/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 52 A concave mirror has a radius of... [FREE SOLUTION] | 91影视

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Chapter 23: Problem 52

A concave mirror has a radius of curvature of \(5.0 \mathrm{m} .\) An object, initially \(2.0 \mathrm{m}\) in front of the mirror, is moved back until it is \(6.0 \mathrm{m}\) from the mirror. Describe how the image location changes.

Short Answer

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Answer: As the object moves from 2.0m to 6.0m in front of the concave mirror, the image location moves closer to the mirror, from 5.0m to 3.75m.

Step by step solution

01

Since we are given the radius of curvature \(R\), we can find the focal length \(f\) using the following formula: \(f = \frac{R}{2}\) where: - \(R=5.0\,m\) (radius of curvature) Now let's calculate the focal length: \(f = \frac{5.0}{2} = 2.5\,m\) #Step 2: Calculate the initial image distance#

To find the initial image distance \(d_{i1}\), we use the mirror equation with the given initial object distance \(d_\text{o1}=2.0\,m\). Plugging the values into the equation: \(\frac{1}{2.5}=\frac{1}{2.0}+\frac{1}{d_{i1}}\) Solving for \(d_{i1}\), we get: \(d_{i1} = \frac{1}{\frac{1}{2.5}-\frac{1}{2}} = 5.0\,m\) #Step 3: Calculate the final image distance#
02

Similarly, for the final image distance \(d_{i2}\), we use the mirror equation with the given final object distance \(d_\text{o2}=6.0\,m\): \(\frac{1}{2.5}=\frac{1}{6.0}+\frac{1}{d_{i2}}\) Solving for \(d_{i2}\), we get: \(d_{i2} = \frac{1}{\frac{1}{2.5}-\frac{1}{6}} = 3.75\,m\) #Step 4: Describe how the image location changes#

The initial image distance was \(5.0\,m\), and the final image distance is \(3.75\,m\). Thus, as the object moves from \(2.0\,m\) to \(6.0\,m\) in front of the concave mirror, the image location moves closer to the mirror, from \(5.0\,m\) to \(3.75\,m\).

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Most popular questions from this chapter

The right-side decides to do an experiment to determine the focal length of this mirror. He holds a plane mirror next to the rearview mirror and views an object that is \(163 \mathrm{cm}\) away from each mirror. The object appears \(3.20 \mathrm{cm}\) wide in the plane mirror, but only \(1.80 \mathrm{cm}\) wide in the rearview mirror. What is the focal length of the rearview mirror? mirror of Mike's car says that objects in the mirror are closer than they appear. Mike
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