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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

A microscope has an objective lens of focal length \(5.00 \mathrm{mm} .\) The objective forms an image \(16.5 \mathrm{cm}\) from the lens. The focal length of the eyepiece is \(2.80 \mathrm{cm} .\) (a) What is the distance between the lenses? (b) What is the angular magnification? The near point is \(25.0 \mathrm{cm} .\) (c) How far from the objective should the object be placed?
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?
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.
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).
Esperanza uses a 35 -mm camera with a standard lens of focal length $50.0 \mathrm{mm}\( to take a photo of her son Carlos, who is \)1.2 \mathrm{m}$ tall and standing \(3.0 \mathrm{m}\) away. (a) What must be the distance between the lens and the film to get a properly focused picture? (b) What is the magnification of the image? (c) What is the height of the image of Carlos on the film?
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