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Chapter 33: Problem 36

To study a tissue sample better, a pathologist holds a \(5.00-\mathrm{cm}\) focal length magnifying glass \(3.00 \mathrm{~cm}\) from the sample. How much magnification can he get from the lens?

Short Answer

Expert verified
Answer: The magnification provided by the magnifying glass is approximately 0.625 times.

Step by step solution

01

Write down the known values

We are given: Focal length of the magnifying glass (f) = 5.00 cm Distance between the lens and the tissue sample (u) = -3.00 cm (negative because the object is on the left side of the lens) We need to find the magnification (M).
02

Use the lens formula to find the image distance (v)

The lens formula is given by: \(\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\) Plug in the given values of f and u: \(\frac{1}{5.00} = \frac{1}{-3.00} + \frac{1}{v}\) To solve for v, we can first find the common denominator and then solve for v: \(\frac{1}{5.00} + \frac{1}{3.00} = \frac{1}{v}\) \(v = \frac{1}{\frac{1}{5.00} + \frac{1}{3.00}}\)
03

Calculate the image distance (v)

Now, calculate the value of v by finding the sum of the fractions and taking the reciprocal: \(v = \frac{1}{\frac{1}{5.00} + \frac{1}{3.00}} = \frac{1}{\frac{8}{15}}\) \(v = \frac{15}{8}\) \(v \approx 1.875 \mathrm{~cm}\)
04

Use the magnification formula to find the magnification (M)

The magnification formula is given by: \(M = -\frac{v}{u}\) Plug in the values of v and u: \(M = -\frac{1.875}{-3.00}\)
05

Calculate the magnification (M)

Now, calculate the magnification (M): \(M = \frac{1.875}{3.00}\) \(M \approx 0.625\) So, the pathologist can get a magnification of approximately 0.625 times from the lens.

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Most popular questions from this chapter

You have found in the lab an old microscope, which has lost its eyepiece. It still has its objective lens, and markings indicate that its focal length is \(7.00 \mathrm{~mm}\). You can put in a new eyepiece, which goes in \(20.0 \mathrm{~cm}\) from the objective. You need a magnification of about 200. Assume you want the comfortable viewing distance for the final image to be \(25.0 \mathrm{~cm}\). You find in a drawer eyepieces marked \(2.00-, 4.00-,\) and \(8.00-\mathrm{cm}\) focal length. Which is your best choice?

Two refracting telescopes are used to look at craters on the Moon. The objective focal length of both telescopes is \(95.0 \mathrm{~cm}\) and the eyepiece focal length of both telescopes is \(3.80 \mathrm{~cm} .\) The telescopes are identical except for the diameter of the lenses. Telescope A has an objective diameter of \(10.0 \mathrm{~cm}\) while the lenses of telescope \(\mathrm{B}\) are scaled up by a factor of two, so that its objective diameter is \(20.0 \mathrm{~cm}\). a) What are the angular magnifications of telescopes \(A\) and \(B\) ? b) Do the images produced by the telescopes have the same brightness? If not, which is brighter and by how much?

Astronomers sometimes place filters in the path of light as it passes through their telescopes and optical equipment. The filters allow only a single color to pass through. What are the advantages of this? What are the disadvantages?

A classmate claims that by using a \(40.0-\mathrm{cm}\) focal length mirror, he can project onto a screen a \(10.0-\mathrm{cm}\) tall bird locat ed 100 . \(\mathrm{m}\) away. He claims that the image will be no less than \(1.00 \mathrm{~cm}\) tall and inverted. Will he make good on his claim?

Jack has a near point of \(32 \mathrm{~cm}\) and uses a magnifier of 25 diopter. a) What is the magnification if the final image is at infinity? b) What is the magnification if the final image is at the near point?
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