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Chapter 33: Problem 77

An object is \(6.0 \mathrm{~cm}\) from a thin lens along the axis of the lens. If the lens has a focal length of \(9.0 \mathrm{~cm},\) determine the image distance.

Short Answer

Expert verified
Answer: The image distance is -18.0 cm.

Step by step solution

01

Write down the known values

We are given the object distance \(d_o = 6.0 ~cm\) and the focal length \(f = 9.0 ~cm\). We want to find the image distance \(d_i\).
02

Apply the lens formula

Using the lens formula, we will plug in the known values and solve for \(d_i\): $$ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} $$ $$ \frac{1}{9.0} = \frac{1}{6.0} + \frac{1}{d_i} $$
03

Solve for the image distance

We need to find the value of \(\frac{1}{d_i}\) by isolating it: $$ \frac{1}{d_i} = \frac{1}{9.0} - \frac{1}{6.0} $$ Now, find the common denominator for the two fractions on the right side of the equation, which is 18: $$ \frac{1}{d_i} = \frac{2}{18} - \frac{3}{18} $$ Combine the two fractions: $$ \frac{1}{d_i} = -\frac{1}{18} $$ Finally, take the reciprocal of both sides to get the image distance: $$ d_i = -18 \mathrm{~cm} $$ Therefore, the image distance is \(-18.0 \mathrm{~cm}\). The negative sign indicates that the image is on the same side of the lens as the object, meaning it is a virtual image.

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Most popular questions from this chapter

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?

Where is the image formed if an object is placed \(25 \mathrm{~cm}\) from the eye of a nearsighted person. What kind of a corrective lens should the person wear? a) Behind the retina. Converging lenses. b) Behind the retina. Diverging lenses. c) In front of the retina. Converging lenses. d) In front of the retina. Diverging lenses.

A person with a near-point distance of \(24.0 \mathrm{~cm}\) finds that a magnifying glass gives an angular magnification that is 1.25 times larger when the image of the magnifier is at the near point than when the image is at infinity. What is the focal length of the magnifying glass?

Galileo discovered the moons of Jupiter in the fall of \(1609 .\) He used a telescope of his own design that had an objective lens with a focal length of \(f_{o}=40.0\) inches and an eyepiece lens with a focal length of \(f_{e}=2.00\) inches. Calculate the magnifying power of Galileo's telescope.

What kind of lens is used in eyeglasses to correct the vision of someone who is a) nearsighted? b) farsighted?
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