Chapter 34: Q94P (page 1042)

An object is placed against the center of a spherical mirror and then moved 70 cm from it along the central axis as the image distance i is measured. Figure 34-48 gives i versus object distance p out to $p_{s} = 40 cm$ . What is the image distance when the object is 70 cm from the mirror?

Short Answer

Expert verified

The image distance is $i_{n e w} = - 21 cm$ .

Step by step solution

Step 1: Given data

Object distance, $p_{g i v e n} = 70 cm$ .

Horizontal Scale, $p_{s} = 40 cm$ .

Determining the concept

The focal length of the lens is constant for every situation. Using this concept, find the focal length from the graph. Using the value in the equation and the given object distance, find the new image distance.

Formulae are as follows:

$\frac{1}{f} = (\frac{1}{p} + \frac{1}{i})$

Here, p is the pole, f is the focal length, and i is the image distance.

Determining the image distance

From the graph, take one point Q having co-ordinate $Q (15, - 10) .$

So,

$(\frac{1}{p} + \frac{1}{i}) = \frac{1}{f}$

$\begin{array}{rcl} (\frac{1}{15} + \frac{1}{- 10}) & = & \frac{1}{f} \\ = & \frac{1}{p_{g i v e n}} + \frac{1}{i_{n e w}} \end{array}$

Rearrange for the i_new;

$\begin{array}{rcl} \frac{1}{i_{n e w}} & = & \frac{- 10 + 15}{- 10 \times 15} - \frac{1}{70} \\ = & - \frac{5}{150} - \frac{1}{70} \end{array}$

Solve for i_new;

$\begin{array}{rcl} \frac{1}{i_{n e w}} & = & - \frac{100}{2100} \\ = & - 21 cm \end{array}$

Therefore, the image distance is $i_{n e w} = - 21 cm$ .

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An object is placed against the center of a spherical mirror and then moved 70 cm from it along the central axis as the image distance i is measured. Figure 34-48 gives i versus object distance p out to $p_{s} = 40 cm$ . What is the image distance when the object is 70 cm from the mirror?

Short Answer

Step by step solution

Step 1: Given data

Determining the concept

Determining the image distance

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An object is placed against the center of a spherical mirror and then moved 70 cm from it along the central axis as the image distance i is measured. Figure 34-48 gives i versus object distance p out to ps=40cm. What is the image distance when the object is 70 cm from the mirror?

Short Answer

Step by step solution

Step 1: Given data

Determining the concept

Determining the image distance

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Particle Model of Matter

Geometrical and Physical Optics

Atoms and Radioactivity

Linear Momentum

Further Mechanics and Thermal Physics

Oscillations

Study anywhere. Anytime. Across all devices.

An object is placed against the center of a spherical mirror and then moved 70 cm from it along the central axis as the image distance i is measured. Figure 34-48 gives i versus object distance p out to $p_{s} = 40 cm$ . What is the image distance when the object is 70 cm from the mirror?