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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 鈮� 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 鈮� 1 + 1.374 M 鈮� 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

You would like to project an upright image at a position \(32.0 \mathrm{cm}\) to the right of an object. You have a converging lens with focal length $3.70 \mathrm{cm}\( located \)6.00 \mathrm{cm}$ to the right of the object. By placing a second lens at \(24.65 \mathrm{cm}\) to the right of the object, you obtain an image in the proper location. (a) What is the focal length of the second lens? (b) Is this lens converging or diverging? (c) What is the total magnification? (d) If the object is \(12.0 \mathrm{cm}\) high, what is the image height?
Show that if two thin lenses are close together \((s,\) the distance between the lenses, is negligibly small), the two lenses can be replaced by a single equivalent lens with focal length \(f_{\mathrm{eq}} .\) Find the value of \(f_{\mathrm{eq}}\) in terms of \(f_{1}\) and \(f_{2}.\)
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?
Telescopes (a) If you were stranded on an island with only a pair of 3.5 -D reading glasses, could you make a telescope? If so, what would be the length of the telescope and what would be the best possible angular magnification? (b) Answer the same questions if you also had a pair of 1.3 -D reading glasses.
A slide projector has a lens of focal length \(12 \mathrm{cm} .\) Each slide is \(24 \mathrm{mm}\) by \(36 \mathrm{mm}\) (see the figure with Problem 16). The projector is used in a room where the screen is \(5.0 \mathrm{m}\) from the projector. How large must the screen be?
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