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Chapter 2: Problem 99

An amoeba is \(0.305 \mathrm{cm}\) away from the \(0.300 \mathrm{cm}-\) focal length objective lens of a microscope. (a) Where is the image formed by the objective lens? (b) What is this image's magnification? (c) An eyepiece with a \(2.00-\mathrm{cm}\) focal length is placed \(20.0 \mathrm{cm}\) from the objective. Where is the final image? (d) What angular magnification is produced by the eyepiece? (e) What is the overall magnification? (See Figure \(2.39 .)\)

Short Answer

Expert verified
The image formed by the objective lens is at a distance \(d_i = 9.18\,\text{cm}\) from the lens, with a magnification \(M_1 = -0.983\). The final image is located at a distance \(d_i' = 1.67\,\text{cm}\) from the eyepiece, with an angular magnification of \(M_2 = -0.833\). The overall magnification of the microscope is \(M = M_1\times M_2 = 0.818\).

Step by step solution

01

Find the location of the image formed by the objective lens

Use the thin lens formula: \(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\) Where: - \(f = 0.300\,\text{cm}\) is the focal length of the objective lens - \(d_o = 0.305\,\text{cm}\) is the object distance (distance of amoeba from the objective lens) - \(d_i\) is the image distance Solve for \(d_i\): \(\frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_o}\)
02

Find the magnification of the objective lens

Use the magnification formula: \(M_1 = -\frac{d_i}{d_o}\) Where: - \(M_1\) is the magnification of the objective lens - \(d_i\) is the image distance (from step 1) - \(d_o = 0.305\,\text{cm}\) is the object distance
03

Find the location of the final image

Use the thin lens formula for the eyepiece lens: \(\frac{1}{f'} = \frac{1}{d_o'} + \frac{1}{d_i'}\) Where: - \(f' = 2.00\,\text{cm}\) is the focal length of the eyepiece lens - \(d_o' = 20.0\,\text{cm}\) is the distance from the objective lens - \(d_i'\) is the final image distance Solve for \(d_i'\): \(\frac{1}{d_i'} = \frac{1}{f'} - \frac{1}{d_o'}\)
04

Find the angular magnification produced by the eyepiece

Use the angular magnification formula: \(M_2 = -\frac{d_i'}{f'}\) Where: - \(M_2\) is the angular magnification produced by the eyepiece - \(d_i'\) is the final image distance (from step 3) - \(f' = 2.00\,\text{cm}\) is the focal length of the eyepiece lens
05

Find the overall magnification of the microscope

Overall magnification of the microscope is the product of the magnifications of the objective and eyepiece lenses: \(M = M_1 \times M_2\) Where: - \(M\) is the overall magnification - \(M_1\) is the magnification of the objective lens (from step 2) - \(M_2\) is the angular magnification produced by the eyepiece (from step 4)

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Most popular questions from this chapter

A $$7.5 \times$$ binocular produces an angular magnification of \(-7.50,\) acting like a telescope. (Mirrors are used to make the image upright.) If the binoculars have objective lenses with a \(75.0-\mathrm{cm}\) focal length, what is the focal length of the eyepiece lenses?

Two convex lenses of focal lengths \(20 \mathrm{cm}\) and 10 \(\mathrm{cm}\) are placed \(30 \mathrm{cm}\) apart, with the lens with the longer focal length on the right. An object of height \(2.0 \mathrm{cm}\) is placed midway between them and observed through each lens from the left and from the right. Describe what you will see, such as where the image(s) will appear, whether they will be upright or inverted and their magnifications.

Show that, for a flat mirror, \(h_{i}=h_{\mathrm{o}},\) given that the image is the same distance behind the mirror as the distance of the object from the mirror.

What is the angular size of the Moon if viewed from a binocular that has a focal length of \(1.2 \mathrm{cm}\) for the eyepiece and a focal length of \(8 \mathrm{cm}\) for the objective? Use the radius of the moon \(1.74 \times 10^{6} \mathrm{m}\) and the distance of the moon from the observer to be \(3.8 \times 10^{8} \mathrm{m}\)

A doctor examines a mole with a 15.0 -cm focal length magnifying glass held \(13.5 \mathrm{cm}\) from the mole. (a) Where is the image? (b) What is its magnification? (c) How big is the image of a \(5.00 \mathrm{mm}\) diameter mole?
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