lenses to correct her vision. What focal length contact lens is needed, and what is its power in diopters?

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Textbook Question

Resolution of a Microscope. The image 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. What is the angular magnification of the microscope?

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