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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

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?
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?
A person on a safari wants to take a photograph of a hippopotamus from a distance of \(75.0 \mathrm{m} .\) The animal is \(4.00 \mathrm{m}\) long and its image is to be \(1.20 \mathrm{cm}\) long on the film. (a) What focal length lens should be used? (b) What would be the size of the image if a lens of \(50.0-\mathrm{mm}\) focal length were used? (c) How close to the hippo would the person have to be to capture a \(1.20-\mathrm{cm}-\) long image using a 50.0 -mm lens?
A cub scout makes a simple microscope by placing two converging lenses of +18 D at opposite ends of a \(28-\mathrm{cm}^{-}\) long tube. (a) What is the tube length of the microscope? (b) What is the angular magnification? (c) How far should an object be placed from the objective lens?
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?
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