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Chapter 24: Problem 29

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?

Short Answer

Expert verified
Answer: The angular magnification of the 5.5-D reading glasses when Thomas's eye is relaxed is approximately 2.374.

Step by step solution

01

Convert the lens power to the focal length

To find the focal length of the lens, use the formula: Focal length (f) = 1 / Power (P) where Power (P) is given in diopters. In this case, the power of the reading glasses is 5.5 D. So, the focal length can be calculated as: f = 1 / 5.5
02

Calculate the focal length

Calculate the focal length by dividing 1 by 5.5: f = 1 / 5.5 f ≈ 0.182 m
03

Find the angular magnification

To find the angular magnification (M) of the lens when Thomas's eye is relaxed, use the formula for a simple magnifier: M = 1 + (D / f) where D is the nearest clear vision distance, which is typically 25 cm or 0.25 m. Now we can substitute the values into the formula to calculate the angular magnification.
04

Calculate angular magnification

Substitute the values for D and f into the formula: M = 1 + (0.25 / 0.182) M ≈ 1 + 1.374 M ≈ 2.374 The angular magnification of the 5.5-D reading glasses when Thomas's eye is relaxed is approximately 2.374.

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Most popular questions from this chapter

Two converging lenses, separated by a distance of \(50.0 \mathrm{cm},\) are used in combination. The first lens, located to the left, has a focal length of \(15.0 \mathrm{cm} .\) The second lens, located to the right, has a focal length of \(12.0 \mathrm{cm} .\) An object, \(3.00 \mathrm{cm}\) high, is placed at a distance of \(20.0 \mathrm{cm}\) in front of the first lens. (a) Find the intermediate and final image distances relative to the corresponding lenses. (b) What is the total magnification? (c) What is the height of the final image?
A dissecting microscope is designed to have a large distance between the object and the objective lens. Suppose the focal length of the objective of a dissecting microscope is \(5.0 \mathrm{cm},\) the focal length of the eyepiece is \(4.0 \mathrm{cm},\) and the distance between the lenses is $32.0 \mathrm{cm} .$ (a) What is the distance between the object and the objective lens? (b) What is the angular magnification?
An insect that is 5.00 mm long is placed \(10.0 \mathrm{cm}\) from a converging lens with a focal length of \(12.0 \mathrm{cm} .\) (a) What is the position of the image? (b) What is the size of the image? (c) Is the image upright or inverted? (d) Is the image real or virtual? (e) What is the angular magnification if the lens is close to the eye?
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?
A slide projector, using slides of width \(5.08 \mathrm{cm},\) produces an image that is \(2.00 \mathrm{m}\) wide on a screen \(3.50 \mathrm{m}\) away. What is the focal length of the projector lens?
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