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Chapter 24: Problem 31

Keesha is looking at a beetle with a magnifying glass. She wants to see an upright, enlarged image at a distance of \(25 \mathrm{cm} .\) The focal length of the magnifying glass is \(+5.0 \mathrm{cm} .\) Assume that Keesha's eye is close to the magnifying glass. (a) What should be the distance between the magnifying glass and the beetle? (b) What is the angular magnification? (tutorial: magnifying glass II).

Short Answer

Expert verified
Answer: The distance between the magnifying glass and the beetle is 6.25 cm, and the angular magnification of the magnifying glass is 5.

Step by step solution

01

Recall the lens formula

First, we need to recall the lens formula, which relates the object distance (p), the image distance (q), and the focal length (f) as follows: \( \frac{1}{f} = \frac{1}{p} + \frac{1}{q} \)
02

Plug in the values

We are given that the image distance (q) is \(25 \mathrm{cm}\) and the focal length (f) is \(+5.0 \mathrm{cm}\). Plugging these values into the lens formula, we get: \( \frac{1}{+5.0} = \frac{1}{p} + \frac{1}{25} \)
03

Solve for the object distance

To find the object distance (p), we can rearrange and solve the equation: \( \frac{1}{p} = \frac{1}{+5.0} - \frac{1}{25} \) \( \frac{1}{p} = \frac{4}{25} \) \( p = \frac{25}{4} \) \( p = 6.25 \mathrm{cm} \) So the distance between the magnifying glass and the beetle should be \(6.25 \mathrm{cm}\).
04

Recall the formula for angular magnification

Next, let's find the angular magnification. Recall the formula for angular magnification (M): \( M = \frac{25 \mathrm{cm}}{f} \)
05

Plug in the values and solve for angular magnification

Now, we can plug in the values for the image distance (q) and the focal length (f) to find the angular magnification: \( M = \frac{25}{5.0} \) \( M = 5 \) The angular magnification of the magnifying glass is 5. So, the distance between the magnifying glass and the beetle should be \(6.25 \mathrm{cm}\), and the angular magnification is 5.

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Most popular questions from this chapter

You plan to project an inverted image \(30.0 \mathrm{cm}\) to the right of an object. You have a diverging lens with focal length \(-4.00 \mathrm{cm}\) located \(6.00 \mathrm{cm}\) to the right of the object. Once you put a second lens at \(18.0 \mathrm{cm}\) 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?
A nearsighted man cannot clearly see objects more than \(2.0 \mathrm{m}\) away. The distance from the lens of the eye to the retina is \(2.0 \mathrm{cm},\) and the eye's power of accommodation is \(4.0 \mathrm{D}\) (the focal length of the cornea-lens system increases by a maximum of \(4.0 \mathrm{D}\) over its relaxed focal length when accommodating for nearby objects). (a) As an amateur optometrist, what corrective eyeglass lenses would you prescribe to enable him to clearly see distant objects? Assume the corrective lenses are $2.0 \mathrm{cm}$ from the eyes. (b) Find the nearest object he can see clearly with and without his glasses.
A simple magnifier gives the maximum angular magnification when it forms a virtual image at the near point of the eye instead of at infinity. For simplicity, assume that the magnifier is right up against the eye, so that distances from the magnifier are approximately the same as distances from the eye. (a) For a magnifier with focal length \(f,\) find the object distance \(p\) such that the image is formed at the near point, a distance \(N\) from the lens. (b) Show that the angular size of this image as seen by the eye is $$ \theta=\frac{h(N+f)}{N f} $$ where \(h\) is the height of the object. [Hint: Refer to Fig. 24.15 .1 (c) Now find the angular magnification and compare it to the angular magnification when the virtual image is at infinity.
A converging lens with a focal length of \(3.00 \mathrm{cm}\) is placed $24.00 \mathrm{cm}\( to the right of a concave mirror with a focal length of \)4.00 \mathrm{cm} .\( An object is placed between the mirror and the lens, \)6.00 \mathrm{cm}\( to the right of the mirror and \)18.00 \mathrm{cm}$ to the left of the lens. Name three places where you could find an image of this object. For each image tell whether it is inverted or upright and give the total magnification.
(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.
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