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Chapter 24: Problem 30

(a) What is the focal length of a magnifying glass that gives an angular magnification of 8.0 when the image is at infinity? (b) How far must the object be from the lens? Assume the lens is held close to the eye.

Short Answer

Expert verified
Answer: The focal length of the magnifying glass is approximately 3.57 cm, and the object should be placed at a distance of approximately 1.39 cm from the lens.

Step by step solution

01

Write the formula for angular magnification and lens formula

The formula for angular magnification (M) of a magnifying glass when the image is at infinity is given by: M = 1 + (D / f) where, M = Angular magnification D = The distance of the nearest clear vision (25 cm) f = Focal length of the lens The lens formula is given by: 1 / f = 1 / u + 1 / v where, f = Focal length of the lens u = Object distance from the lens v = Image distance from the lens (a) We need to find the focal length (f) when angular magnification (M) is 8.0. (b) After finding the focal length, we will find the object distance (u) by using the lens formula.
02

Solve the angular magnification formula for the focal length (f)

Rearrange the formula for angular magnification to find the value of focal length (f): f = D / (M - 1) Now substitute the given values: M = 8.0 D = 25 cm f = 25 / (8 - 1) f = 25 / 7 f = 3.57 cm So, the focal length of the magnifying glass is 3.57 cm.
03

Use the lens formula to find the object distance (u)

When the image is at infinity, the image distance (v) is considered to be infinite. The lens formula will become: 1 / f = 1 / u Now, rearrange the formula to find the value of the object distance (u): u = f / (1 - f) Substitute the value of the focal length (f = 3.57 cm): u = 3.57 / (1 - 3.57) u = 3.57 / -2.57 u = -1.39 cm Since the distance cannot be negative, we'll take the absolute value of the result: u = 1.39 cm So, the object must be 1.39 cm away from the lens.

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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?
The distance from the lens system (cornea + lens) of a particular eye to the retina is \(1.75 \mathrm{cm} .\) What is the focal length of the lens system when the eye produces a clear image of an object \(25.0 \mathrm{cm}\) away?
An object is located \(16.0 \mathrm{cm}\) in front of a converging lens with focal length \(12.0 \mathrm{cm} .\) To the right of the converging lens, separated by a distance of \(20.0 \mathrm{cm},\) is a diverging lens of focal length \(-10.0 \mathrm{cm} .\) Find the location of the final image by ray tracing and verify using the lens equations.
A photographer wishes to take a photograph of the Eiffel Tower $(300 \mathrm{m}\( tall ) from across the Seine River, a distance of \)300 \mathrm{m}$ from the tower. What focal length lens should she use to get an image that is 20 mm high on the film?
Angular Magnification and the Simple Magnifier Thomas wants to use his 5.5 -D reading glasses as a simple magnifier. What is the angular magnification of this lens when Thomas's eye is relaxed?
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